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The average attendance at a cricket club dropped from 5640 last year to 3820 this year.
What was the percent decrease from last year to this year?
Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the equation.
60 * 2 * 3 * 6 * 5 * 43
Two numbers A and B are such that the sum of 3% of A and 6% of B is four-fifths of the sum of 4% of A and 6% of B. Find the ratio of A + B and A − B.
Which two numbers should be interchanged to make the given equation correct?
$$36 \times 81 \div 9 - (88 \div 4) + 14 + (22 + 7) = 169$$
The income of three playback singers Aswath, Sunita and Ramdin are in the ratio of 12 : 9 : 7 and their expenditures are in the ratio 15 : 9 : 8. If Aswath saves 25% of his income, what is the ratio of the savings of Aswath, Sunita and Ramdin?
The monthly income of three cricketers Ankit, Sanjay and Roshan, from different sources, are in the ratio of 12 : 9 : 7, and their expenditures are in the ratio 15 : 9 : 8. If Ankit saves 25% of his income for future investments, what is the ratio of the savings of Ankit, Sanjay and Roshan?
The total of three numbers is 240. The second number is four times the first number. The third number is three times the first number. What will be the average of the three numbers?
A,B, C subscribe a sum of ₹75,500 for a business. A subscribes ₹3,500 more than B, and B subscribes ₹4,500 more than C. Out ofa total profit of ₹45,300, how much(in ₹) does A receive?
The value of $$\frac{427\times427\times427+325\times325\times}{42.7\times 42.7 +32.5\times32.5-42.7\times32.5}$$ is:
If 25% of 400 + 35% of 1260 + 27% of 1800 = 1020+ x, then the value of x lies between:
The value of $$\frac{2}{3}\div\frac{3}{10} $$ of $$\frac{4}{9}-\frac{4}{5}\times1\times\frac{1}{9}\div\frac{8}{15}+\frac{3}{4}\div\frac{1}{2}$$ is:
The value $$ \frac{4.35\times4.35\times4.35+3.25\times3.25\times 3.25}{43.5\times43.5\times+32.5\times32.5-43.5\times32.5}$$ is:
If a nine-digit number 785x3678y is divisible by 72, then the value of (x + y) is:
The value of $$1 - 3 \div 6$$ of $$2 + (4 \div 4 of \frac{1}{4}) \div 8 + (4 \times 8 \div \frac{1}{4}) \times \frac{1}{8}$$ is:
Ina school, $$\frac{5}{12}$$ of the number of students are girls and the rest are boys $$\frac{4}{7}$$ of the number of boys are below 14 years of age, and $$\frac {2}{5}$$ of the number of girls are 14 years or above 14 years of age . If the number of students below 14 years of age is 1120, then the total number of students in the school is
The value of $$\frac{5.35 \times 5.35 \times 5.35 + 3.65 \times 3.65 \times 3.65}{53.5 \times 53.5 + 36.5 \times 36.5 - 53.5 \times 36.5}$$ is:
Out of the total number of players, 100/3 % are in hotel X and the remaining are in hotel Y. If 20 players from hotel Y are shifted to hotel X, then the number of players in hotel X becomes 50% of the total number of players. If 20 players from hotel X are shifted to hotel Y, then the number of players in hotel X becomes what per cent of the total number of players?
Select the correct sequence of mathematical signs to replace the * signs so as to balance the given equation.
$$72\times12\times8\times6\times22=32$$
Whatis the least numberof soldiers that can be drawn upin troops of 10, 12, 15, 18 and 20 soldiers, and also in form of a solid square ?
The value of $$-7 \div [5 + 1 \div 2 - \left\{4 + (4 of 2 \div 4) + (4 \div 4 of 2)\right\}]$$ is:
The value of $$7 \div[5+1\div 2- \left\{ 4 + (4 of 2 \div 4) + (5 \div 5 of 2)\right\}]$$
A tap can fill up a tank of 1250 litres in 4 hours, whereas another tap can fill the same tank in 8 hours. An outlet tap can empty that tank in 6 hours.If all the three taps are opened simultaneously, then how much time will it take to fill the tank completely?
Identify the number which when added to itself 14 times gives 195.
There are 28 persons present at a press conference. After the conference they all shake hands with each other. If 7 of them refuse to shake hands at all, then how many hands shakes will be there altogether?
When number X multiplied to its next number, the product 1260 is obtained. When Number X is added to Number Y, a total of 106 is obtained. Find the value of Number Y. (Assume numbers to be positive)
Out of three numbers, the ratio of the first and the second numbers is 3 : 4 and the ratio of the second and the third numbers is 5 : 6. If the difference between the first and the third numbers is 1125, find the average of the second and third numbers.
Rajesh purchased 6 mangoes, 3 bananas and 10 guavas in ₹136. If the ratio of the cost (per piece) of mangoes, bananas and guavas is 3 : 2 : 1, what will be the total cost of 1 mango, 2 bananas and 3 guavas?
₹2,871 is to be divided among A, B and in the ratio of 9 : 11 : 13, respectively. How much more money(in ₹) will C get as compared to A?
Which two digits can be interchanged so as to balance the given equation?
$$76 + 108 \div 9 - 11 \times 2 = 18$$
Which two numbers should be interchanged to make the given equation correct?
$$42 \div 7 \times 5 + 35 - 49 = 18$$
Which two signs should be interchanged to make the given equation correct?
$$7 + 3 - 24 \div 6 \times 12 = 29$$
Abhay's uncle sent him some mangoes from Konkan. If he was to eat some specific number of mangoes every day, they would have lasted for 60 days. But, Abhay's cousin Rajiv came to spend the holidays with him and both of them finished the mangoes in 36 days. If Rajiv alone was to eat the mangoes, then how many days would they have lasted?
If the signs ‘+’ and ‘$$\times$$’ are interchanged, which of the following equations would be
correct?
In a certain language, if the signs $$+$$ and $$\times$$, and the digits 3 and 8 are interchanged, then what is the value of the following expression?
$$6 \times 35 \div 5 + 8 - 9$$
Select the correct combination of mathematical signs to replace the * signs and to balance the given equation.
5 * 7 * 36 * 18 * 2 * 8
Which two signs should be interchanged to make the given equation correct?
36 - 6 $$\div$$ 6 $$\times$$ 6 + 30 = 0
If A denotes ‘addition’, B denotes ‘multiplication’, C denotes ‘subtraction’, and D
denotes ‘division’, then what will be the value of the following expression?
5 B 3 A 4 B (6 C 2) C (18 D 3) D 2
In a certain language, if '$$+$$' means 'subtraction', '$$\times$$' means 'division', '$$ \div$$' means 'addition', and '$$-$$' means 'multiplication', then find the value of the following expression
(BODMAS rule does not apply in that language).
$$8 \div 16 \times 4 + 2 - 3$$
Select the correct combination of mathematical signs to sequentially replace the *
signs and balance the given equation.
17 * 3 * 6 * 2 * 7 * 55
Which two signs should be interchanged to make the given equation correct?
12 + 6 $$\times$$ 4 $$-$$ 6 $$\div$$ 3 = 5
Which two signs should be interchanged to make the given equation correct?
$$45 \times 10 - 125 \div 25 + 5 = 30$$
Which two signs should be interchanged to make the given equation correct?
$$32 + 14 \times 3 - 91 \div 7 = 3$$
In a certain language, if ' + ' means 'division', '$$\times$$' means 'subtraction', '$$\div$$' means 'addition' and ' - ' means 'multiplication', then find the value of the following expression (apply BODMAS).
$$24 \div 6 - 2 + 4 \times 2$$
Five players, ‘a’, ‘b’, ‘c’, ‘d’ and ‘e’, scored some runs during a match.
1. ‘b’ scored a half century, but did not score a century.
2. ‘d’ scored more runs than ‘c’, but less runs than ‘b’.
3. ‘a’ scored 37 runs, which is less than ‘c’.
4. ‘e’ scored 29 runs more than ‘d’.
5. ‘c’ scored 21 runs less than ‘b’.
What is likely to be the score of ‘e’?
If ‘A’ denotes ‘addition’, ‘B’ denotes ‘multiplication’, ‘C’ denotes ‘subtraction’, and ‘D’ denotes ‘division’, then what
will be the value of the following expression?
35B2A5B(40C 37)A(8B4)D16C 14=?
In a certain language, if the digits 7 and 2 are interchanged and 3 and 4 are
interchanged, then what is the value of the following expression?
52$$\div$$ 4 - 7 $$\times$$ 5 + 3
Select the correct sequence of mathematical signs to replace the * signs so as to balance the given equation.
24*4* 16*4*15 = 85
Select the correct sequence of mathematical signs to replace the * signs so as to
balance the given equation.
42 * 36 * 5 * 78 * (8 * 5) = 216
Which two numbers should be interchanged to make the given equation correct?
$$45 \div 5 \times 7 + 18 - 9 = 48$$
If “$$+$$’ is interchanged with ‘$$\times$$’, and ‘$$-$$’ is interchanged with ‘$$\div$$’, then which of the following equations is correct ?
Which two signs should be interchanged to make the given equation correct?
$$4 + 5 - 16 \times 4 \div 2 = 1$$
On a farm, there are 48 ducks, 42 goats and 10 cows with some attendants. If the total number of feet is 216 more than the number of heads, What is the number of attendants on the farm ?
Select the correct combination of mathematical signs to sequentially replace the *
signs and to balance the given equation.
72 * 4 * 15 * 3 * 12 = 51
If the signs $$-$$ and $$+$$ are interchanged, then which of the following equations would be correct?
If the signs $$+$$ and $$\div$$ are interchanged, then which of the following equations would be correct?
Select the correct sequence of mathematical signs to sequentially replace the * signs
so as to balance the given equation.
46 * 12 * 32 * 8 * (96 * 23) = 437
Which two digits and signs can be interchanged so as to balance the given equation?
46 $$\times$$ 6 + 32 - 12 $$\div$$ 8 = - 34
Which two signs should be interchanged to make the given equation correct?
$$8 \times 4 - 7 + 8 \div 2 = 35$$
If A denotes ‘addition’, B denotes ‘multiplication’, C denotes ‘subtraction’, and D
denotes ‘division’, then what will be the value of the following expression?
14 B (18 D 3) A 5 B 7 C 12 B (24 D 4)
If $$-$$ is interchanged with $$\div$$ and $$+$$ is interchanged with $$\times$$, then which of the following equations is correct?
If N > G > E and F = E > Q = R, then which of the following options is NOT correct?
Which two signs and two digits can be interchanged so as to balance the given equation?
$$75 \div 15 - 18 \times 12 + 17 = 79$$
Which two signs should be interchanged to make the given equation correct?
$$48\div12\times3+5-4=21$$
Which two signs should be interchanged to make the given equation correct?
8 $$\times$$ 9 $$\div$$ 15 + 30 - 5 = 63
If the signs $$-$$ and $$\div$$ are interchanged, then which of the following equations would be
correct?
If the signs $$+$$ and $$\times$$ are interchanged, then which of the following equations would be correct?
Select the correct combination of mathematical signs to replace the * signs and balance the given equation.
25 * 5 * 6 * 15 * 3 * 50
Which two numbers should be interchanged to make the given equation correct?
$$14\times7-25\div5+95=104$$
Which two numbers should be interchanged to make the given equation correct?
$$8\times 7 - 42\div 14 \times 2 + 21 = 66$$
Which two numbers should be interchanged to make the given equation correct?
$$72 + 63 \div 9 \times 5 - 36 = 67$$
Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation.
19 * 24 * 8 * 4 * 6 * 40
Which two signs should be interchanged to make the given equation correct?
$$17\times3\div6-2+7=55$$
Which two digits and signs can be interchanged so as to balance the given equation?
$$36\div2-159+78\times18=135$$
Which two signs can be interchanged so as to balance the given equation?
$$8 - 13 + 32 \div 8 \times 17 = 91$$
Which two digits can be interchanged so as to balance the given equation?
$$87\times2-65+182\div38=155$$
Which two numbers should be interchanged to make the given equation correct?
$$81 + 45 \div 3 - 18 \times 9 = 32$$
Which two signs should be interchanged to make the given equation correct?
$$10 \div 5 - 4 \times 3 + 6 = 13$$
Select the correct sequence of mathematical signs to replace the * signs so as to
balance the given equation.
78 * 26 * 4 * 13 * 28 = 58
Which two signs should be interchanged to make the given equation correct?
$$25-5\times 50\div10+35$$
If G > T, H = B, T > H, M = T and B > K, then which of the following expressions is
correct?
Select the correct combination of mathematical signs that can sequentially replace the * signs from left to right to balance the following equation.
31*2*60*30*15*19
Which two numbers should be interchanged to make the given equation correct?
$$63 \div 21 - 42 + 8\times 7 =135$$
Which two signs should be interchanged to make the given equation correct?
$$15 + 5 - 10 \times 8 \div 4 = 15$$
Which two signs should be interchanged to make the given equation correct?
$$25 - 15 \div 5 \times 10 + 20 = 35$$
Which two signs should be interchanged to make the given equation correct?
$$18 \div 9 + 12 \times 4 - 8 = 15$$
If B = D, C = U, B > G, U > R and C > S, then which of the following expressions is NOT
correct?
If the signs + and ÷ are interchanged, then which of the following equations would be
correct?
In a certain language, if '$$+$$' means 'multiplication', '$$\times$$' means 'division', '$$\div$$' means
'subtraction', and '-' means 'addition', then find the value of the following expression.
(Apply BODMAS)
18 $$\div$$ 6 $$\times$$ 3 - 4 + 5
Which two numbers should be interchanged to make the given equation correct?
$$14 + 32- 56 \div 28 \times 5 = 40$$
Which two numbers should be interchanged to make the given equation correct?
$$39 \times 6 + 27 \div 3 - 52 = 123$$
Which two signs should be interchanged to make the given equation correct?
$$8 + 6 \times 4 \div 2 - 10 = 6$$
One day, 90 students were travelling in a bus and the ratio of the number of boys to that of girls was 2 : 1. The next day,
the number of students remained the same, but the ratio of the number of boys to that of girls became 3 : 2. What was
the difference between the numbers of boys travelling in the bus on both days ?
Renuka bought some chocolates for her daughters. She put them on the table and
went out for her doctor's appointment. Then Ayushi came home. She took one-third of
the chocolates and went to her friend's house. Then came Sadhana. She thought that
she was the first one to come home. She took one-third of the remaining chocolates
and went out. At last Tanya came home. Thinking that she was the first one to arrive,
she took one-third of the remaining chocolates. When Renuka came back, she found
24 chocolates lying on the table. She distributed them among her daughters, ensuring
everyone got an equal share.
How many chocolates did Renuka give to Sadhana in the end?
The cost of four cycle tyres and three tubes is ₹720, whereas the cost of three cycle tyres and four tubes is ₹610. What is the cost of a tube?
If H > M = D > P and K = H > T > Z, then which of the following options is NOT correct?
In a certain language, if 4 and 6 are interchanged and 5 and 9 are interchanged, then which
of the following numbers will be the highest?
Select the correct sequence of mathematical signs to sequentially replace the * signs and balance the given equation.
16 * 280 * 6 * 84 * 4 = 0
Which two numbers and signs can be interchanged so as to balance the given
equation?
18 $$\times$$ 7 $$\div$$ 36 + 78 -14 =86
If the signs ‘+’ and ‘-’ are interchanged, which of the following equations would be
correct?
If ‘x' means ‘addition’, ‘+’ means ‘multiplication’, ‘+’ means ‘subtraction’, and ‘-’ means ‘division’, then what is the value of the following expression?
$$16-4\times 12 \div +18$$
Two numbers are named as Number A and Number B. The sum of Number A,its square and its cube is 399. The sum of Number B,its square and its cube is 819. What would be the square of the number obtained by adding Number A and Number B?
If $$\div$$ is interchanged with +, and $$\times$$ is interchanged with -, then which of the following
equations is correct?
Which two numbers should be interchanged to make the given equation correct?
$$64 - 24 \div 3 + 32 \times 12 = 158$$
Which two signs can be interchanged so as to balance the given equation?
72 $$\div$$ 36 + 12 $$\times$$ 13 $$-$$ 48 = 63
Which two signs should be interchanged to make the given equation correct?
15 + 15 $$\div$$ 15 - 15 $$\times$$ 15 = 15
A man ordered 10 physics book and some chemistry book.The price of chemistry book is twice the price of a physics book.While preparing the bill,the cleark interchanged the number of physics and chemistry book by mistake,which decreased the bill by $$12\frac{1}{2}$$%.The ratio of the number of physics book to the number of chemistry in the original order is:
A sum of ₹4,095 is divided between A, B, C and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 2 : 5 and that of C and Dis 2 : 3. What is the difference (in ₹) between the shares of B and D?
If the difference of the mode and median of a data is 38, then the difference of the median and mean is:
If the mean of the following data is 9,then find the value of k.
11, (k-),7 (k-1), 11, 16, 12, 15, (k-1), 13
Kamal saves x% of her monthly income. When her monthly expenditure is increased by 20% and the monthly income is increased by 26%, then her monthly savings increased by 60%. What is the value of x ?
The value of $$14 - 20 \times [7 - \left\{18 \div 2 \text{of} 3 - (15 - 25 \div 5 \times 4)\right\}]$$ is:
$$14 - 20 \times [7 - \left\{18 \div 2 \text{of} 3 - (15 - 25 \div 5 \times 4)\right\}]$$
= $$14-20\times[7-\left\{18\div2 \text{of} 3-(15-5\times4)\right\}]$$
= $$14-20\times[7-\left\{18\div2 \text{of} 3-(15-20)\right\}]$$
= $$14-20\times[7-\left\{18\div2 \text{of} 3+5\right\}]$$
= $$14-20\times[7-\left\{18\div6+5\right\}]$$
= $$14-20\times[7-\left\{3+5\right\}]$$
= $$14-20\times[7-8]$$
= $$14-20\times[-1]$$
= $$14+20$$
= $$34$$
Hence, the correct answer is Option D
The value of $$16+\left[0.2\div0.004+5.2 of 2\div\left(0.7\times2+0.84\div0.7\right)\right]$$ is:
The value of $$18-\left[6-\left\{13-\left(78-8\div2\times5 of 3\right)\right\}\right]$$ is:
The value of $$5\frac{1}{4}+\frac{1}{4}\div\frac{1}{4}of\frac{1}{8}-\frac{9}{4}+1\frac{1}{3}\div1\frac{1}{4}of\left[2\frac{3}{5}-2\frac{1}{3}\right]$$ is:
If the ratio of the mean and median of a certain data is 4: 5, then the ratio of its mode and mean is:
The value of $$1\frac{1}{8}\div1\frac{4}{5}$$ of $$\left[3\frac{1}{4}-\left(\frac{14}{25}+\frac{2}{5}\times2\frac{4}{5}\div\frac{5}{3} of \frac{7}{15}\right)\right]$$ is:
The value of $$21-\left[29-\left\{27-\left(43-15\div3\times4of3+2\right)\right\}\right]$$ is:
The value of $$\frac{3\frac{1}{4}-\frac{4}{5} \ of \ \frac{5}{6}}{4\frac{1}{3}-\div\frac{1}{5}-(\frac{3}{10}+21\frac{1}{5})}-(2\frac{1}{3} \ of \ 1\frac{1}{2})$$
Two numbers are in the ratio 7:9. If the sum of their squares is 8320, then the sum of the two nmnbers is:
Out of two numbers, the first number is three-founh of the second number. If the average of the reciprocals of the two numbers is $$\frac{7}{72}$$, then the sum of the two numbers is:
Radha saves X % of her income. If her income increases by 28%and the expenditure increases by 20%, then her savings increase by 40%. What is the value of x ?
The value of $$\frac{4}{5}\times1\frac{1}{9}\div\frac{8}{15}+\left(5\frac{1}{4}\div\frac{3}{7} of \frac{1}{4}\times\frac{2}{7}\right)\div5\frac{3}{5}-\frac{1}{4}\div\frac{3}{2}$$ is:
What is the mean of the range and median of the given data?
11, 16, 14, 7, ll, 23, 10, 30, 20, 33, 19, 12, 17, 14
900 4 Mass Pudding Flour, sugar and butter are the three ingredients. in comparison to sugar Has three times more flour and twice as much sugar than butter. How Much Flour in Dishes Recipe g is?
A, B and C divide a certain sum of money among themselves. The average of the amounts with them is ₹4520. Share of A is $$10\frac{2}{3}\%$$ more than share of B and $$33\frac{1}{3}\%$$ less than share of C. What is the share of B (in ₹)?
Share of A is $$10\frac{2}{3}\%$$ more than share of B.
A = B + $$\frac{\frac{32}{3}}{100}\times$$B
A = B + $$\frac{8}{75}\times$$B
A = $$\frac{83}{75}$$B........(1)
Share of A is $$33\frac{1}{3}\%$$ less than share of C.
A = C - $$\frac{\frac{100}{3}}{100}\times$$C
A = C - $$\frac{1}{3}\times$$C
A = $$\frac{2}{3}$$C
$$\frac{83}{75}$$B = $$\frac{2}{3}$$C
C = $$\frac{83}{50}$$B........(2)
The average of the amounts of A, B and C is ₹4520.
Sum of the amounts of A, B and C = 4520 x 3
A + B + C = 13560
$$\frac{83}{75}$$B + B + $$\frac{83}{50}$$B = 13560
$$\frac{166B+150B+249B}{150}=13560$$
$$\frac{565B}{150}=13560$$
B = ₹3600
Hence, the correct answer is Option C
Simplify the foHowing expression.
$$4-3$$ of $$\left(1\frac{1}{2}+\frac{1}{3}\div\frac{1}{2} of 4 -\frac{1}{4}\right)$$
If the mean of the distribution
is 24.6, then the value of $$x$$ is:
Lucky spends 85% of her income. If her expenditure increases by x %, savings increase by 60% and income increases by 26%, then what is the value of x ?
Let the income of Lucky = 100L
Lucky spends 85% of her income.
Expenditure of Lucky = $$\frac{85}{100}\times$$100L = 85L
Savings of Lucky = 100L - 85L = 15L
According to the problem,
[100L + $$\frac{26}{100}\times$$100L] = [15L + $$\frac{60}{100}\times$$15L] + [85L + $$\frac{\text{x}}{100}\times$$85L]
126L = 24L + 85L + $$\frac{\text{x}}{100}\times$$85L
126L = 109L + $$\frac{\text{x}}{100}\times$$85L
17L = $$\frac{\text{x}}{100}\times$$85L
x = 20
Hence, the correct answer is Option C
Simplify the following expression.
$$\frac{(375 + 125)^2 - (125 - 375)^2}{375 \times 375 - 125 \times 125}$$
The simplified value of $$\frac{119[48\div6-7\left\{5\times12\div3-(15-\overline{3-8})\right\}]}{24\div3-9 \ of \ 3+(52-\overline{8-4})\div6}$$
The value of $$32 \div 12 of 3 \times [5 - (15 - 12) \div 9] of \frac{3}{7} + 4 - 8 \div 2 of 4$$ is:
The value of $$5 - 5 \div5\times5+\left(6\div6 of 6\right)\times6-\left(3\frac{2}{3}\div\frac{11}{30}of\frac{2}{3}\right)\div5$$ is:
The value of $$\frac{1}{5}\div\frac{3}{10}$$ of $$\frac{4}{9}-\frac{4}{5}\times1\frac{1}{9}\div\frac{8}{15}-\frac{3}{4}+\frac{3}{4}\div\frac{1}{2}$$ is:
A, Band Care three boxes containing marbles in the ratio 3 : 5 : 7, and the total number of marbles is 75. If 3 marbles are transferred from B to A, and 5 marbles are transferred from C to B, then the new ratio of the marbles is:
The simplifiled value of 6 $$-\left[\left\{\left(\frac{20}{24}\div\frac{1}{2}\right)+\frac{48}{56}-\frac{6}{7}\right\} of \frac{6}{10}-7\right]$$
The value of $$3 \div of 3 \times 6 - 22 \times 6 \div 18 - 3 \div 2 + 10 - 3 \div 9 of 3 \times 9$$ is:
The value of $$4\frac{1}{3}+\left[7\frac{2}{3}-\frac{4}{3}\left(\frac{25}{3}-\frac{1}{6}-\frac{2}{3}\right)\right]$$ is:
The value of $$5\frac{6}{29}-\left[\frac{15}{4}\div\left\{\frac{3}{4}\times\left(\frac{3}{2}-\frac{1}{5}-\frac{1}{3}\right)\right\}\right]$$ is:
The value of $$\frac{7}{10}\div\frac{7}{5}$$ of $$\left[\frac{21}{10}+\frac{13}{5}\right]+\left[\frac{1}{10}\times\frac{10}{47}-\frac{6}{47}\right]$$ is:
The value of $$\frac{\frac{1}{4}\div\frac{1}{2}\left(\frac{2}{5}-\frac{1}{3}\right)}{1\frac{2}{3 } of \frac{3}{4}-\frac{1}{4} of \frac{2}{3}}$$ is:
The value of $$\frac{\frac{8}{3}\div\frac{3}{5}\times\frac{7}{5}}{\frac{5}{3}\div\frac{5}{7}\times\frac{8}{9}}\div15$$ is:
The value of $$\left(4\frac{1}{5}-3\frac{1}{10} of 1\frac{1}{7}\right)\div\left(6\frac{1}{3}-3\frac{1}{5} of 1\frac{1}{2}\right)$$ is:
Three persons A, B and C donate 10%, 7% and 9% respectively of their monthly salaries to a charitable trust. Monthly salaries of A and B are equal and the difference between the donations of A and B is ₹900. If the total donation by A and B is ₹600 more than that of C, then what is the monthly salary (in ₹) of C?
Monthly salaries of A and B are equal.
Let the monthly salaries of A and B are 'p'.
The difference between the donations of A and B is ₹900.
$$\frac{10}{100}p-\frac{7}{100}p=900$$
$$\frac{3}{100}p=900$$
p = 30000
The monthly salaries of A and B are ₹30000.
The total donation by A and B is ₹600 more than that of C.
$$\frac{10}{100}\times30000+\frac{7}{100}\times30000$$ = Donation by C + 600
$$\frac{17}{100}\times30000$$ = Donation by C + 600
5100 = Donation by C + 600
Donation by C = ₹4500
Let the monthly salary of C = t
$$\frac{9}{100}\times t=4500$$
t = 50000
Monthly salary of C = ₹50000
Hence, the correct answer is Option C
If a, b and c are the median. mode and range, respectively, of the data: 8, 5, 4, 3, 2, 7, 3, 10, 9, 17, 12, 3, 8, 4, then what is the value of $$\left(3a-2b+c\right)$$?
In a week, the prices of bag of tea were ₹350, ₹280, ₹340, ₹270, ₹360, ₹310, and ₹300. The range (in ₹) is:
The numbers 5, 7, 8, 1O, 12, 13 and are arranged in ascending order. If the mean of the numbers is equal to the median, the value of N is:
The numbers 8, 9, 11, 15, 17, 21 and N are arranged in ascending order. The mean of these numbers is equal to the median of the numbers. The value of N is:
The value of $$145-[125-\left\{64\div8 \ of \ 4-(4\times8\div2)\right\}]$$ is:
The value of $$5-5\div5\times5+\left(7\div7 of 6\right)\times6-\left(3\frac{2}{3}\div\frac{11}{30} of \frac{2}{3}\right)\div5$$ is:
What is the ratio of the mean proportional between 24.2 and 7.2, and the third proportional of 2.8 and 4.2?
Simplify the following expression :
$$6 \div 4 of 3 - 4 \div 6 \times (13 - 10) - 2 \times 15 \div 6 \times 6$$
There are three positive numbers. If the average of any two of them is added to the third number, the resulting sums are 154, 148 and 132. The sum of the original three numbers is:
If the variance of 5 values is 0.81, then what is its standard deviation?
The value of $$\frac{2-(\frac{6}{7}of21+5.25)}{\frac{4}{3}of(15.8-3.4)+5\times2.39}$$ is:
A retailer opens her outlet on all seven days of the week. It is observed that her average sales for Saturdays and Sundays combined is ₹300, and ₹200 for the remaining five days combined. For a month starting on a saturday, it was found that the total sales were ₹7000. Which among the following months it could be?
Ramesh invested 30% more than Suresh. Suresh invested 40% less than Arm, who invested ₹8,000. The total amount invested by all of them together is:
The simplified value of $$\frac{109-\left\{121\div\left(11 of 11\right)-\left(-4\right)-\left(3-\overline{8-1}\right)\right\}}{125-\left(-3\right)\left(4-\overline{6-2}\right)\div3\left\{5+\left(-3\right) of \left(-6\right)\right\}}$$ is:
The value of $$36\div[24+\left\{30-(60-60\div4\times5of 2)\right\}]$$ is:
A labourer was engaged for a certain number of days for ₹8,500, but due to his absence for some days, he was paid ₹6,050 only. Find the number of days that he was absent.
Atul purchased Bread costing ₹20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination ₹2, ₹5 and ₹10. If these coins are in the ratio 5 : 4: 1, then how many ₹5 coins did the shopkeepergive?
If the median of the following data is 11, then find the value of k.
3, 21 , 10, 7, 6, 9, (k+6 ), 15, 20, 16
The value of $$25 \div 15 of 4 \times [4 \div 5 \times (9 - 7)] - (20 \div 5 of 9)$$ is:
The value of $$3\frac{1}{9}\div\frac{4}{9}of\left(7\frac{3}{10}+3\frac{3}{5}\right)+\frac{4}{5}\div2\frac{2}{5}$$ is:
Simplify : $$-20\div\frac{4}{7}of55\frac{1}{8}\times\frac{9}{5}-\left(\frac{6}{7}+1\right)$$.
Study the given data and answer the question that follows.
If x is the lower limit of the median class and y is the upper limit of the modal class, then the value of $$(3x + 2y)$$ is:
The value of $$90 \div 20 \text{of} 6 \times [11 \div 4 \text{of} \left\{3 \times 2 - (3 - 8)\right\}] \div (9 \div 3 \times 2)$$ is:
$$90 \div 20 \text{of} 6 \times [11 \div 4 \text{of} \left\{3 \times 2 - (3 - 8)\right\}] \div (9 \div 3 \times 2)$$
= $$90 \div 120 \times [11 \div 4 \text{of} \left\{3 \times 2 - (-5)\right\}] \div (3 \times 2)$$
= $$\frac{90}{120} \times [11 \div 4 \text{of} \left\{3 \times 2 +5\right\}] \div 6$$
= $$\frac{3}{4} \times [11 \div 4 \text{of} \left\{6+5\right\}] \div 6$$
= $$\frac{3}{4} \times [11 \div 4 \text{of} 11] \div 6$$
= $$\frac{3}{4} \times [11 \div 44] \div 6$$
= $$\frac{3}{4} \times [\frac{1}{4}] \div 6$$
= $$\frac{3}{4} \times [\frac{1}{4}] \times \frac{1}{6}$$
= $$\frac{1}{32}$$
Hence, the correct answer is Option B
The value of $$\frac{6.25+\frac{6}{7}of21-3}{\frac{3}{4}of (15.8 -3.4)+5\times2.39}$$ is:
The values of the mode and median are 7.52 and 9.06, respectively, in a moderately asymmetrical distribution. The mean of the distribution is:
what is the mean of the range and median of the given data?
9, 8, 7, 5, 11 , 10, l3, 16, 15, 23, 19, 7, 9, 11
What is the range of the distribution of a variable which takes the ten values:
17, 18, 27, 11, 24, 21, 34, 21, 17, 32 ?
What is the simplified value of $$\frac{9\div9 of 9+9}{9\div9\times9+9}$$ ?
What is the simplified value of $$\left[\left\{\left(3-\frac{2}{1+\frac{1}{4+\frac{2}{3}}}\right) of 1\frac{13}{21}\div3\frac{2}{7}\right\}-\frac{1}{3}\right]\times\frac{9}{10}$$?
What is the value of $$x$$, if $$(5+4^{2})\div3$$ of $$x-2\times4=-7$$ ?
If the mode of the following data is 11, then find the value of k.
$$11,8,9,(2k-1),11,12,12,18,14,16$$
Price of a one gram gold coin decreased by 10% on its initial price on Monday and increased by 20% on Tuesday and again increased by 8% on Wednesday, and 5% increase on Thursday. If the final price on Thursday is ₹5511.24, then the initial price (in ₹) of one gram gold coin on Monday was?
Let the initial price of one gram gold coin on Monday was 'P'.
According to the problem,
P$$\times\frac{90}{100}\times\frac{120}{100}\times\frac{108}{100}\times\frac{105}{100}$$ = 5511.24
P$$\times\frac{9}{10}\times\frac{12}{10}\times108\times\frac{21}{20}$$ = 551124
P$$\times\frac{9}{10}\times\frac{12}{10}\times27\times\frac{21}{5}$$ = 551124
P = 4500
The initial price of one gram gold coin on Monday was ₹4500.
Hence, the correct answer is Option C
The numbers 25, 34, 46, 48, 2$$x$$+1, 4$$x$$+3, 105, 110, 114, 122 are written in ascending order and their median is 77.The value $$x$$ is:
The value of $$120\div[13+\left\{47-(36-36\div9 \ of \ 2\times3)\right\}]$$ is:
The value of $$5 of 8-6+\left[\left(27-3\right)\div6-4\right]$$ is:
Three numbers are in the ratio 2 : 3 : 4. The sum of their squares is 2349. Find the average of these three numbers.
Chamanial, Arshad and Jagjit Singh contested an election. All the votes polled were valid. Arshad got 35% ofthe total votes. For every 35 votes Chamanilal got 14 votes. The winner got 4950 more votes than the person who received the least number of votes. Find the total number of votes polled.
In an examination, the average score of a student was 67.6. If he would have got 27 more marks in Mathematics, 10 more marks in Computer Science, 18 more marks in History and retained the same marks in other subjects, then his average score would have been 72.6. How may papers were there in the examination?
Let the number of papers = n
The average score of a student was 67.6.
Sum of the scores of the student = 67.6n
Average after the increase in marks = 72.6
Sum of the scores of the student after increase in marks = 72.6n
$$\Rightarrow$$ 67.6n + 27 + 10 + 18 = 72.6n
$$\Rightarrow$$ 5n = 55
$$\Rightarrow$$ n = 11
Number of papers in the examination = n = 11
Hence, the correct answer is Option A
Simplify $$\frac{10^{2}of(\frac{1}{5})^{3}\div\frac{1}{4\times}4-\frac{2}{5}of15}{\frac{4}{5}(5\div5of12+\frac{1}{6})}$$
The value of $$15\frac{7}{10}+3\frac{1}{5} of \left[5\frac{1}{8}-\left(2\frac{1}{4}+\frac{5}{3}\times\frac{15}{14}\div\frac{10}{9} of \frac{3}{14}\right)\right]$$ is:
The value of $$54\div16 \text{of} 3\times[12\div4 \text{of} \left\{6\times3\div(11-2)\right\}]\div(12\div8\times2)$$ is:
$$54\div16 \text{of} 3\times[12\div4 \text{of} \left\{6\times3\div(11-2)\right\}]\div(12\div8\times2)$$
= $$54\div16 \text{of} 3\times[12\div4 \text{of} \left\{6\times3\div9\right\}]\div(\frac{12}{8}\times2)$$
= $$54\div16 \text{of} 3\times[12\div4 \text{of} \left\{6\times\frac{3}{9}\right\}]\div3$$
= $$54\div16 \text{of} 3\times[12\div4 \text{of} 2]\div3$$
= $$54\div16 \text{of} 3\times[12\div8]\div3$$
= $$54\div16 \text{of} 3\times\frac{12}{8}\div3$$
= $$54\div48\times\frac{12}{8}\div3$$
= $$\frac{54}{48}\times\frac{12}{8\times3}$$
= $$\frac{9}{16}$$
Hence, the correct answer is Option D
When $$x$$ is added to each of 7, 13, 19 and 29, the numbers so obtained in this order are in proportion. What is the mean proportional between $$\left(3x - 8\right)$$ and $$\left(x + 5\right)$$ ?
70 males and 100 females are working in a firm. During one mass recruitment drive, an equal number of males and females are recruited and their ratio becomes 3 : 4. The total number of people working in the firm after recruitment is:
Simplify the following expression:
$$8\div4 \text{of} 2-15\div2 \text{of} 5-6\div5\times(-7+5) \text{of} 2$$
$$8\div4 \text{of} 2-15\div2 \text{of} 5-6\div5\times(-7+5) \text{of} 2$$
= $$8\div4 \text{of} 2-15\div2 \text{of} 5-6\div5\times(-2) \text{of} 2$$
= $$8\div8-15\div10-6\div5\times(-4)$$
= $$\frac{8}{8}-\frac{15}{10}-\frac{6}{5}\times(-4)$$
= $$1-\frac{3}{2}+\frac{24}{5}$$
= $$\frac{10-15+48}{10}$$
= $$\frac{43}{10}$$
= $$4\frac{3}{10}$$
Hence, the correct answer is Option D
The present population of a village is 15280. If the number of males increases by 25% and the number of females increases by 15%, then the population will become 18428. The difference between present population of males and females in the village is:
The present population of a village is 15280.
Let the number of males and females of the village are M and F respectively.
M + F = 15280............(1)
If the number of males increases by 25% and the number of females increases by 15%, then the population will become 18428.
$$\frac{125}{100}$$M + $$\frac{115}{100}$$F = 18428
125M + 115F = 18428 x 100
25M + 23F = 368560.........(2)
Solving 25 x (1) - (2), we get
25F - 23F = 382000 - 368560
2F = 13440
F = 6720
Substituting F = 6720 in equation (1),
M + 6720 = 15280
M = 8560
The difference between present population of males and females in the village = 8560 - 6720 = 1840
Hence, the correct answer is Option A
The value of $$0.2\div0.025+39+0.92\div0.2\times5-4.9\div0.07$$ is:
What is the mean of the median and range of the data:
45, 40, 38, 60, 55, 36, 31, 52, 42, 44 ?
A reduction of 15% in the price of sugar enables Aruna Rai to buy 6 kg more for ₹272. The reduced price of sugar per kg is:
Simplify the following expression:
$$7 \times 4 \div 21 \text{of} 4 - 5 \div 4 \times (9 - 13) + 2 - 2 \div 8$$
$$7 \times 4 \div 21 \text{of} 4 - 5 \div 4 \times (9 - 13) + 2 - 2 \div 8$$
= $$7 \times 4 \div 84 - 5 \div 4 \times (-4) + 2 - 2 \div 8$$
= $$7\times\frac{4}{84}-\frac{5}{4}\times(-4)+2-\frac{2}{8}$$
= $$\frac{1}{3}+5+2-\frac{1}{4}$$
= $$7+\frac{4-3}{12}$$
= $$7\frac{1}{12}$$
Hence, the correct answer is Option A
The value of $$(16\frac{2}{3}\div10)-[(\frac{8}{3}\times\frac{5}{4}) \ of \frac{2}{5}+\frac{16}{3}\times\frac{11}{8}-(\frac{1}{4}\div\frac{1}{28})]$$ is:
The value of $$17-\left[16-\left\{38-\left(49-72\div6\times4 of 2\right)\right\}\right]$$ is:
The value of $$2\frac{1}{4}\div1\frac{1}{2} of \left[4\frac{1}{6}-\left(\frac{17}{21}+\frac{4}{3}\times2\frac{1}{8}\div1\frac{1}{6}of\frac{3}{4}-\frac{5}{7}\right)\right]$$ is:
The value of $$39-[30-\left\{33-(19-4\div3of8\times6)\right\}]$$ is:
The value of $$4\times2\div3 of 12-3\div2\times\left(2-3\right)\times2+3\div2 of 3$$ is:
The value of $$500\div\frac{3}{8}$$ of $$\frac{2}{3}\div\left[\frac{5}{3} of 300+7\frac{1}{2}\div5\frac{1}{2}\times1100\right]$$ is:
The value of $$6\times2\div3$$ of $$12-3\div2\times(2-3)\times2+3\div2$$ of 3 is:
Simplify the following expression:
$$15 \div 3 \text{of} 2 \times 4 + 9 \div 18 \text{of} 2 \times 3 - 4 \div 8 \times 2$$
$$15 \div 3 \text{of} 2 \times 4 + 9 \div 18 \text{of} 2 \times 3 - 4 \div 8 \times 2$$
= $$15\div6\times4+9\div36\times3-4\div8\times2$$
= $$\frac{15}{6}\times4+\frac{9}{36}\times3-\frac{4}{8}\times2$$
= $$10+\frac{3}{4}-1$$
= $$9\frac{3}{4}$$
Hence, the correct answer is Option D
Simplify the following expression:
$$3\times8\div9 \text{of} 6-2\div3\times(5-2)\times2+18\div3 \text{of} 3$$
$$3\times8\div9 \text{of} 6-2\div3\times(5-2)\times2+18\div3 \text{of} 3$$
= $$3\times8\div54-2\div3\times3\times2+18\div9$$
= $$3\times\frac{8}{54}-\frac{2}{3}\times3\times2+\frac{18}{9}$$
= $$\frac{4}{9}-4+2$$
= $$\frac{4-36+18}{9}$$
= $$\frac{-14}{9}$$
= $$-1\frac{5}{9}$$
Hence, the correct answer is Option A
A is 120% of B and B is 65% of C. If the sum of A, B and C is $$121\frac{1}{2}$$, then the value of $$2C-4B+A$$ is:
In a week, the weights of a bag of tea were 350 kg, 280 kg, 340 kg, 270 kg, 360 kg, 310 kg, 300 kg. The range (in kg) is:
A number was divided by 8, instead of being multiplied by 8. As a result of this, there was an error in the answer. What is the percentage difference ( correct to two places of decimal) in the answer due to this miscalculation?
Between two consecutive years, my income is in the ratio 2 : 5 and expenses are in the ratio 4 : 7. If my income in the second year is ₹75,000 and my expenses in the first year are ₹20,000, then my total savings in the two years together are:
How much time (in seconds) does the earth take to rotate through an angle of 135 degrees about its axis?
The value of $$16-4\times\left[4-\left\{98\div2 of 7-\left(6-36\div6\times2\right)\right\}\right]$$ is:
What is the average of numbers from 1 to 50 which are multiples of 2 or 5? (correct to one decimal place)
Which two digits and signs can be interchanged so as to balance the given equation?
$$25 - 9 + 42 \div 6 \times 7 =17$$
A fruit vendoe brings 1092 apples and 3432 oranges to a market. He arranges them in heaps of equal number of oranges as well as apples such that every heap consists of the maximum possible number of the fruits. What is this number?
The value of $$\frac{2}{3}\div(\frac{4}{5}-\frac{1}{2})\times\frac{18}{25}-(\frac{4}{5}\div\frac{5}{6} \ of \ 2\frac{2}{3})+3\frac{1}{5}\div\frac{8}{5}\times\frac{2}{5}$$ is:
If a number is first increased by 15%, then reduced by 15%, it results in 782. If the same numberis first reduced by 25%, then increased by 25%and again reduced by 20%, then what will be the resulting number?
If $$x$$ is a positive quantity, then what is the value of $$3x$$, if $$0.4\overline{23}-0.2$$ of $$52.5\div0.84=x^{2}-(0.0\overline{21}+12.5)$$ ?
Solve for $$x$$, if $$ \left(3 \times 22\right) +\left(5^{2} + 2^{3} \right) - 2^{x} = -$$ 30
The value of $$\frac{1}{5}\div\frac{3}{10}of\frac{4}{9}-\frac{4}{5}\times1\frac{1}{9}\div\frac{8}{15}+\frac{3}{4}+\frac{3}{4}\div\frac{1}{2}$$ is:
The value of $$\frac{\frac{1}{4}\div\frac{3}{4}(\frac{2}{5}-\frac{1}{3})}{1\frac{2}{3} \ of \ \frac{3}{4}-\frac{1}{4} \ of \ \frac{2}{3}}$$ is:
For a 14-days camp, sufficient supplies are available for 300 people. 500 more people arrive on day 1 itself. For how many days will these supplies be sufficient for all these people?
If a number P is divisible by 2 and another number Q is divisible by 3, then which of the following is true?
P is divisible by 2.
Let P = 2t
Q is divisible by 3.
Let Q = 3s
P$$\times$$Q = 2t$$\times$$3s = 6st
So, P$$\times$$Q is divisible by 6.
Hence, the correct answer is Option C
In a library, the ratio of the number of mathematics books to that of physics books, is the same as the ratio of the number of the physics books to that of chemistry books. If there are 144 mathematics books and 100 chemistry books, then the ratio of the total no of mathematics and physics books to the total number of chemistry and physics books is:
Simplify the following expression:
$$\frac{108 \times 108 \times 108 - 92 \times 92 \times 92}{108 \times 108 + 92 \times 92 + 108 \times 92}$$
The value of $$48\div[5+\left\{19-(16-16\div4\times3of2)\right\}]$$ is:
The value of $$79-[128-\left\{75-(72\div16\times4)+(18\div2of6)\times4 \right\}]$$ is:
The value of $$\frac{13}{70}\div\left[\frac{4}{5}\left(\frac{1}{3}-\frac{1}{4}\times\frac{1}{5}\right)\div2\frac{5}{6}\right]-1\frac{9}{28}$$ is:
The value of $$\frac{5}{16}+\frac{3}{5}\times1\frac{7}{8}\div\frac{2}{3}-6\frac{1}{8}\div(5\frac{1}{4}\div\frac{3}{7} \ of \ \frac{1}{2}) \ of \ \frac{6}{7}$$ is:
The value of $$\frac{52 - 1170 \div 26 + 13 \times 2}{2 + 1\frac{1}{8} of 2 - 1\frac{1}{4}}$$ is:
The value of $$\left(120\div\frac{5}{4}\right)-\left\{\left(105-5\times3+2 of 17\div\frac{1}{6}\right)\div\left(5+\frac{1}{4}\right)\right\}$$ is:
The median of a set of 7 distinct observation is 16.5. If each of the largest 3 observations of the set is increased by 5, then the median of the new set:
The value of $$18 \div [26 - \left\{25 - (15 - 5) \div 2\right\}] of 12 + 2 - 2 \div 4 \times 16$$ is:
The value of $$20 \div 5 of 8 \times [9 \div 6 \times (6 - 3)] - (10 \div 2 of 20)$$ is:
What is the mean of the median and range of the following data?
3, 8, 7, 12, 4, 3, 16, 20, 23, 10, 9, 15, 2, 7
If the ratio of the mode and median of a certain data is 9 : 8, then the ratio of its mean and median is:
In a constituency, 60% of the voters are males and the rest are females. 40% of the males are illiterate and 25% of the females are literate. By what percentage is the number of illiterate males more than that of literate females?
The value of $$12\times\left[\left(9-4\right)\div\left\{\left(8\div8 of 4\right)+\left(4\div4 of 2\right)\right\}\right]$$ is:
What is the simplified value of $$\left\{\left(4-\frac{2}{1+\frac{2}{1-\frac{1}{2+\frac{3}{4}}}}\right)\div1\frac{5}{12} of \frac{17}{145}-\left(4+3\div0.5-1\right)\right\}$$?
A sum of ₹2,130 is to be divided into three parts. The second part is 60% of the first, ai1d the ratio of the first to third pan is 5:7. What are the parts (in ₹)?
The simplified value of $$\frac{1\div\frac{3}{7} of \left(6+8\times\overline{3-2}\right)+\left[\frac{1}{5}\div\frac{7}{25}-\left\{\frac{3}{7}+\frac{8}{14}\right\}\right]}{18\div\overline{10-4}+32\div\left(4+10\div2-1\right)}$$ is:
The value of $$21\times[(9-4)\div\left\{(8\div8 of4)+(4\div4 of 2)\right\}]$$ is:
Two clock where synchronised at 11 a.m. Sunday. There after, every day they were, respectively, found to gain and lose one minute per day. What time, expressed in hours and minutes, will the second clock show when the first clock shows 10 p.m. on the next Friday?
What is the mean of the mode and median of the given data?
5, 4, 6, 9, 3, 2, 5, 6, 7, 8, 9, 5, 7, 3
Which two numbers and two signs can be interchanged so as to balance the given equation?
$$16\times4+12\div4-15=59$$
Which two numbers should be interchanged to make the given equation correct?
$$78 \div 48 \times 8 + (26 \times 7) - 39 + (45 + 15) = 210$$
Which two signs should be interchanged to make the given equation correct?
$$156 - 13 + 9 \times 18 \div 5 = 169$$
Four friends, Priya, Kavya, Gaurvi and Shalini, have different amounts of money with them. If Priya takes ₹88 from Kavya, then she will have an amount equal to what Gaurvi has. Shalini and Kavya together have a total of ₹550. If Gaurvi takes ₹25 from Shalini, she will have an amount equal to what Kavya has. If the total amount with Shalini, Kavya and Gaurvi is ₹840, how much money does Priya have?
Vineet, Rajesh and Kriti have different amounts of money with them. Rajesh has just double the amount of money than Vineet. The total amount of money that Rajesh and Kriti have is ₹147. Kriti has ₹6 more than the amount Vineet has. How much money does Kriti have ?
Amount of Rajesh = 2 $$\times$$ amount of Vineet
Amount of Kriti = 6 + amount of Vineet ---(1)
Total amount of Rajesh and Kriti = 147
Amount of Rajesh + amount of Kriti = 147
2 $$\times$$ amount of Vineet + 6 + amount of Vineet = 147
Amount of Vineet = 141/3 = 47
From eq (1),
Amount of Kriti = 6 + 47 = Rs. 53
$$\therefore$$ The correct answer is option B.
Which of the following pairs of numbers and signs, when their positions are interchanged, will correctly solve the given mathematical equation?
$$17 \times 15 + 3 - 11 \div 3 = 45$$
such type of question are solved by checking the given answers in expression. so let put all given options in expression..
OPTION A..LHS $$17\times15+3-11\div3$$ now replace 15and11,,,+and$$\times$$
LHS becomes $$ 17+11\times3-15\div3$$
now solve it according to bodmas
LHS=$$17+11\times3-5$$
LHS=$$17+33-5$$
LHS=$$50-5$$
LHS=45=RHS
verified
Which two numbers should be interchanged to make the given equation correct?
$$9 + 7 \times 5 - 18 \div 2 = 3 \times 4 - 10 + 45 \div 5$$
$$9 + 7 \times 5 - 18 \div 2 = 3 \times 4 - 10 + 45 \div 5$$
By the option B,
To interchange the 7 and 4,
$$9 + 4 \times 5 - 18 \div 2 = 3 \times 7 - 10 + 45 \div 5$$
$$9 + 4 \times 5 - 9 = 3 \times 7 - 10 + 9$$
$$9 + 20 - 9 = 21 - 10 + 9$$
20 = 20
$$\therefore$$ The correct answer is option B.
The two given expressions on either side of the ‘=’ sign will have the same value if two numbers on either side or on the same side are interchanged. Find from the given option the correct numbers to be interchanged.
$$4 + 6 \times 2 - 27 \div 3 = 8 \times 2 - 4 + 9 \div 3$$
Given that expression
$$4 + 6 \times 2 - 27 \div 3 = 8 \times 2 - 4 + 9 \div 3$$
we check option (A) 6,2 replace to each other
$$4 + 2 \times 6 - 27 \div 3 =8 \times 6 - 4 + 9 \div 3$$
from the LHS $$4 + 2 \times 6 - 27 \div 3$$
$$\Rightarrow 4 + 12 - 9$$
$$\Rightarrow 16 - 9$$
$$\Rightarrow 7 $$
from RHS$$ 8 \times 6 - 4 + 9 \div 3$$
$$\Rightarrow 48-4+3 = 51-4 = 47 $$
then RHS is not equal to LHS
then we check option (B)6,8
$$4 + 8 \times 2 - 27 \div 3 = 6 \times 2 - 4 + 9 \div 3$$
then LHS $$4 + 8 \times 2 - 27 \div 3$$
$$\Rightarrow 4 + 8 \times 2 - 9$$
$$\Rightarrow 4 + 16- 9$$
$$\Rightarrow 20- 9 = 11 $$
From RHS $$6 \times 2 - 4 + 9 \div 3$$
$$\Rightarrow 6 \times 2 - 4 + 3$$
$$\Rightarrow 12 - 4 + 3$$
$$\Rightarrow 15- 4 = 11 $$
therefore LHS = RHS then
option (B) is staisfied the given expression
Ans (B) 6,8
The Value of $$\frac{(2.8)^3 + (2.2)^3}{(28)^2 - 28 \times 22 + 484}$$ is:
$$\frac{(2.8)^3 + (2.2)^3} {(28)^2 - 28 \times 22 + 484} $$
$$\Rightarrow\frac{ (2.8)^3 +(2.2)^3} {784 +484 - 616) }$$
$$\Rightarrow\frac{ 21.952 + 10 .648} { 1268 - 616}$$
$$\Rightarrow\frac{ 32.6}{652}$$
$$\Rightarrow 0.05$$ Ans
The value of $$\frac{(0.321)^3+(0.456)^3-(0.777)^3}{0.9 \times (0.107)(0.76)(0.777)}$$ is
$$\frac {(0.321)^3 + (0.456)^3 - (0.777)^3} { 0.9 \times (0.107) (0.76) (0.777)}$$
$$\Rightarrow\frac { (0.321)^3 + (0.456)^3 -( 0.321 + 0.456 )^3 } { 0.9 \times (0.107) (0.76) (0.777)}$$
$$\Rightarrow\frac {( 0.321)^3 + (0.456)^3 - [(0.321)^3 + (0.456)^3 + 3 \times (0.321) (0.456) (0.777)]} {0.9 \times (0.107)(0.76) (0.777)}$$
$$\Rightarrow\frac {- 3 \times( 0.321)(0.456)(0.777)} {0.9 \times (0.107)(0.76)(0.777)}$$
$$\Rightarrow\frac {- (0.321)(0.456)} {0.3 \times (0.107) (0.76)}$$
$$\Rightarrow\frac {- (0.321)(0.456)} { (0.321) (0.76)}$$
$$\Rightarrow\frac {- (0.456)} { (0.76)}$$
$$\Rightarrow {- 6} $$
If ‘$$+$$’ means ‘$$-$$’, ‘$$-$$’ means ‘$$\times$$’, ‘$$\times$$’ means ‘$$\div$$’ and ‘$$\div$$’ means ‘$$+$$’, then what will be the value of the following expression?
$$27 - 2 + 24 \times 8 \div 4$$
Given expression $$27 - 2 + 24 \times 8 \div 4$$
$$\Rightarrow 27 \times 2 - 24 \div 8 + 4$$ (we chage Sign according to question)
$$\Rightarrow 27 \times 2 - 3 + 4$$
$$\Rightarrow 54 - 3 + 4$$
$$\Rightarrow 54 - 3 + 4$$
$$\Rightarrow 58 - 3 $$
$$\Rightarrow 55 $$ Ans
In a certain a group of men and horses, the total number of legs is 14 more than twice the number of heads. How many horses are there in the group?
The total number of legs is 14 more than twice the number of heads.
A horse have 2 more legs than man so,
Number of horse = 14/2 = 7
$$\therefore$$ The correct answer is option B.
Product A is costlier than product B by ₹2. If the price of product A is increased by two times the price of product B, the new price of product A becomes ₹17. What is the price of product B?
Let the price of product A be x, so the price of product B = x - 2.
According to the question,
x + 2(x-2) = 17, solving this we get,
x + 2x - 4 = 17,
3x = 17 + 4
3x = 21, x = 7
Price of Product A = Rs. 7, so Price of Product B = 7 - 2 = Rs 5.
Select the correct combination of mathematical signs to replace * signs and to balance the following equation.
(9 * 8 * 7) * 13 * 5
Given expression (9 * 8 * 7) * 13 * 5
we check mathematical signs to replace * signs
we check option (A) but it is not staisfied similar option (B) but (A) is not staisfied
check option (B ) $$\times , -, \div, = $$ in the given expression
$$(9 \times 8 - 7) \div 13 = 5 $$
From the LHS $$(9 \times 8 - 7) \div 13 $$
$$\Rightarrow (65)\div 13 $$
$$\Rightarrow 5 $$ RHS it is staisfied.
therefore (B) Ans
Which twosigns should be interchanged to make the given equation correct?
$$121 \div 11 + 54 - 9 \times 3$$ = 128
$$121 \div 11 + 54 - 9 \times 3$$ = 128
From option C,
After the interchanging sign,
$$121 - 11 + 54 \div 9 \times 3$$ = 128
$$121 - 11 + 6 \times 3$$ = 128
$$121 - 11+ 18$$ = 128
128 = 128
$$\therefore$$ The correct answer is option C.
Two persons A and B are paid a total of ₹2,040 per week by their employer. If B is paid 140 per cent of the sum paid to A, then how muchis A paid per week?
Let the amount paid to A per week = $$x$$
according to question,
amount paid to B per week B = 140 % of$$ x $$= $$ \dfrac{140}{100} x $$
total amount = $$ x$$ +$$ \dfrac{140}{100}x $$
Now, taking LCM,
$$ \dfrac{100}{100}x +\dfrac{140}{100}x = 2040$$
$$\Rightarrow \dfrac {100 x +140 x} {100} = 2040$$ (making same denominater)
$$\Rightarrow 240x = 2040 x 100$$
$$\Rightarrow x=\dfrac{ 2040 \times 100} {240} $$
$$\Rightarrow x = 850$$ Ans
What is the simplified value of:
$$7\frac{1}{3}\div2\frac{1}{2} of 1\frac{3}{5} - \left(\frac{3}{8} + \frac{1}{7} \times 1\frac{3}{4}\right) - \frac{5}{24}$$
Given that expression
$$7\frac{1}{3}\div2\frac{1}{2} of 1\frac{3}{5} - \left(\frac{3}{8} + \frac{1}{7} \times 1\frac{3}{4}\right) - \frac{5}{24}$$
$$\Rightarrow \frac{22}{3}\div\frac{5}{2} of \frac{8}{5} - \left(\frac{3}{8} + \frac{1}{7} \times \frac{7}{4}\right) - \frac{5}{24}$$
$$\Rightarrow \frac{22}{3}\div\frac{4}{1} - (\frac{3}{8} + \frac{1}{7} \times \frac{7}{4} - \frac{5}{24}$$
$$\Rightarrow \frac{11}{6} - \dfrac {3+2}{8} - \frac{5}{24}$$
$$\Rightarrow \frac{11}{6} - \frac{5}{8} - \frac{5}{24}$$
$$\Rightarrow \dfrac{11\times 4-5\times3 -5\times1}{24}$$
$$\Rightarrow \dfrac {44-20}{24}$$
$$\Rightarrow \dfrac{24}{24}$$
$$\Rightarrow 1 $$ Ans
The value of $$\frac{5 - 2 \div 4 \times [5 - (3 - 4)] + 5 \times 4 \div 2 of 4}{4 + 4 \div 8 of 2 \times (8 - 5) \times 2 \div 3 - 8 \div 2 of 8}$$
$$\frac {5 -2 \div 4 \times[ 5-(3-4)] + 5 \times 4 \div 2 of 4 } { 4 + 4 \div 8 of 2 \times ( 8-5) \times 2 \div 3 - 8 \div 2 of 8 }$$
$$\Rightarrow \frac {5-2 \div 4 \times[ 5 - (-1)] + 5 \times 4 \div 2 of 4 } { 4 + 4 \div 8 of 2 \times ( 3) \times 2 \div 3 - 8 \div 2 of 8 } $$
$$\Rightarrow \frac {5-2 \div 4 \times 6 + 5 \times 4 \div 8} {4+4 \div 16 \times 3 \times 2 \div 3 -8 \div 16 } $$
$$\Rightarrow \frac { 5- 1/2 \times 6 +5 \times 1/2 } {4 + 1/4 \times 3 \times 2/3 - 1/2 }$$
$$\Rightarrow \frac { 5 -3 +5/2} {4 + 1/2 -1/2} $$
$$\Rightarrow \frac {9/2} {4} $$
$$\Rightarrow \frac {9} {8} $$
What is the Value of $$\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3 + (0.41)^3 - 8(0.39)^3}$$?
Expression : $$\frac{0.74 \times 1.23 \times 0.13}{(0.37)^3 + (0.41)^3 - 8(0.39)^3}$$
= $$\frac{(0.37\times2) \times (0.41\times3) \times 0.13}{(0.37)^3 + (0.41)^3 - (2\times0.39)^3}$$
= $$\frac{0.37 \times 0.41\times 0.78}{(0.37)^3 + (0.41)^3 - (0.78)^3}$$
Let $$x=0.37$$, $$y=0.41$$ and $$z=-0.78$$
$$\because$$ $$x+y+z=0$$, => $$x^3+y^3+z^3=3xyz$$
=> $$\frac{xy(-z)}{x^3+y^3-z^3}=\frac{-1}{3}$$
=> Ans - (A)
The value of $$\frac{4 - 3 \div 2 \times (4 - 2) - 3 + 4 \times 3 \div 2 + 4}{4 + 3 \div 4 \times (2 - 4) \times 4 + 3 \div 4 of 3}$$ is ..........
solve by using BODMAS rule,
= $$\frac{4 - 3 \div 2 \times (4 - 2) - 3 + 4 \times 3 \div 2 + 4}{4 + 3 \div 4 \times (2 - 4) \times 4 + 3 \div 4 of 3}$$
= $$\frac{4 - 3 \div 2 \times 2 - 3 + 4 \times 3 \div 2 + 4}{4 + 3 \div 4 \times (-2) \times 4 + 3 \div 12}$$
= $$\frac{4 - 3 - 3 + 6 + 4}{4 - 6 + \frac{1}{4}}$$
= $$\frac{8}{-\frac{7}{4}}$$
= $$\frac{-32}{7}$$
A student was asked to find the value of
$$\left[\frac{4}{9} \div \left(\frac{3}{5} \div \frac{3}{2} \right)\times \frac{9}{25} \right] \times \frac{\left[\frac{2}{3} of \frac{4}{9} \div \left(3 \times \frac{3}{5} of \frac{4}{5}\right)\right]}{\frac{2}{3} \div \frac{3}{4} of \frac{5}{6}}$$ His answer was $$\frac{2}{9}$$.
What is the difference between his answer and the correct answer?
Expression : $$\left[\frac{4}{9} \div \left(\frac{3}{5} \div \frac{3}{2} \right)\times \frac{9}{25} \right] \times \frac{\left[\frac{2}{3} of \frac{4}{9} \div \left(3 \times \frac{3}{5} of \frac{4}{5}\right)\right]}{\frac{2}{3} \div \frac{3}{4} of \frac{5}{6}}$$
= $$\left[\frac{4}{9} \div \left(\frac{3}{5} \times \frac{2}{3} \right)\times \frac{9}{25} \right] \times \frac{\left[\frac{8}{27}\div \left(\frac{36}{25}\right)\right]}{\frac{2}{3} \div \frac{5}{8}}$$
= $$\left[\frac{4}{9} \times \frac{5}{2}\times \frac{9}{25} \right] \times \frac{\left[\frac{8}{27}\times \frac{25}{36}\right]}{\frac{2}{3} \times \frac{8}{5}}$$
= $$\frac{2}{5}\times\frac{\frac{50}{243}}{\frac{16}{15}}$$
= $$\frac{2}{5}\times\frac{50}{243}\times\frac{15}{16}$$
= $$\frac{25}{81\times4}=\frac{25}{324}$$
A student was asked to find the value of $$\frac{\left(2 \frac{1}{3} + 2 \frac{1}{2} - \frac{1}{6} \right) \div 2\frac{1}{3} \times 5 \frac{2}{3} \div 1\frac{2}{3} of 4\frac{1}{4}}{3 \frac{1}{5} \div 4 \frac{1}{2} of 5 \frac{1}{3} + 5\frac{1}{3} \times \frac{3}{4} \div 2\frac{2}{3}}$$. His answer was $$\frac{6}{7}$$.what is the difference between correct answer and his answer?
As per the question,
$$\frac{\left(2 \frac{1}{3} + 2 \frac{1}{2} - \frac{1}{6} \right)\div 2\frac{1}{3} \times 5 \frac{2}{3} \div 1\frac{2}{3} of 4\frac{1}{4}}{3 \frac{1}{5} \div 4 \frac{1}{2} of 5 \frac{1}{3} + 5\frac{1}{3} \times \frac{3}{4} \div 2\frac{2}{3}}$$
$$\Rightarrow \frac{\left(2 \frac{1}{3} + 2 \frac{1}{2} - \frac{1}{6} \right)\div2\frac{1}{3} \times 5 \frac{2}{3} \div \frac{7}{3} of \frac{17}{4}}{3\frac{1}{5} \div \frac{9}{2} of \frac{16}{3} + 5\frac{1}{3} \times\frac{3}{4} \div 2\frac{2}{3}}$$
$$\Rightarrow \frac{\left(2 \frac{1}{3} + 2 \frac{1}{2} - \frac{1}{6} \right)\div2\frac{1}{3} \times 5 \frac{2}{3} \div \frac{119}{12}}{3\frac{1}{5} \div 24 + 5\frac{1}{3} \times\frac{3}{4} \div 2\frac{2}{3}}$$
$$\Rightarrow \frac{\left(\frac{7}{3} + \frac{5}{2} - \frac{1}{6}\right)\div\frac{7}{3} \times \frac{17}{3} \div \frac{119}{12}}{\frac{16}{5} \div 24 + \frac{16}{3} \times\frac{3}{4} \div \frac{2}{3}}$$
$$\Rightarrow \frac{\left(\frac{28}{6}\right)\div\frac{7}{3} \times \frac{17}{3} \div \frac{119}{12}}{\frac{2}{15}+ \frac{16}{3} \times\frac{9}{8}}$$
$$\Rightarrow \frac{2 \times \frac{17\times 12}{3\times 119}}{\frac{2}{15}+ \frac{16}{3} \times\frac{9}{8}}$$
$$\Rightarrow 2 \times \frac{17\times 12\times 15}{3\times 119\times 92}$$
$$\Rightarrow \frac{ 12\times 5}{ 7\times 41}=\dfrac{60}{287}$$
Hence the required difference $$=\dfrac{6}{7}-\dfrac{60}{287}=\dfrac{246-60}{287}$$
$$=\dfrac{246-60}{287}=\dfrac{186}{287}$$
The value of $$\frac{(0.13)^2 + (0.21)^2}{(0.39)^2 + 81(0.07)^2} \div \frac{(2.4)^4 + 3 \times (11.52) + 9}{(2.4)^6 + 6(2.4)^4 + 3 \times (17.28)}$$ lies between:
Given that
$$\frac{(0.13)^2 + (0.21)^2}{(0.39)^2 + 81(0.07)^2} \div \frac{(2.4)^4 + 3 \times (11.52) + 9}{(2.4)^6 + 6(2.4)^4 + 3 \times (17.28)}$$
$$\Rightarrow \frac{(0.13)^2 + (0.21)^2}{(0.39)^2 + 81(0.07)^2} \times \frac{(2.4)^6 + 6(2.4)^4 + 3 \times (17.28)}{(2.4)^4 + 3 \times (11.52) + 9}$$
$$\Rightarrow \frac{0.0169+ 0.0441}{0.1521 + 81\times 0.0049} \times \frac{191.10+ 33.1776 + 51.84}{5.76 + 34.56 + 9}$$
$$\Rightarrow \frac{0.061}{0.549} \times \frac{276.1176}{49.32}$$
$$\Rightarrow \frac{16.84317}{27.07668}$$
$$\Rightarrow 0.6222$$
then It lies between 0. 6 and 0.7
therefore Option (C) 0.6 and 0.7 Ans
The Vale of $$\frac{17.35 + \frac{7}{5} of 55 - 7}{(42 \div 6 \times 8.35) - \frac{3}{7} of \left(\frac{2}{3} - \frac{1}{5}\right) + [291 \div (80 \div 8)]}$$ is:
$$\dfrac {17.35 +\dfrac {7}{5} of 55 - 7 } {( 42\div 6 \times 8.35 ) - \dfrac{3}{7}of \left(\dfrac {2}{3} - \dfrac{1}{5}\right)+ [291 \div (80 \div 8)]}$$
$$\Rightarrow \dfrac {17.35 +77 -7 } {(7\times 8.35) -\dfrac {3}{7} of \dfrac{10-3}{15} + 291 \div 10}$$
$$\Rightarrow \dfrac { 17.35 +77 -7} {(58.45) -\dfrac {3}{7} \times \dfrac{7}{15} + 29.1}$$
$$\Rightarrow \dfrac { 94.35 -7} {(58.45) + 29.1 -\dfrac {1}{5}}$$
$$\Rightarrow \dfrac { 87.35} {87.55 - 0.2}$$
$$\Rightarrow \dfrac { 87.35} {87.35 }$$
$$\Rightarrow 1 Ans $$
Which two signs should be interchanged to make the given equation correct?
$$121 + 11 - 42 \times 6 \div 7 =83$$
$$121 + 11 - 42 \times 6 \div 7 =83$$
From the option C,
$$121 + 11 - 42 \div 6 \times 7 =83$$
$$121 + 11 - 42 \div \frac{1}{6} \times 7 =83$$
$$121 + 11 - 49 =83$$
83 = 83
$$\therefore$$ The correct answer is option C.
The value of $$9 \times [((9 - 4) \div \left\{(8 \div 8 of 4) + (4 \div 4 of 2)\right\}]$$ is:
Expression : $$9 \times [(9 - 4) \div \left\{(8 \div 8 of 4) + (4 \div 4 of 2)\right\}]$$
= $$9 \times [(5) \div \left\{(8 \div32) + (4 \div 8)\right\}]$$
= $$9 \times [(5) \div \left\{\frac{1}{4}+\frac{1}{2}\right\}]$$
= $$9\times[5\times\frac{4}{3}]$$
= $$3\times20=60$$
=> Ans - (B)
The value of $$\dfrac{4.669 \times 4.669 - 9 \times (0.777)^2}{(4.669)^2 + (2.331)^2 + 14(0.667)(2.331)}$$ is (1 - k), where k = ?
Expression : $$\dfrac{4.669 \times 4.669 - 9 \times (0.777)^2}{(4.669)^2 + (2.331)^2 + 14(0.667)(2.331)}$$
= $$\dfrac{4.669 \times 4.669 - (2.331)^2}{(4.669)^2 + (2.331)^2 + 2(4.669)(2.331)}$$
Let $$x=4.669$$ and $$y=2.331$$
= $$\dfrac{x^2-y^2}{x^2+y^2+2xy}$$
= $$\dfrac{(x-y)(x+y)}{(x+y)^2}=\dfrac{x-y}{x+y}$$
= $$\dfrac{4.669-2.331}{4.669+2.331}=\dfrac{2.338}{7}=0.334$$
According to ques, => $$k=1-0.334=0.666$$
=> Ans - (A)
The value of $$\frac{1}{\sqrt{17 + 12\sqrt{2}}}$$ is closest to .......
$$\frac{1}{\sqrt{17 + 12\sqrt{2}}}$$
= $$\frac{1}{\sqrt{17 + 12\times 1.414}}$$
= $$\frac{1}{\sqrt{17 + 16.97}}$$
= $$\frac{1}{\sqrt{34}}$$
= $$\frac{1}{6}$$ = 0.166 = 0.17(Approx)
Which one among the following is the smallest?
If the difference between all the pairs is same, then the pair whose first number is the greatest will be the smallest pair, and vice-versa the pair with smallest number will be largest.
Here, difference in each pair is 2, thus $$\sqrt{401}-\sqrt{399}$$ is smallest, and $$\sqrt{101}-\sqrt{99}$$ is largest.
=> Ans - (A)
Select the correct combination of mathematical signs to sequentially replace the * signs, to balance the following equation.
(12 * 7 * 6) * 13 * 6
(12 * 7 * 6) * 13 * 6
From the option A,
(12 $$\times 7 - 6) \div$$ 13 = 6
78 $$\div$$ = 6
6 = 6
$$\therefore$$ The correct answer is option A.
The value of $$\frac{(0.013)^3 + (0.007)(0.000049)}{(0.007)^2 + 0.013(0.013 - 0.007)}$$ is:.......
$$\frac{(0.013)^3 + (0.007)(0.000049)}{(0.007)^2 + 0.013(0.013 - 0.007)}$$
$$\frac{(0.013)^3 + (0.007)(0.007)^2}{(0.007)^2 + 0.013(0.013 - 0.007)}$$
$$\frac{(0.013)^3 + (0.007)^3}{(0.007)^2 + 0.013(0.006)}$$
$$\frac{0.000002197 + 0.000000343}{0.000049 + 0.000078}$$
$$\frac{0.02197 + 0.00343}{0.49 + 0.78}$$
$$\frac{0.0254}{1.27}$$ = 0.02
The value of $$\sqrt{6 - \sqrt{17 - 2\sqrt{72}}}$$ is closest to:
$$\sqrt{6 -\sqrt{17 - 2\sqrt{72}}}$$
$$\Rightarrow \sqrt{6 -\sqrt{17-2 \sqrt { 2^2\times 3^2 \times 2 }}} $$
$$\Rightarrow \sqrt { 6 - \sqrt{ 17 - 2\times 6 \sqrt{2 }}} $$
$$\Rightarrow \sqrt {6 - \sqrt {17 - 12 \sqrt {2}}}$$
$$\Rightarrow \sqrt {6 - \sqrt {17-12\times 1.41 }}$$
$$\Rightarrow \sqrt {6 - 0.03 } $$
$$\Rightarrow \sqrt {5.97 } $$
$$\Rightarrow 2.44 Ans $$
The value of $$\frac{\frac{1}{3} + \left[4\frac{3}{4} - \left(3\frac{1}{6} - 2\frac{1}{3}\right)\right]}{\left(\frac{1}{5} of \frac{1}{5} \div \frac{1}{5}\right)\div \left(\frac{1}{5} \div \frac{1}{5} \times \frac{1}{5}\right)}$$ lies between:
$$\frac{\frac{1}{3} + \left[4\frac{3}{4} - \left(3\frac{1}{6} - 2\frac{1}{3}\right)\right]}{\left(\frac{1}{5} of \frac{1}{5} \div \frac{1}{5}\right)\div \left(\frac{1}{5} \div \frac{1}{5} \times \frac{1}{5}\right)}$$
$$\Rightarrow\frac{\frac{1}{3} + \left[4\frac{3}{4} - \left(\dfrac {19}{6} - \dfrac{7}{3}\right)\right]}{\left(\dfrac{1}{25} \div \dfrac{1}{5} \div \dfrac{1}{5}\right)}$$
$$\Rightarrow\frac{\frac{1}{3} + \dfrac{19}{4} - \dfrac{5}{6}}{\left(\dfrac{1}{25} \times \dfrac{5}{1} \times \dfrac{5}{1}\right)}$$
$$\Rightarrow\frac{1}{3} + \dfrac{19}{4} - \dfrac{5}{6}$$
$$\Rightarrow\dfrac{4+57-10}{12}$$
$$\Rightarrow\dfrac{61-10}{12}$$
$$\Rightarrow\dfrac{51}{12}$$
$$\Rightarrow\dfrac{17}{4}$$
$$\Rightarrow 4\dfrac{1}{4}$$
$$\Rightarrow 4.25$$
Here 4.2<4.25<4.4
therefore Option (B) 4.2 and 4.4 Ans
The value of $$\sqrt{11 + 2\sqrt{18}}$$ is closest to:
Given that $$\sqrt{11 + 2\sqrt{18}}$$
$$\Rightarrow \sqrt{11 + 2 \times 3\sqrt{2}}$$
$$\Rightarrow \sqrt{11 + 6\sqrt{2}}$$
$$\Rightarrow \sqrt{11 + 6\times 1.44}$$
$$\Rightarrow \sqrt{11 + 8.64}$$
$$\Rightarrow \sqrt{19.64}$$
$$\Rightarrow 4.4142$$ = 4.4 Ans
The value of $$\frac{\sqrt{0.6912} + \sqrt{0.5292}}{\sqrt{0.6912} - \sqrt{0.5292}}$$ is:
Expression : $$\frac{\sqrt{0.6912} + \sqrt{0.5292}}{\sqrt{0.6912} - \sqrt{0.5292}}$$
Using rationalization, = $$\frac{\sqrt{0.6912} + \sqrt{0.5292}}{\sqrt{0.6912} - \sqrt{0.5292}}$$ $$\times\frac{\sqrt{0.6912} + \sqrt{0.5292}}{\sqrt{0.6912} + \sqrt{0.5292}}$$
= $$\frac{(\sqrt{0.6912}+\sqrt{0.5292})^2}{(\sqrt{0.6912})^2-(\sqrt{0.5292})^2}$$
= $$\frac{0.6912+0.5292+2\sqrt{0.6912\times0.5292}}{0.6912-0.5292}$$
= $$\frac{1.2204+1.2096}{0.162}=15$$
=> Ans - (C)
The value of $$\frac{56 + \frac{2}{3} of 27 - 8}{15 - \frac{3}{5} of (29 - 14)}$$ is:
according to bodmass
$$\dfrac{56+\dfrac{2}{3}of27-8}{15-\dfrac{3}{5}of(29-14)}$$
$$\dfrac{56+\dfrac{2}{3}of27-8}{15-\dfrac{3}{5}of15}$$
$$\dfrac{56+18-8}{15-9}$$
$$\dfrac{74-8}{15-9}$$
$$\dfrac{66}{6}$$
$$11$$
The value of $$\sqrt{9-2\sqrt{11-6\sqrt{2}}}$$ is closest to:
$$\sqrt{9-2\sqrt{11-6\sqrt{2}}}$$
As per the given data,
$$\Rightarrow 6\sqrt{2}=6\times 1.414=8.484$$
Now, $$\sqrt{9-2\sqrt{11-8.484}}$$
$$\Rightarrow \sqrt{9-2\sqrt{2.526}}$$
$$\Rightarrow \sqrt{9-2\times 1.589}=2.4$$
The Value of $$\frac{0.325\times0.325+0.175\times0.175-25\times0.00455}{5\times0.0065\times3.25-7\times0.175\times0.025}$$ lies between
Given that $$\frac{0.325\times0.325+0.175\times0.175-25\times0.00455}{5\times0.0065\times3.25-7\times0.175\times0.025}$$
$$\Rightarrow \frac{(0.325)^2+(0.175)^2- 0.11375}{0.10563-0.03063}$$
$$\Rightarrow \frac{(0.015)^2}{0.075}$$
$$\Rightarrow \frac{0.0225}{0.075}$$
$$\Rightarrow 0.3 $$
then its lies between 0.25 and 0.35
therefore Option (A)0.25 and 0.35 Ans
What is the simplified value of
$$\left(1 - \frac{1}{4 - \frac{2}{1 + \frac{1}{\frac{1}{3} + 2}}}\right) \times \frac{15}{16} \div \frac{2}{3} of 2\frac{1}{4} - \frac{3 + 4}{3^3 + 4^3}$$
Expression : $$\left(1 - \frac{1}{4 - \frac{2}{1 + \frac{1}{\frac{1}{3} + 2}}}\right) \times \frac{15}{16} \div \frac{2}{3} of 2\frac{1}{4} - \frac{3 + 4}{3^3 + 4^3}$$
= $$\left(1 - \frac{1}{4 - \frac{2}{1 + \frac{3}{7}}}\right) \times \frac{15}{16} \div \frac{2}{3} of \frac{9}{4} - \frac{3 + 4}{3^3 + 4^3}$$
= $$\left(1 - \frac{1}{4 - \frac{14}{10}}\right) \times \frac{15}{16} \div \frac{3}{2} - \frac{3 + 4}{3^3 + 4^3}$$
= $$\left(1 - \frac{10}{26}\right) \times \frac{15}{16} \times \frac{2}{3} - \frac{7}{91}$$
= $$\frac{8}{13}\times\frac{5}{8}-\frac{1}{13}$$
= $$\frac{5}{13}-\frac{1}{13}=\frac{4}{13}$$
=> Ans - (D)
The value of $$5\div[5 + 8 - \left\{ 4 + (4 of 2 \div 4) - (2 \div 4 of 2)\right\}]$$ is
$$5\div[5 + 8 - \left\{ 4 + (4 of 2 \div 4) - (2 \div 4 of 2)\right\}]$$
$$\Rightarrow 5\div[13 - \left\{ 4 + (4 \times \dfrac {2}{4}) - (2 \div 4 \times 2)\right\}]$$
$$ \Rightarrow 5\div[13 - \left\{ 4 + (2) - (2 \div 8)\right\}]$$
$$ \Rightarrow 5\div[13 - \left\{ 6 - (\dfrac {1}{4})\right\}]$$
$$ \Rightarrow 5\div[13 -\dfrac {23}{4}]$$
$$ \Rightarrow 5\div[\dfrac {52-23}{4}] $$
$$ \Rightarrow 5\div[\dfrac {29}{4}] $$
$$ \Rightarrow 5\times \dfrac {4}{29}$$
$$ \Rightarrow \dfrac {20}{29}$$ Ans
The value of $$8 \div [(9 - 5) \div \left\{(4 \div 2 of 4) - (8 \div 8 of 16) + (4 \times 2 \div 8)\right\}]$$ is:
Given that $$8 \div [(9 - 5) \div \left\{(4 \div 2 of 4) - (8 \div 8 of 16) + (4 \times 2 \div 8)\right\}]$$
$$\Rightarrow 8 \div [(4) \div \left\{(4 \div 8) - (8 \div 128) + (8 \div 8)\right\}]$$
$$\Rightarrow 8 \div [4\div { \frac{1}{2} - \frac{1}{16}+1}] $$
$$\Rightarrow 8 \div [ 4 \div { \frac {8-1+16}{16}}] $$
$$\Rightarrow 8 \div [ 4 \div {\frac{23}{16}}] $$
$$\Rightarrow 8 \div [ 4 \times \frac{16}{23}]$$
$$\Rightarrow \frac {8\times 23} {4\times 16} $$
$$\Rightarrow \frac{23}{8} $$ Ans
If $$\sqrt{0.00576 \times y} = 2.4$$, then y is equal to:
Given,
$$\sqrt{0.00576y=2.4}$$
on squiring both sides,
$$0.00576y=(2.4)^2$$
$$0.00576y=5.76$$
$$y=\dfrac{5.76}{0.00576}$$
$$y=1000$$
The value of $$(5\frac{1}{4}\div\frac{3}{7} of \frac{1}{2})\div(5\frac{1}{9}-7\frac{7}{8}\div9\frac{9}{20})\times \frac{11}{21}+(2 \div 2 of \frac{1}{2})$$ is :
Given that $$(5\frac{1}{4}\div\frac{3}{7} of \frac{1}{2})\div(5\frac{1}{9}-7\frac{7}{8}\div9\frac{9}{20})\times \frac{11}{21}+(2 \div 2 of \frac{1}{2})$$
According to Bod mass Rule
$$\Rightarrow (\frac{21}{4}\div\frac{3}{7} \times \frac{1}{2})\div(\frac{46}{9}-\frac{63}{8}\div \frac{189}{20})\times \frac{11}{21}+(2 \div 2 \times \frac{1}{2})$$
$$\Rightarrow (\frac{21}{4} \times \frac{14}{3})\div(\frac{46}{9}-\frac{63}{8}\times \frac{20}{189})\times \frac{11}{21}+(2 \div 1)$$
$$\Rightarrow (\frac{21}{4} \times \frac{14}{3})\div(\frac{46}{9}-\frac{5}{6})\times \frac{11}{21}+2$$
$$\Rightarrow (\frac{49}{2})\div(\frac{92-15}{18})\times \frac{11}{21}+2$$
$$\Rightarrow (\frac{49}{2})\div(\frac{92-15}{18})\times \frac{11}{21}+2$$
$$\Rightarrow 3+2 $$
$$\Rightarrow 5 $$ Ans
The value of $$\frac{5-[2+3(2-2 \times 2 + 5) - 5] \div 5}{4 \times 4 \div 4 of (4 + 4 \div 4 of 4)}$$ is
What is $$(0.08 \% of 0.008 \% of 8)^{\frac{1}{9}}$$?
Expression : $$(0.08 \% of 0.008 \% of 8)^{\frac{1}{9}}$$
= $$(\frac{0.08}{100}\times\frac{0.008}{100}\times8)^{\frac{1}{9}}$$
= $$(\frac{8}{10000}\times\frac{8}{100000}\times8)^{\frac{1}{9}}$$
= $$(\frac{2^9}{10^9})^{\frac{1}{9}}$$
= $$\frac{2}{10}=0.2$$
=> Ans - (B)
The value of $$\frac{\left(3\frac{1}{3} - 2\frac{1}{2}\right) \div \frac{1}{4} of 1\frac{1}{4}}{\frac{3}{10} + \frac{1}{6} \times \frac{1}{3}}$$ of $$\frac{4}{15} \div \frac{\frac{1}{3} \div \frac{1}{3} of \frac{1}{9}}{\frac{1}{9} \times \frac{1}{3} \div \frac{1}{6}}$$ is:
$$\frac{\left(3\frac{1}{3} - 2\frac{1}{2}\right) \div \frac{1}{4} of 1\frac{1}{4}}{\frac{3}{10} + \frac{1}{6} \times \frac{1}{3}}$$ of $$\frac{4}{15} \div \frac{\frac{1}{3} \div \frac{1}{3} of \frac{1}{9}}{\frac{1}{9} \times \frac{1}{3} \div \frac{1}{6}}$$
$$\Rightarrow \frac{\left(\frac{10}{3} - \frac{5}{3}\right) \div \frac{1}{4} of \frac{5}{4}}{\frac{3}{10} + \frac{1}{6} \times \frac{1}{3}}$$ of $$\frac{4}{15} \div \frac{\frac{1}{3} \div \frac{1}{3} of \frac{1}{9}}{\frac{1}{9} \times \frac{1}{3} \div \frac{1}{6}}$$
$$\Rightarrow \frac{\frac{20-15}{6} \div \frac{5}{16}}{\frac{3}{10} + \frac{1}{18}}$$ of $$\frac{4}{15} \div \frac{\frac{1}{3} \div \frac{1}{27}}{\frac{1}{9} \times 2}$$
$$\Rightarrow \frac{\frac{5}{6} \div \frac{5}{16}}{\frac{27+5}{90}}$$ of $$\frac{4}{15} \div\frac{ 9}{\frac{2}{9} }$$
$$\Rightarrow \frac{\frac{5}{6} \times \frac{16}{5}}{\frac{32}{90}}$$ of $$\frac{4}{15} \div\frac{ 9\times 9}{2} $$
$$\Rightarrow \frac{8}{3} \times \frac{90}{32} of \frac{4}{15} \div \frac{81}{2}$$
$$\Rightarrow \frac{15}{2} \times \frac{4}{15} \div \frac{81}{2}$$
$$\Rightarrow 2 \div \frac{81}{2} $$
$$ \Rightarrow 2 \times \frac{2}{81} $$
$$\Rightarrow \frac{4}{81} $$
therefore Option (C) $$\frac{4}{81} $$ Ans
$$(320 + 342+ 530 + 915) \div (20 + 22 - x + 18) = 43$$, then the value of x is:
Expression : $$(320 + 342+ 530 + 915) \div (20 + 22 - x + 18) = 43$$
=> $$60-x=\frac{2107}{43}=49$$
=> $$x=60-49=11$$
=> Ans - (A)
Which two numbers should be interchanged to make the given equation correct?
$$28+ 49-35 \div 7 \times 4=68$$
$$28+ 49-35 \div 7 \times 4 = 68$$
From option A,
On interchanging,
$$35 + 49-28 \div 7 \times 4 = 68$$
$$35 + 49 - 16 = 68$$
68 = 68
$$\therefore$$ The correct answer is option A.
Which two signs and two numbers should be interchanged to make the given equation correct?
$$11 \times 7 \div 35 - 64 + 56 = 47$$
$$11 \times 7 \div 35 - 64 + 56 = 47$$
From the option B,
on changing the sign,
$$35 \div 7 \times 11 - 64 + 56 = 47$$
55 - 64 + 56 = 47
47 = 47
$$\therefore$$The correct answer is option B.
In an exam of 80 questions, a correct answer is given +1 mark, a wrong answer is given —1 mark, and if a question is not attempted there are zero marks. If a student attempted only 80% of the questions and got 32 marks, then how many questions did he answer correctly?
Attempted questions = 80 $$\times \frac{80}{100}$$ = 64
Marks got = 32
Marks deduct = 64 - 32 = 32
So, Wrong answer = 32/2 = 16
So, Correct answer = 32 + 16 = 48
$$\therefore$$ The correct answer is option B.
Select the correct equation after interchanging operations ‘+’ and ‘-’ and numbers ‘4’ and ‘8’.
We check all option sequentially
Check option (A) $$ 2+8-4= 9 $$
Interchange opration + and - and numbers 4 and 8
$$ 2-4+8 = 9$$
From LHS $$ 2-4+8 $$
$$\Rightarrow 10- 4 $$
$$\Rightarrow 6 $$ its not staisfied.
check option (B) $$8+4-2=10$$
Interchange opration + and - and numbers 4 and 8
LHS $$ 4-8+2 $$
$$\Rightarrow 6-8$$
$$\Rightarrow -2 $$ its not staisfied .
check option (C) $$4-8+11 =1 $$
Interchange opration + and - and numbers 4 and 8
From LHS $$ 8+4-11 $$
$$\Rightarrow 12-11 $$
$$\Rightarrow 1 $$ RHS its staisfied .
therefore (C) is staisfied Ans
Which two signs need to be interchanged to make the following equation correct?
$$45 - 9 \div 3 + 5 \times 6 = 32$$
Given expression $$45 - 9 \div 3 + 5 \times 6 = 32$$
we check option (A) $$\times and \div$$
we put Sign in the expression
$$45 - 9 \times 3 + 5 \div 6 = 32$$
From LHS $$45 - 9 \times 3 + 5 \div 6$$
$$\Rightarrow 45 - 27 + 0.833 $$
$$\Rightarrow 18 +0.833 $$
$$\Rightarrow 18.833 $$ RHS it is not staisfied .
check another option $$\div and + $$
we put Sign in the expression
$$45 - 9 +3 \div5 \times 6 = 32$$
From LHS $$45 - 9 +3 \div5 \times 6$$
$$\Rightarrow 45 - 9+ 0.6 \times 6 $$
$$\Rightarrow 45 -9 + 3.6 $$
$$\Rightarrow 36 +3.6 $$
$$\Rightarrow 39.6 $$ RHS it is not staisfied .
We check another option $$\times and + $$
we put sign in the given expression
$$45 - 9 \div 3 \times 5 + 6 = 32$$ Similar we check it is also not stiasfied .
we check another option $$\div and - $$
we put sign in the given expression
$$45 \div 9 - 3 + 5 \times 6 = 32$$
From LHS $$45 \div 9 - 3 + 5 \times 6$$
$$\Rightarrow 5 - 3 +30 $$
$$\Rightarrow 35-3 $$
$$\Rightarrow 32 $$ RHS it is staified.
therefore (D) $$ \div and - $$ Ans
If 7x = 8k and 5y = 6k then the value of ratio x is to y is
7x = 8k
x = 8k/7
and 5y = 6k
y = 6k/5
x : y = $$\frac{8k}{7} : \frac{6k}{5} = 20 : 21
In a class of 100 students, every student has passed in one or more of the three subjects, i.e. History, Economics and English. Among all the students, 24 students have passed in English only, 14 students have passed in History only, 11 students have passed in both English and Economics only, and 12 students have passed in both English and History only. A total of 50 students have passed in History. If only 5 students have passed in all three subjects, then how many students have passed in Economics only?
Students have passed in English only = 24
Students have passed in History only = 14
Students have passed in both English and Economics only = 11
Students have passed in both English and History only = 12
Students have passed in History = 50
Students have passed in all three subjects = 5
Students have passed in Economics only = 100 - students have passed in History - students have passed in English only - students have passed in both English and Economics only = 100 -50 - 24 - 11 = 15
$$\therefore$$ The correct answer is option A.
Find the smallest number which when divided by 25, 40, or 56 has in each case 13 as remainder.
Smallest number = (LCM of 25, 40 and 56) + remainder
Factor of 25 = $$5^2$$
Factor of 40 = $$2^3.5$$
Factor of 56 = $$2^3.7$$
LCM of 25, 40 and 56 = $$2^3.5^2.7$$ = 1400
Smallest number = 1400 + 13 = 1413
If $$+$$ means $$-$$, $$-$$ means $$\times$$, $$\times$$ means $$\div$$, and $$\div$$ means $$+$$, then what will be the value of following expression?
$$13 - 3 + 15 \times 3 \div 5 = ?$$
From the question,
$$+$$ means $$-$$, $$-$$ means $$\times$$, $$\times$$ means $$\div$$ , $$\div$$ means $$+$$ then
$$13-3 + 15\times 3\div 5$$
Now substituting the symbol as per the given question,
$$\Rightarrow 13\times 3 - 15 \div 3 + 5 $$
$$\Rightarrow 39 - 5 + 5 $$
$$\Rightarrow 44 -5 $$
$$\Rightarrow 39 $$ Ans
Select the set of symbols which can be fitted correctly in the equation,
8_____4_____2_____6_____3 = 32
From option A),
LHS
8 $$\times 4 - 2 + 6 \div 3$$
32 - 2 + 2
= 32
RHS
$$\therefore$$ Option A is the correct answer
A private taxi company charges a fixed charge along with a per kilometre charge based on the distance covered. For a journey of 24 km, the charges paid are ₹368 and for a journey of 32 km,the charges paid are ₹464. How much will a person have to pay for travelling a distance of 15 km?
Charge for 24 km = 368
Charge for 32 km = 464
Difference in km = 32 - 24 = 8 km
Charge for 8 km = 464 - 368 = 96
Charge for 1 km = 96/8 = Rs. 12
Fixed charge = 368 - 12 $$\times$$ 24 = 368 - 288 = 80
Charge for 15 km = 80 + 12 $$\times$$ 15 = 80 + 180 = Rs.260
$$\therefore$$ The correct answer is option C.
Which two signs should be interchanged to make the given equation correct ?
$$14\times3\div27+54-9=21$$
$$14\times3\div27+54-9=21$$
From the option C,
On interchanging the $$\div$$ and -,
$$14 \times3 - 27 + 54 \div 9=21$$
42 - 27 + 6 = 21
21 = 21
$$\therefore$$ The correct answer is option C.
Among 160 players in a tournament, 57 did not participate in any of the three games,i.e. Cricket, Hockey and Badminton. A total of 37 players participated in only one game,10 players participated in both Cricket and Hockey but not in Badminton, 9 players participated in both Hockey and Badminton but not in Cricket, and 13 players participated in both Cricket and Badminton but not in Hockey. How many students participated in all the three games
Total students participate = 160 - 57 = 103
Participant in 1 game = 37
Players participated in both Cricket and Hockey but not in Badminton = 10
Players participated in both Hockey and Badminton but not in Cricket = 9
Players participated in both Cricket and Badminton but not in Hockey = 13
Students participated in all the three games = 103 - 37 - 100 - 9 - 13 = 34
$$\therefore$$ The correct answer is option D.
Which two signs should be interchanged to make the given equation correct?
$$12+81-27\times9\div3$$=36
$$12+81-27\times9\div3$$ = 36
From the option A,
On changing the sign,
$$12 + 81 \div 27 \times 9 - 3$$ = 36
12 + 27 - 3 = 36
36 =36
$$\therefore$$ The correct answer is option A.
Select the correct combination of mathematical signs to replace * signs and to balance the following equation.
(18 * 9 * 14) * 37 * 4
Given Expression (18 * 9 * 14) * 37 * 4
we check option (A) $$\div-\times= $$
we put above Sign in the given expression
$$ (18 \div 9- 14 )\times 37 = 4 $$
From LHS $$ (18 \div 9- 14 )\times 37$$
$$\Rightarrow (2-14)\times 37 $$
$$\Rightarrow -12 \times 37 $$ it is not satisfied LHS and RHS is equal .
then Check option (B) $$\times-\div= $$
we put the sign in the given expression
$$ (18\times 9 - 14) \div 37 = 4 $$
From LHS $$ (18\times 9 - 14) \div 37$$
$$\Rightarrow (162-14)\div 37 $$
$$\Rightarrow 148 \div 37 $$
$$\Rightarrow 4 $$ RHS it is satisfied to LHS = RHS
then option (B)$$\times-\div= $$ Ans
A recent survey of married couples in Indian metro cities showed that 20% of the couples have only one child, 45% of the remaining couples have two children, and the rest of the couples have three or more children. What is the percentage of couples with three or more children?
Let the total couple be 100.
Couple with one child = 20
Remaining couples = 100 - 20 = 80
Couple with two child = 45% of the remaining = 80 $$\times{45}{100}$$ = 36
Couples with three or more children = 80 - 36 = 44%
If $$+$$ means $$−$$, $$−$$ means $$\times$$, $$\times$$ means $$\div$$, and $$\div$$ means $$+$$, then what will be the value of following expression?
$$50 + 10 \div 25 \times 5 - 3 = ?$$
Given expression $$50 + 10 \div 25 \times 5 - 3 = ?$$
$$\Rightarrow 50 - 10 + 25 \div 5 \times 3 = ? $$ ( change to the sign for given condition )
$$\Rightarrow 50 - 10 + 5 \times 3 = ? $$
$$\Rightarrow 50 - 10 + 15= ? $$
$$\Rightarrow 65 - 10 = ? $$
$$\Rightarrow ? = 55 $$ Ans
The two given expressions on both theside of the ‘=’ sign will have the same value if two numbers from either side or both side are interchanged. Select the correct numbers to be interchanged from the given options.
$$3 + 5 \times 4 - 24 \div 3 = 7 \times 4 - 3 + 36 \div 6$$
$$3 + 5 \times 4 - 24 \div 3 = 7 \times 4 - 3 + 36 \div 6$$
From option B,
On interchanging 5 and 7,
$$3 + 7 \times 4 - 24 \div 3 = 5 \times 4 - 3 + 36 \div 6$$
$$3 + 28 - 8 = 20- 3 + 6$$
23 = 23
$$\therefore$$ The correct answer is option B.
Which two signs need to be interchanged to make the following equation correct?
$$32 - 8 \div 4 + 5 \times 6 = 30$$
From the given expression $$32 - 8 \div 4 + 5 \times 6 = 30$$
we check option (A) , (B),(D) similar to given below
we check option (C) $$ \div and - $$
we interchange sign in the given expression
$$32 \div 8 - 4 + 5 \times 6 = 30$$
from LHS $$ 32 \div 8 - 4 + 5 \times 6$$
$$\Rightarrow 4 -4 + 30$$
$$\Rightarrow 30 $$ RHS it is staisfied .
therefore option (C) Ans
Which two signs should be interchanged to make the given equation correct?
$$36 \div 2 \times 12 + 3 - 6 = 24$$
$$36 \div 2 \times 12 + 3 - 6 = 24$$
From the option B,
$$36 \div 2 - 12 + 3 \times 6 = 24$$
$$18 - 12 + 18 = 24$$
24 = 24
$$\therefore$$ The correct answer is option B.
In the following equations, if ‘+’ is interchanged with ‘—’ and ‘6’ is interchanged with ‘7’, then which equation would be correct?
From the option A,
67 - 76 + 43 = 100
On the interchanging,
76 + 67 - 43 = 100
143 - 43 = 100
100 = 100
$$\therefore$$ The correct answer is option A.
Which two digits should be interchanged to make the given equation correct?
$$32 \div 6 + 26 - 13 \times 6 = 54$$
$$32 \div 6 + 26 - 13 \times 6 = 54$$
From the option C,
On interchanging,
$$36 \div 2 + 62 - 13 \times 2 = 54$$
$$18 + 62 - 26 = 54$$
54 = 54
$$\therefore$$ The correct answer is option C.
The average. age of 10 children in a class is 12 years. If two children aged 14 and 16 years join the class,itwill raise the average age by how much?
Sum of ages of children at start = 12*10 = 120 years
Sum of ages after new joinees join = 120 + 14 + 16 = 150 years
Average age now = 150/12 = 12.5 years
Hence, average age has increased by 6 months.
If ‘$$\times$$’ stands for ‘$$+$$’, ‘$$+$$’ stands for ‘$$\div$$’, ‘$$-$$’ stands for ‘$$\times$$’ and ‘$$\div$$’ stands for ‘$$-$$’, then find the value of the given equation.
$$76 \div 5 - 6 + 3 \times 4 = ?$$
Given expression $$76 \div 5 - 6 + 3 \times 4 = ?$$
$$76 - 5 \times 6\div 3 + 4 = ?$$ (we change sign according to given in question )
$$\Rightarrow 76 - 5 \times 2 + 4 = ?$$
$$\Rightarrow 76 - 10 + 4 = ?$$
$$\Rightarrow 80- 10 = ?$$
$$\Rightarrow 70 = ?$$
$$\Rightarrow ? = 70 $$Ans
Select the correct equation after interchanging operators ‘+’ and ‘÷’, and numbers ‘2’ and ‘8’.
we check option (A)
$$2+8\div4 = 2 $$
we change operators $$ + and + $$ and numbers 2 and 8
then $$ 8 \div 2 +4 = 8 $$
LHS $$ 8 \div 2 + 4 $$
$$\Rightarrow 4 + 4 $$
$$\Rightarrow 8 $$ RHS Ans
therefore it is staisfied
Ans (A)
A car covers the first half. of the distance between two places at 40 km/hr and the second half of the distance at 60 km/hr. So what is the average speed of the car?
Let the total distance be 120 km.
Hence, first half covered in 60/40 = 1.5 hours and second half covered in 60/60 = 1 hour.
Total time taken = 2.5 hours to cover 120 km
Hence, average speed = 120/2.5 = 48 kmph
Which two signs need to be changed to make the following equation correct?
$$64 - 8 \div 3 + 7 \times 5 = 40$$
Given that
$$64 - 8 \div 3 + 7 \times 5 = 40$$
we check option (A) $$\times and + $$
put the sign in the given expression
$$64 - 8 \div 3 \times7 +5 = 40$$
LHS $$ 64 - \dfrac {8}{3} \times 7 + 5 $$
$$\Rightarrow 64 - 2.66 \times 7 + 5$$
$$\Rightarrow 64 - 18.62 + 5$$
$$\Rightarrow 51.62 $$ its not staisfied RHS
check option (B) $$\times and \div $$
we put Sign in the given option
$$64 - 8 \times 3 + 7 \div 5 = 40$$
LHS $$64 - 8 \times 3 + 7 \div 5$$
$$\Rightarrow 64 - 24 + 1.4 $$
$$\Rightarrow 65.4-24$$
$$\Rightarrow 41.4$$ its not to RHS .
Again check option (C)$$\div and - $$
we put the Sign in the given expresseion
$$64 \div 8 - 3 + 7 \times 5 = 40$$
LHS $$64 \div 8 - 3 + 7 \times 5$$
$$\Rightarrow 8 - 3 +35 $$
$$\Rightarrow 43 -3 $$
$$\Rightarrow 40 $$ R HS it is staisfied
then option (C) $$\div and - $$ Ans
Two cars started from a particular spot. The car A ran Straight at the speed of 30 kmph for 2 hours north and then took a right turn. It run 40 km and again turned right. It stopped after east at the speed of 20 kmph for 2 hours and tuned left. it ran for 100 km and then stopped. How far were there two cars from each other when both of them stopped at last ?
If 7x - 5y = 20 and 12x + 5y = 75, what is the value of xy?
7x - 5y = 20 ---(1)
12x + 5y = 75 ---(2)
Eq(1) + (2),
19x =95
x = 5
From eq(1),
7$$\times$$5 - 5y = 20
5y = 15
y = 3
xy = 5 $$\times$$ 3 = 15
If P stands for $$\div$$, Q standsfor $$\times$$, R stands for $$+$$, then
18 Q 12 P 4 R 5 = ?
According to the problem,
18 Q 12 P 4 R 5 $$=18\times12\div4+5$$
$$=18\times3+5$$
$$=54+5$$
$$=59$$
Hence, the correct answer is Option A
The two given expressions on either side of the ‘=’ sign will have the same value if two terms on either side or on the same side are interchanged. Find from the given option the correct terms to be interchanged.
$$5 \times 2 + 8 \div 2 - 1 = 9 - 6 \div 3 + 6 \times 3$$
As per the given question,
$$5 \times 2 + 8 \div 2 - 1 = 9 - 6 \div 3 + 6 \times 3 $$
In this type of question, we will solve it by the given option, by hit and trial method.
If we check option A (8, 9)
L H S $$5 \times 2 + 8 \div 2 - 1 $$
we replace 8 = 9
then $$ 5 \times 2 + 9 \div 2 -1 $$ = $$ 5 \times 2 + 4.5 -1 $$ = 10 - 3.5
= 6.5
R H S $$ 9 - 6 \div 3 + 6 \times 3 $$
we replace 9 = 8
then $$ 8 - 6 \div 3 + 6 \times 3 $$ = 8 - 2 + 6 x 3 = 24
L H S not equal to RHS
Then we check option B ( 5, 9)
L H S $$5 \times 2 + 8\div 2 - 1 $$
we replace 5 = 9
then $$9 \times 2 + 8 \div 2 -1$$ = 18 + 4 -1 = 21
R H S $$9 - 6 \div 3 + 6 \times 3 $$
we replace 9 = 5
then $$ 5 - 6 \div 3 + 6 \times 3 $$ = 5 - 2 +18 = 21
then L H S = R H S is right
then B ( 5, 9 ) is verified.
In the following equation, two signs and two numbers need to be interchanged to make it correct. Select the appropriate signs and numbers from the given alternatives.
$$6 \times 8 + 2 = 20$$
Given expression $$6 \times 8 + 2 = 20$$
we check (A), (B), (C), it is not staisfied that LHS = RHS
then we check option (D) $$ + and \times $$, 6 and 8
we Interchange two Signs and two numbers in the given expression
$$ 8 + 6 \times 2 = 20$$
From LHS $$ 8 + 6 \times 2 $$
$$ \Rightarrow 8 + 12 $$
$$ \Rightarrow 20 $$ RHS
that means its is staisfied .
therefore (D) Ans
If $$+$$ means $$-$$, $$-$$ means $$\times$$, $$\times$$ means $$\div$$, and $$\div$$ means $$+$$, then what will be the value of following expression?
$$15 - 2 \div 90 \times 9 + 10$$
Given expression $$15 - 2 \div 90 \times 9 + 10$$
$$15 \times 2 + 90 \div 9 -10$$ ( we change Sign according to the given question)
$$\Rightarrow 15 \times 2 + 10 -10$$
$$\Rightarrow 30 + 10 -10$$
$$\Rightarrow 40 -10$$
$$\Rightarrow 30 $$ Ans
If $$+$$ means $$−$$, $$−$$ means $$\times$$, $$\times$$ means $$\div$$, and $$\div$$ means $$+$$, then what will be the value of following expression?
$$12 - 3 + 15 \times 5 \div 6 = ?$$
Given expression $$12 - 3 + 15 \times 5 \div 6 = ?$$
$$12 \times 3 -15 \div 5 + 6 = ? $$ ( We change the Sign according to given in question)
$$\Rightarrow 12 \times 3 -3 + 6 = ? $$
$$\Rightarrow 36 -3 + 6 = ? $$
$$\Rightarrow 42 -3 = ? $$
$$\Rightarrow 39 = ? $$
$$\Rightarrow ? = 39 $$Ans
A party consisted of a man, his wife, his three sons and their wives and three children in each son’s family. How many werethere in the party ?
First generation: Man and wife - 2 people
Second generation: 3 couples of (son and wife) - 6 people
Third generation: Each of 3 couples of gen 2 have 3 children - 9 people
Hence, total number of people = 17
₹ 6,500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got ₹ 30 less. Find the original numberof persons.
Let the number of persons be N.
$$\frac{6500}{N}-30=\frac{6500}{N+15}$$
One can either solve the equation by theoretical approach or one can substitute N with given options.
N = 50 gives the answer.
Murthy drove from town A to town B. In the fist hour, he travelled $$\frac{1}{4}$$ of the journey. In the next one hour, he travelled $$\frac{1}{2}$$ of the journey. In the last 30 minutes, he travelled 80 km. Find the distance of the whole journey.
Let the total journey be x km.
Remaining distance of the journey = 80 km
x - $$\frac{x}{4} - \frac{x}{2}$$ = 80 km
$$\frac{x}{4} = 80$$
x = 320 km
$$\therefore$$ Total distance is 320 km of whole journey.
60 students participated in one or more of the three competitions,i.e. Quiz, Extempore and Debate. A total of 22 students participated either in Quiz only or in Extempore only. 4 students participated in all three competitions. A total of14 students participated in any of the two competitions only. How many students participated in Debate only?
Total students = 60
Students participated either in Quiz only or in Extempore only = 22
Students participated in all three competitions = 4
Students participated in any of the two competitions only = 14
Students participated in Debate only = 60 - 22 - 4 - 14 = 20
$$\therefore$$ The correct answer is option B.
The ratio of the present ages of Asha and Lata is 5 : 6. If the difference between their ages is 6 years, then what will be Lata's age will be after 5 years?
The ratio of the present ages of Asha and Lata is 5 : 6.
Let the age of Asha and Lata be 5x and 6x respectively.
The difference between their ages = 6 years
6x - 5x = 6
x = 6
Age of Lata after 5 years = 6x + 5 = 6 $$\times$$ 6 + 5 = 41 years
$$\therefore$$ The correct answer is option B.
Which two signs need to be interchanged to make the following equation correct?
$$48 - 8 \div 4 + 5 \times 6 = 32$$
Given expression $$48 - 8 \div 4 + 5 \times 6 = 32$$
check option (A) $$\times and + $$
we put the sign from the given expression
$$48 - 8 \div 4 \times 5 +6 = 32$$
LHS $$48 - 8 \div 4 \times 5 +6$$
$$\Rightarrow 48-2\times 5 +6 $$
$$\Rightarrow 48 - 10 +6 $$
$$\Rightarrow 44 $$ its not staisfied RHS
then we check option (B) $$\div and - $$
we put sign from the given option
$$48 \div 8 -4 + 5 \times 6 = 32 $$
LHS $$48 \div 8-4 +5 \times 6$$
$$\Rightarrow 6-4 + 30 $$
$$\Rightarrow 32 $$ RHS it is verified RHS
therefore option (B)$$ \div and - $$ Ans
Select the correct combination of mathematical signs to replace * signs and to balance the following equation.
86 * (5 * 8 * 4) * 9 * 85
Given that expression 86 * (5 * 8 * 4) * 9 * 85
We check Option A $$ -, \times. \div, +, = $$
we put option A Sign in the above expression
$$ 86 - (5 \times 8 \div 4) + 9 = 85 $$
From the LHS $$ 86 - (5 \times 8 \div 4) + 9 $$
$$\Rightarrow 86 - (5 \times 2) + 9 $$
$$\Rightarrow 86 - (10 ) +9 $$
$$\Rightarrow 95 - 10 $$
$$\Rightarrow 85 $$ RHS
Hence it is satisfied there fore A is Right Ans
If ‘$$\div$$’ standsfor ‘$$\times$$’, '-' for ‘+’, '+' for ‘$$\div$$’, then which of the following equationsis correct ?
Substituting the symbols with the appropriate mathematical operation:
Option A: LHS = 21+(3/9)*12 = 21+4 = 25 and RHS = 51 Hence, incorrect
Option B: LHS = (21/3)*9+12 = 63+12 = 75 and RHS = 75. Hence, correct.
Select the correct equation after interchanging the operators ‘$$-$$’ and ‘$$\times$$’ and the numbers ‘4’ and ‘3’.
We check to interchange the operators ‘$$-$$’ and ‘$$\times$$’ and the numbers ‘4’ and ‘3’
we check (A)$$9-4\times 3=21 $$
interchange ‘$$-$$’ and ‘$$\times$$’ and the numbers ‘4’ and ‘3’
$$9\times 3- 4 = 21 $$
From LHS $$9\times 3- 4$$
$$\Rightarrow 27 - 4 $$
$$\Rightarrow 23 $$ RHS it is not satisfied.
we check option (B) $$4-3\times 9= 3 $$
Interchange ‘$$-$$’ and ‘$$\times$$’ and the numbers ‘4’ and ‘3’
$$ 3\times 4 - 9 = 3 $$
From LHS $$ 3\times 4 - 9 $$
$$\Rightarrow 12 -9 $$
$$\Rightarrow 3 $$ RHS it is satisfied .
therefore (B) Ans
If $$+$$ stands for division
$$-$$ stands for equai to
$$\times$$ stands for addition
$$\div$$ stands for greater than
$$=$$ standsfor less than
$$>$$ stands for multiplication
$$<$$ stands for subtraction
then of the given alternatives which one is correct?
Converting symbols in option A to actual operations, we get:
5+3-7>(8/4)-2 i.e. 1>0 which is true.
Similarly converting other options and solving them, we find that only A is correct. Hence, answer.
Postal PIN codes of 25 letters are given below. The first digit from the left indicates the zone and the last three digits the delivery Post Office. How many maximum letters are meant for the same delivery Post Office under Zone 2 ?
11 Pin Codes start with digit 2, hence, for Zone 2.
Of these, 6 end with 054 which means the same post office. Hence, the answer.
Select the combination of mathematical signs that when sequentially placed in the blanks of the given equation will balance the equation.
(157_13)_36_1_5
Given that (157_13)_36_1_5
we check Option (A)$$+ \div - = $$
the above sign put in the given equestion
$$(157+13)\div36-1=5 $$
From LHS $$(157+13)\div36-1 $$
$$\Rightarrow 170 \div 36 -1$$
$$ \Rightarrow 4.72-1 $$
$$\Rightarrow 3.72 $$ it is not satisfied RHS
We check Option (B) $$- \div + = $$
we put above Sign in the expression
$$ (157-13\div 36+1= 5$$
From LHS $$ (157-13\div 36+1$$
$$\Rightarrow 144 \div36 +1$$
$$\Rightarrow 4 +1 $$
$$\Rightarrow 5 $$ RHS it is satisfied .
therefore Option (B) $$-\div+=$$ Ans
Select the correct combination of mathematical signs to replace * signs and to balance the following equation.
$$\frac{1}{6} * \frac{1}{24} * 2 * 8 * 35 * 23$$
Given expression $$\frac{1}{6} * \frac{1}{24} * 2 * 8 * 35 * 23$$
we check given option But A, B, C is not satisfied to the given expression
then check option (D) given below same as check option A,B,C
$$\div,-, \times,+, = $$
we put the given sign in the given expression
$$\frac{1}{6} \div \frac{1}{24} - 2 \times 8 +35 =23$$
From the LHS $$\frac{1}{6} \div \frac{1}{24} - 2 \times 8 +35$$
$$\Rightarrow \frac{1}{6} \times \frac{24}{1} - 2 \times 8 +35$$
$$\Rightarrow 4 - 16 +35 $$
$$\Rightarrow -12 +35 $$
$$\Rightarrow 23 $$ RHS
therefore option (D) $$\div,-, \times,+, = $$ Ans
Select the option in which the numbers share the same relationship as that shared by the given pair of numbers.
72 - 14
Given that 72 - 14
then $$ 72 - 7\times 2 $$
$$ \Rightarrow 72-14$$
therefore $$45 - 4\times 5 $$
$$ 45 - 20 $$ Ans
Hemant buys a dozen eggs for ₹ 5.50 per egg. While carrying them, two eggs get wasted when they fall down and get damaged. He sells the balance eggs at 7.70 per egg. Find the net profit earned by him in the overall deal.
Cost price of the dozen eggs = 5.50 $$\times$$ 12 = 66
Number of eggs Hemant sells = 12 - 2 = 10
($$\because$$ 2 eggs get damaged)
Selling price of 10 eggs = 7.70 $$\times$$ 10 = 77
Profit = 77 - 66 = ₹ 11
$$\therefore$$ The correct answer is option A.
Select the option in which the numbers do NOT share the same relationship as that shared by the given pair of numbers.
(98, 107, 125)
Given that (98, 107, 125)
that follows the pattern 107-98= 9
and 125-107 = 18
same pattern follow given option (A)(319,328,346)
the pattern is follow 328-319= 9
and 346-328 =18
same as (B)(122,131,149)
here 131-122= 9 and 149-131= 18
and (C)(29,38,56)
the above pattern follow 38-29= 9 and 56-38 = 18
But (D)(73,82,99) is not follow that pattern
82-73= 9, and 99-82 = 17
therefore it is not follow that pattern
Ans Option (D) (73,82,99)Ans
Solve the following expression.
$$11+11\times11-11\div11$$
$$11+11\times11-11\div11$$
= 11 + 121 - 1 = 131
The value of $$-\frac{5}{2} + \frac{3}{2} \div 6 \times \frac{1}{2}$$ is equal to:
$$-\frac{5}{2} + \frac{3}{2} \div 6 \times \frac{1}{2}$$
$$-\frac{5}{2} + \frac{1}{4} \times \frac{1}{2}$$
$$-\frac{5}{2} + \frac{1}{8} $$
$$-\frac{19}{8} $$
When a positive integer is divided by d, the remainder is 15. When ten times of the same number is divided by d. the remainder is 6. The least possible value of d is:
When a positive integer is divided by d, the remainder is 15 and When ten times of the same number is divided by d. the remainder is 6.
So,
15 will be also ten times so,
Remainder = 150
By the option B)
When 150 is divided by 16 then remainder will be 6.
Hence, correct answer is option B) 16.
The value of $$3 - (9 - 3 \times 8 \div 2)$$ is
$$3 - (9 - 3 \times 8 \div 2)$$
Solve using by BODMAS,
= $$3 - (9 - 3 \times 4)$$
= $$3 - (9 - 12)$$
= $$3 + 3$$ = 6
The value of $$515\times485$$ is:
$$515\times485$$
= $$(500 + 15)\times(500 - 15)$$
= $$(500)^2 - (15)^2$$
($$\because (a - b)(a + b) = a^2 - b^2$$)
= 250000 = 225 = 249775
Solve the following
$$113 \times 87 = ?$$
$$113 \times 87 = ?$$
$$(100 + 13) \times (100 - 13) = ?$$
$$(a + b)(a - b) = a^2 - b^2$$
$$(100)^2 - (13)^2 = ?$$
? = 10000 - 169 = 9831
The value of $$-1 + \frac{1}{4} \div \frac{1}{2} \times 2 + 5$$ is:
$$-1 + \frac{1}{4} \div \frac{1}{2} \times 2 + 5$$
= $$-1 + \frac{1}{4} \times 2 \times 2 + 5$$
= $$-1 + 1 + 5$$ = 5
The value of $$\left(18 \div 2 of \frac{1}{4}\right) \times \left(\frac{2}{3} \div \frac{3}{4} \times \frac{5}{8}\right) \div \left(\frac{2}{3} \div \frac{3}{4} of \frac{3}{4}\right)$$ is:
$$\left(18 \div 2 of \frac{1}{4}\right) \times \left(\frac{2}{3} \div \frac{3}{4} \times \frac{5}{8}\right) \div \left(\frac{2}{3} \div \frac{3}{4} of \frac{3}{4}\right)$$
= $$\left(18 \div \frac{1}{2}\right) \times \left(\frac{2}{3} \div \frac{3}{4} \times \frac{5}{8}\right) \div \left(\frac{2}{3} \div \frac{9}{16} \right)$$
= $$36 \times \left(\frac{2}{3} \times \frac{4}{3} \times \frac{5}{8}\right) \div \left(\frac{2}{3} \times \frac{16}{9} \right)$$
= $$36 \times \frac{5}{9}\div \frac{32}{27} $$
= $$36 \times \frac{5}{9}\times \frac{27}{32} $$
= $$9 \times \frac{5}{9}\times \frac{27}{8} $$ =135/8
= $$16 \frac{7}{8}$$
The value of $$1\frac{1}{8} \div \left(4\frac{1}{4} \div \frac{3}{5} of 8\frac{1}{2}\right) - \frac{2}{5} \times 1\frac{1}{3} \div \frac{4}{5} of 1\frac{2}{3} + \frac{11}{20}$$ is:
$$1\frac{1}{8} \div \left(4\frac{1}{4} \div \frac{3}{5} of 8\frac{1}{2}\right) - \frac{2}{5} \times 1\frac{1}{3} \div \frac{4}{5} of 1\frac{2}{3} + \frac{11}{20}$$
= $$\frac{9}{8} \div \left(\frac{17}{4} \div \frac{3}{5} of \frac{17}{2}\right) - \frac{2}{5} \times \frac{4}{3} \div \frac{4}{5} of \frac{5}{3} + \frac{11}{20}$$
= $$\frac{9}{8} \div \left(\frac{17}{4} \div \frac{51}{10}\right) - \frac{2}{5} \times \frac{4}{3} \div \frac{4}{3} + \frac{11}{20}$$
= $$\frac{9}{8} \div \left(\frac{17}{4} \times \frac{10}{51}\right) - \frac{2}{5} \times \frac{4}{3} \times \frac{3}{4} + \frac{11}{20}$$
= $$\frac{9}{8} \div \frac{5}{6} - \frac{2}{5} + \frac{11}{20}$$
= $$\frac{9}{8} \times \frac{6}{5} - \frac{2}{5} + \frac{11}{20}$$
= $$\frac{27}{20} - \frac{2}{5} + \frac{11}{20}$$ = $$\frac{3}{2}$$ = 1$$\frac{1}{2}$$
The value of $$\frac{36 \div 42 of 6 \times 7 + 24 \times 6 \div 18 + 3 \div (2 - 6) - (4 + 3 \times 2) \div 8}{21 \div 3 of 7}$$ is:
$$\frac{36 \div 42 of 6 \times 7 + 24 \times 6 \div 18 + 3 \div (2 - 6) - (4 + 3 \times 2) \div 8}{21 \div 3 of 7}$$
= $$\frac{36 \div 252 \times 7 + 24 \times 6 \div 18 + 3 \div (2 - 6) - (4 + 3 \times 2) \div 8}{21 \div 21}$$
= $$36 \div 252 \times 7 + 24 \times 6 \div 18 + 3 \div (-4) - (10) \div 8$$
= $$36 \times \frac{1}{252} \times 7 + 24 \times 6 \times \frac{1}{18} - 3 \times \frac{1}{4} - (10) \times \frac{1}{8}$$
= $$1 + 8 - \frac{3}{4} - \frac{5}{4}$$
= 1 + 8 - 2 = 7
If '+' means '-', '-' means '+', '$$\times$$' means '$$\div$$', and '$$\div$$' means '$$\times$$', then the value of $$\frac{42 - 12 \times 3 + 8 \div 2 + 15}{8 \times 2 - 4 + 9 \div 3}$$ is:
$$\frac{42 - 12 \times 3 + 8 \div 2 + 15}{8 \times 2 - 4 + 9 \div 3}$$
On changing the sign,
$$\frac{42 + 12 \div 3 - 8 \times 2 - 15}{8 \div 2 + 4 - 9 \times 3}$$
= $$\frac{42 + 4 - 8 \times 2 - 15}{4 + 4 - 9 \times 3}$$
= $$\frac{42 + 4 - 16 - 15}{4 + 4 - 27}$$
= $$\frac{15}{19}$$
Solve the following.
$$\frac{4}{3} \div \frac{1}{6} \times 2 - 1 = ?$$
$$\frac{4}{3} \div \frac{1}{6} \times 2 - 1 = ?$$
$$\frac{4}{3} \times 6 \times 2 - 1 = ?$$
16 - 1 = ?
? = 15
The value of $$(26-13\times2)\div2+1$$ is:
$$(26-13\times2)\div2+1$$
= $$(26- 26)\div2+1$$ = 0 + 1 = 1
The value of $$\frac{7 - [4 + 3(2 - 2 \times 2 + 5) - 8] \div 5}{2 \div 2 of (4 + 4 \div 4 of 4)}$$ is:
$$\frac{7 - [4 + 3(2 - 2 \times 2 + 5) - 8] \div 5}{2 \div 2 of (4 + 4 \div 4 of 4)}$$
= $$\frac{7 - [4 + 3(2 - 4 + 5) - 8] \div 5}{2 \div 2 of (4 + 4 \div 16)}$$
= $$\frac{7 - [4 + 3(3) - 8] \div 5}{2 \div 2 of (4 + \frac{1}{4})}$$
= $$\frac{7 - 5 \div 5}{2 \div 2 of \frac{17}{4}}$$
= $$\frac{7 - 1}{2 \div \frac{17}{2}}$$
= $$\frac{6}{2 \times \frac{2}{17}}$$
= $$\frac{51}{2}$$ = $$25\frac{1}{2}$$
The value of $$\frac{[54-(5 \div 2)\times 8]+13}{48-4 \div 3 \times 8-2}$$
$$\frac{[54-(5 \div 2)\times 8]+13}{48-4 \div 3 \times 8-2}$$
= $$\frac{[54-(2.5)\times 8]+13}{48-4 \times \frac{1}{3} \times 8-2}$$
= $$\frac{[54-20]+13}{48- \frac{32}{3} -2}$$
= $$\frac{47}{\frac{106}{3}}$$
= $$\frac{141}{106}$$
The value of $$\frac{8 \div [(8 - 3) \div \left\{(4 \div 4 of 8) + 4 - 4 \times 4 \div 8\right\} - 2]}{8 \times 8 \div 4 - 8 \div 8 of 2 - 7}$$ is:
$$\frac{8 \div [(8 - 3) \div \left\{(4 \div 4 of 8) + 4 - 4 \times 4 \div 8\right\} - 2]}{8 \times 8 \div 4 - 8 \div 8 of 2 - 7}$$
$$\frac{8 \div [(8 - 3) \div \left\{(4 \div 32) + 4 - 4 \times 4 \div 8\right\} - 2]}{8 \times 8 \div 4 - 8 \div 16 - 7}$$
$$\frac{8 \div [5 \div \left\{\frac{1}{8} + 4 - 4 \times \frac{1}{2}\right\} - 2]}{8 \times 2 - \frac{1}{2} - 7}$$
$$\frac{8 \div [5 \div \left\{\frac{1}{8} + 4 - 2\right\} - 2]}{16 - \frac{1}{2} - 7}$$
$$\frac{8 \div [5 \div \frac{17}{8} - 2]}{ \frac{17}{2}}$$
$$\frac{8 \div [5 \times \frac{8}{17} - 2]}{ \frac{17}{2}}$$
$$\frac{8 \div [ \frac{40}{17} - 2]}{ \frac{17}{2}}$$
$$\frac{8 \div\frac{6}{17}}{ \frac{17}{2}}$$
$$\frac{8 \times \frac{17}{6}}{ \frac{17}{2}}$$
=$$\frac{8}{3}$$
The value of $$1800\div20\times [(12-6)+(24-12)]$$ is:
$$1800\div20\times [(12-6)+(24-12)]$$
= $$1800\div20\times [(6)+(12)]$$
= $$90\times [(6)+(12)]$$
= $$90\times 18$$ = 1620
Solve the following expression.
$$ 5.6 - \left\{2 + 0.6 of (2.1 - 2.6 \times 1.12)\right\}$$
$$ 5.6 - \left\{2 + 0.6 of (2.1 - 2.6 \times 1.12)\right\}$$
= $$ 5.6 - \left\{2 + 0.6 of (2.1 - 2.912)\right\}$$
= $$ 5.6 - \left\{2 + 0.6 \times (-0.812)\right\}$$
= $$ 5.6 - \left\{2 - 0.4872\right\}$$
= 5.6 - 1.5128 = 4.0872
Tf ‘+’ means ‘-’,‘-’ means ‘+’, ‘x’ means ‘$$\div$$’ and ‘$$\div$$’ means ‘x’, then the value of $$\frac{[(30\times5)+(84\times6)]\div5}{[\frac{2}{3}\div18]-[4\div2]}$$ is:
$$\frac{[(30\times5)+(84\times6)]\div5}{[\frac{2}{3}\div18]-[4\div2]}$$
On change the sign,
= $$\frac{[(30\div5)-(84\div6)]\times5}{[\frac{2}{3}\times18]+[4\times2]}$$
= $$\frac{[6-14]\times5}{12+8}$$ = -40/20 = -2
The value of $$151^2 - 149^2$$ is:
$$151^2 - 149^2$$
= $$(149 + 2)^2 - 149^2$$
= $$149^2 + 2^2 + 2 \times 2 \times 149 - 149^2$$
= 4 + 596 = 600
If a sum of ₹1,180 is to be divided among A, B and C,such that 2 times A’s share, 5 times B’s share and 7 times C’s share, are equal, then A’s share is:
According to the question,
2$$\times A = 5 \times B = 7 \times C$$
Ratio of the share of A, B and C = $$\frac{1}{2} : \frac{1}{5} : \frac{1}{7} = 35 : 14 : 10$$
A’s share = $$\frac{35}{59} \times 1180$$ = ₹ 700
The value of $$\frac{3}{5} \times 1 \frac{7}{8} \div 1\frac{1}{3} of \frac{3}{16} - \left(3 \frac{1}{5} \div 4 \frac{1}{2} of 5 \frac{1}{3}\right) \times 2\frac{1}{2} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}$$ is:
$$\frac{3}{5} \times 1 \frac{7}{8} \div 1\frac{1}{3} of \frac{3}{16} - \left(3 \frac{1}{5} \div 4 \frac{1}{2} of 5 \frac{1}{3}\right) \times 2\frac{1}{2} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}$$
By BODMAS rule,
$$\frac{3}{5} \times \frac{15}{8} \div \frac{4}{3} of \frac{3}{16} - \left( \frac{16}{5} \div \frac{9}{2} of \frac{16}{3}\right) \times \frac{5}{2} + \frac{1}{2} + \frac{1}{8} \div \frac{1}{4}$$
$$\frac{3}{5} \times \frac{15}{8} \div \frac{1}{4} - ( \frac{16}{5}\div 24) \times \frac{5}{2} + \frac{1}{2} + \frac{1}{8} \times \frac{4}{1}$$
$$\frac{3}{5} \times \frac{15}{8} \times 4 - ( \frac{16}{5} \times \frac{1}{24}) \times \frac{5}{2} + \frac{1}{2} + \frac{1}{2}$$
$$\frac{3}{5} \times \frac{15}{2} - \frac{2}{15} \times \frac{5}{2} + \frac{1}{2} + \frac{1}{2}$$
$$\frac{9}{2} - \frac{1}{3} + \frac{1}{4} = \frac{53}{12}$$ = 4\frac{5}{12}
The value of $$\frac{3\frac{2}{3} \div \frac{11}{30} of \frac{2}{3} - \frac{1}{4} of 2\frac{1}{2} \div \frac{3}{5} \times 4 \frac{4}{5}}{\frac{2}{5} of 7\frac{1}{2} \div \frac{3}{4} - \frac{3}{4} \times 1\frac{1}{2} \div 2\frac{1}{4}}$$ is:
$$\frac{3\frac{2}{3} \div \frac{11}{30} of \frac{2}{3} - \frac{1}{4} of 2\frac{1}{2} \div \frac{3}{5} \times 4 \frac{4}{5}}{\frac{2}{5} of 7\frac{1}{2} \div \frac{3}{4} - \frac{3}{4} \times 1\frac{1}{2} \div 2\frac{1}{4}}$$
= $$\frac{\frac{11}{3} \div \frac{11}{30} of \frac{2}{3} - \frac{1}{4} of \frac{5}{2} \div \frac{3}{5} \times \frac{24}{5}}{\frac{2}{5} of \frac{15}{2} \div \frac{3}{4} - \frac{3}{4} \times \frac{3}{2} \div \frac{9}{4}}$$
= $$\frac{\frac{11}{3} \div \frac{11}{45} - \frac{5}{8} \div \frac{3}{5} \times \frac{24}{5}}{3 \div \frac{3}{4} - \frac{3}{4} \times \frac{3}{2} \div \frac{9}{4}}$$
= $$\frac{\frac{11}{3} \times \frac{45}{11} - \frac{5}{8} \times \frac{5}{3} \times \frac{24}{5}}{3 \times \frac{4}{3} - \frac{3}{4} \times \frac{3}{2} \times \frac{4}{9}}$$
= $$\frac{15 - 5}{4 -\frac{1}{2}}$$
= $$\frac{10}{\frac{7}{2}}$$
= $$\frac{20}{7} = 2\frac{6}{7}$$
If ‘$$+$$’ means ‘$$-$$’, ‘$$-$$’ means ‘$$\times$$’, ‘$$\times$$’ means ‘$$\div$$’ and ‘$$\div$$’ means ‘$$+$$’, then what will be the value of the following expression?
$$25 - 2 + 32 \times 8 \div 4$$
As forgiven question $$25 - 2 + 32 \times 8 \div 4$$
$$\Rightarrow 25 \times 2 -32 \div 8 + 4$$ (we change the sign for the given condition)
$$\Rightarrow 25 \times 2 - 4 + 4$$
$$\Rightarrow 50 - 4 + 4$$
$$\Rightarrow 50 $$ Ans
The two given expressions on both the side of the ‘=’ sign will have the same value if two numbers from either side or both side are interchanged. Select the correct numbers to be interchanged from the given options.
$$4 + 6 \times 7 - 27 \div 3 = 7 \times 8 - 4 + 39 \div 3$$
$$4 + 6 \times 7 - 27 \div 3 = 7 \times 8 - 4 + 39 \div 3$$
After interchanged,
$$4 + 8 \times 7 - 27 \div 3 = 7 \times 6 - 4 + 39 \div 3$$
$$4 + 8 \times 7 - 9 = 7 \times 6 - 4 + 13$$
$$4 + 56 - 9 = 42 - 4 + 13$$
51 = 51
$$\therefore$$ The correct answer is option B.
Which two signs and two numbers should be interchanged to make the given equation correct?
$$28 - 32 \div 2 \times 8 + 34 = 132$$
$$28 - 32 \div 2 \times 8 + 34 = 132$$
From the option C,
$$28 + 34 \div 2 \times 8 - 32 = 132$$
$$28 + 17 \times 8 - 32 = 132$$
136 - 4 = 132
132 = 132
$$\therefore$$ The correct answer is option C.
Which two signs should be interchanged to make the given equation correct?
$$225 + 5 \times 3 \div 5 - 7 = 133$$
$$225 + 5 \times 3 \div 5 - 7 = 133$$
From the option B,
$$225 \div 5 \times 3 + 5 - 7 = 133$$
$$45 \times 3 + 5 - 7 = 133$$
$$135 + 5 - 7 = 133$$
133 =133
$$\therefore$$ The correct answer is option B.
Insert the arithmetic signs in the following numerical figure:
6, 3, 6 = 24
From option A,
LHS,
6 + 3 $$\times$$ 6
= 6 + 18
= 24
RHS
Hence, Option A is the correct answer.
Insert the arithmetic signs in the following numerical figure:
9, 3, 4, 6 = 29
From the option C) -
LHS-
9 $$\times$$ 3 - 4 + 6
= 27 - 4 + 6
= 29
RHS
$$\therefore$$ Option C is correct answer.
$$ \frac{6^2 + 7^2 + 8^2 + 9^2 + 10^2}{\sqrt{7} + 4\sqrt{3} - \sqrt{4} + 2\sqrt{3}} $$ is equal to
In division sum, the divisor is 4 times the quotient and twice the remainder.If a and b are respectively the divisor and the divided, then
The value of $$\frac{7 + 8 \times 8 \div 8 of 8 + 8 \div 8 \times 4 of 4}{4 \div 4 of 4 + 4 \times 4 \div 4 - 4 \div 4 of 2}$$ is:
$$\frac{7 + 8 \times 8 \div 8 of 8 + 8 \div 8 \times 4 of 4}{4 \div 4 of 4 + 4 \times 4 \div 4 - 4 \div 4 of 2}$$
On solving by the BODMAS rule,
= $$\frac{7 + 8 \times 8 \div 64 + 8 \div 8 \times 16}{4 \div 16 + 4 \times 4 \div 4 - 4 \div 8}$$
= $$\frac{7 + 1 + 1 \times 16}{\frac{1}{4} + 4 \times 1 - \frac{1}{2}}$$
= $$\frac{7 + 1 + 16}{\frac{1}{4} + 4 - \frac{1}{2}}$$
= $$\frac{24}{\frac{15}{4}}$$
= $$\frsc{96}{15}$$ = 6.4
$$\therefore$$ The correct answer is option D.
Twenty one times of a positive number is less than its square by 100. The value of the positive number is
Which two numbers should be interchanged to make the given equation correct?
$$4 \times 2 - 8 + 9 \div 3 = 9 \div 3 + 4 \times 2 - 8$$
Which two numbers should be interchanged to make the following equation correct?
$$8 + 12 \div 9 \times 6 - 4 = 12 \div 6 \times 8 + 9 - 1$$
Which two signs should be interchanged to make the given equation correct?
$$16 + 3 - 5 \times 2 \div 4 = 9$$
Find out the two signs to be interchanged to make the following equation correct.
$$22 + 11 \times 22 - 2 \div 3 = 45$$
Given that $$\sqrt{4096}+\sqrt{40.96}+\sqrt{0.004096}$$ is
$$\sqrt{4096}+\sqrt{40.96}+\sqrt{0.004096}$$
= 64 + 6.4 + .064 = 70.464
Hence option B
N = $$2^{48} - 1$$ and N are exactly divisible by two numbers between 60 and 70. What is the sum of those two numbers?
$$2^{48}-1$$
$$=\left(2^{24}+1\right)\left(2^{24}-1\right)$$
$$=\left(2^{24}+1\right)\left(2^{12}+1\right)\left(2^{12}-1\right).$$
$$=\left(2^{24}+1\right)\left(2^{12}+1\right)\left(2^6+1\right)\left(2^6-1\right).$$
So, Those two numbers are $$\left(2^6+1\right)\ and\ \ \left(2^6-1\right).$$
or, 65 and 63.
Sum of these numbers=65+63=128.
A is correct choice.
Simplify$$ \sqrt[3]{-2197}\times\sqrt[3]{-125}\div\sqrt[3]{\frac{27}{512}}$$
The value of ($$1 \frac{1}{3}÷2\frac{6}{7}of 5 \frac{3}{5}$$)÷($$ 6 \frac{2}{5}÷4\frac{1}{2}of 5 \frac{1}{3}$$) $$\times$$ ($$ \frac{3}{4}\times 2\frac{2}{3}÷\frac{5}{9} of $$1$$\frac{1}{5}) = 1 + k$$,where $$k$$ lies between
($$1 \frac{1}{3}÷2\frac{6}{7}of 5 \frac{3}{5}$$)÷($$ 6 \frac{2}{5}÷4\frac{1}{2}of 5 \frac{1}{3}$$) $$\times$$ ($$ \frac{3}{4}\times 2\frac{2}{3}÷\frac{5}{9} of $$1$$\frac{1}{5}) = 1 + k$$
($$ \frac{4}{3}÷\frac{20}{7}of \frac{28}{5}$$)÷($$ \frac{32}{5}÷\frac{9}{2}of \frac{16}{3}) \times (\frac{3}{4}\times \frac{8}{3}÷\frac{2}{3} of \frac{6}{5})$$ = 1 + k
$$ \frac{1}{12}÷\frac{4}{15} \times (\frac{3}{4}\times4)$$ = 1 + k
$$ \frac{1}{12}÷\frac{4}{15} \times 3$$ = 1 + k
$$ \frac{1}{12} \times \frac{15}{4} \times 3$$ = 1 + k
15/16 = 1 + k
k = 0.9375 - 1 = -0.0625
So, k lies between -0.07 and -0.06.
$$\therefore$$ The correct answer is option A.
Two baskets together have 640 oranges. If ($$\frac{1}{5}$$)th of the oranges in the first basket be taken to the second basket. The number of oranges in the firstbasket is
$$3 \times 7 + 4 - 6 \div 3 - 7 + 45 \div 5 \times 4 + 49$$ is equal to:
If the six digit number 4x4y96 is divisible by 88, then what will be the value of (x + 2y)?
Find out the two signs to be interchanged to make the following equation correct.
$$14 + 16 \times 14 - 7 \div 3 = 43$$
Find out the two signs to be interchanged to make the following equation correct.
$$24 + 2 \times 2 - 6 \div 3 = 22$$
What will be the value of the following equation if ‘$$\div$$’ means ‘addition’, ‘$$+$$’ means ‘subtraction’, ‘$$-$$’ means ‘multiplication’ and ‘$$\times$$’ means 'division'?
$$49 \times 7 - 3 \div 9 + 4 = ?$$
$$(8 + 4 - 2) \times (17 - 12) \times 10 - 89$$ is equal to:
$$(8 + 4 - 2) \times (17 - 12) \times 10 - 89 = 10 \times 5 \times 10 - 89$$
$$= 500 - 89 = 411$$
The value of $$6\frac{1}{5}-\left[4\frac{1}{2}-\left\{\frac{5}{6}-\left(\frac{3}{5}+\frac{3}{10}-\frac{7}{15}\right)\right\}\right]$$ is:
$$\sqrt{4+\sqrt{144}}$$ is equal to:
$$\sqrt{\ 4+\sqrt{\ 144}}$$
$$\sqrt{\ 4+\sqrt{\ 12\times\ 12}}$$
$$\sqrt{\ 4+12}$$
$$\sqrt{\ 16}$$
$$\sqrt{\ 4\times\ 4}$$
$$4$$
$$\frac{14 - 6 \times 2}{15 \div 3 + 3}$$ is equal to:
$$\frac{3}{5}\times4[7-(\frac{2}{5}\times(13+2))]$$ is equal to:
$$\frac{3}{5}\times\ 4\left[7-\left(\frac{2}{5}\times\ \left(13+2\right)\right)\right]$$
By using BODMAS
$$\frac{3}{5}\times\ 4\left[7-\left(\frac{2}{5}\times\ 15\right)\right]$$
$$\frac{3}{5}\times\ 4\left[7-6\right]$$
$$\frac{3}{5}\times\ 4$$
$$2\frac{2}{5}$$
If $$a = \frac{\sqrt3 + \sqrt2}{\sqrt3 - \sqrt2}$$ and $$b = \frac{\sqrt3 - \sqrt2}{\sqrt3 + \sqrt2}$$, then what is the value of $$a^2 + b^2 - ab$$?
From given data , ab=1 .
And, $$a+b=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}=\frac{3+2+2\sqrt{6}+3+2-2\sqrt{6}}{3-2}=10\ .$$
So, $$a^2+b^2-ab=\left(a+b\right)^2-3ab=10^2-3.1=97\ .$$
A is correct choice.
What is the value of $$(2+\sqrt{2})+\left(\frac{1}{2+\sqrt{2}}\right)+\left(\frac{1}{2-\sqrt{2}}\right)+(2-\sqrt{2})$$?
$$(2+\sqrt{2})+\left(\frac{1}{2+\sqrt{2}}\right)+\left(\frac{1}{2-\sqrt{2}}\right)+(2-\sqrt{2})$$
$$=(2+\sqrt{2})+\left(\frac{2-\sqrt{2}}{4-2}\right)+\left(\frac{2+\sqrt{2}}{4-2}\right)+(2-\sqrt{2})$$
$$=\left(2+2\right)+\left(\frac{2-\sqrt{2}+2+\sqrt{2}}{2}\right)\ .$$
$$=4+\left(\frac{4}{2}\right)\ .$$
$$=6\ .$$
D is correct choice.
What is the value of $$\surd121 + \surd12321 + \surd1234321 + \surd123454321$$?
We know that
11^2 =121
111^2 = 12321
1111^2 =1234321
11111^2=123454321
Now therefore taking root of RHS and adding we get
11+111+1111+11111 = 12344
Which two signs should be interchanged, as given in the options. to make the following equation correct?
$$7 \div 3 - 4 + 6 \times 2 = 20$$
$$15 - \left\{5 + 24 \div (3 \times 9 - 15)\right\}$$ is equal to.
$$5\frac{5}{6}+[2\frac{2}{3}-[{3\frac{3}{4}(3\frac{4}{5}\div9\frac{1}{2})}]]$$
$$5\frac{5}{6}+[2\frac{2}{3}-[{3\frac{3}{4}(3\frac{4}{5}\div9\frac{1}{2})}]]$$
According to question,
$$\frac{35}{6}+\left[\frac{8}{3}-\left[\frac{15}{4}\left(\frac{19}{5}\ \times\ \frac{2}{19}\right)\right]\right]$$
$$\frac{35}{6}+\left[\frac{8}{3}-\left[\frac{15}{4}\times\ \frac{2}{5}\right]\right]$$
$$\frac{35}{6}+\left[\frac{8}{3}-\frac{3}{2}\right]$$
$$\frac{35}{6}+\frac{7}{6}=7\ Ans$$
An oil merchant has 3 varieties of oil of volumes 432, 594 and 702 litres respectively. The number of cans of equal size that would be required to fill the oil separately is:
It is given that :oil merchant has 3 varieties of oil of volumes 432, 594 and 702 litres respectively.
Now If we need can of equal size
Then the size of can should be HCF of (432,594,702)
=54
So cans required = 432/54 , 594/54 , 702/54 = 8,11,13
The Square root of which of the following is a rational number?
$$\frac{0.72 \times 0.72 \times 0.72 - 0.39 \times 0.39 \times 0.39}{0.72 \times 0.72 + 0.72 \times 0.39 + 0.39 \times 0.39}$$ is equal to:
Given fraction is in the form of $$\dfrac{a^3-b^3}{a^2+ab+b^2}$$ which is $$a-b$$
Here, $$a = 0.72$$ and $$b = 0.39$$
Therefore, $$a-b = 0.72-0.39=0.33$$
$$\frac{6.75 \times 6.75 \times 6.75 - 4.25 \times 4.25 \times 4.25}{67.5 \times 67.5 + 42.5 \times 42.5 + 67.5 \times 42.5}$$ is equal to:
The value of $$3\frac{1}{5}-[2\frac{1}{2}-(\frac{5}{6}-(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}))]$$ is:
$$\frac{16}{5\ }-\ \left[\frac{5}{2}-\left(\ \frac{5}{6}\ -\ \left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right)\right]$$According to question ,
$$\frac{16}{5}-\left(\frac{5}{2}-\left(\frac{5}{6}-\frac{7}{30}\right)\right)=$$
11/10 Ans
The students of a class donated ₹3,481 towards relief fund. Each student donated an amount equal to the number of students in the class. The number of students in the class is:
$$(-4) \times (1020 \div 85 \times 3 - 22)$$ is equal to.-
$$5\frac{1}{5}-\left[ 3\frac{1}{2}-\left\{ \frac{5}{6}-\left( \frac{3}{5}+\frac{1}{10}-\frac{4}{15}\right)\right\}\right]$$ is equal to:
$$\sqrt[3]{(13.068)^{2}-(13.392)^{2}}$$ is equal to
$$13 \div \left\{4 of 2 - 3 + 4 \times (6 - 4)\right\}$$ is equal to:
A gardener planted 1936 saplings in a garden such that there were as many rows of saplings as the columns. The number of rows planted is:
The square root of which of the following is a rational number?
If $$x + \frac{1}{x} = 5$$, then $$x^3 + \frac{1}{x^3}$$ is equal to:
$$(24 \div 6 - 2) + ( 3 \times 2 + 4)$$ is equal to:
To what power -3 should be raised to get -2187?
$$(-4)\times(-8)\div(-2)+3\times5$$ is equal to:
$$(-4)×(-8)\div (-2)+3×5$$
$$=(-4)×4+3×5.$$
$$=-16+15.$$
$$=-1.$$
A is correct choice.
Which two signs should be interchanged to make the given equation correct?
$$27 \div 3 -18 + 3 \times 2 = 18$$
The least number that should be added to 10000 so that it is exactly divisible by 327 is:
327 is a multiple of 3.
So, a number should be added to 10000 which will make it divisible by 3.
And 327 is also a multiple of 109.
So, To make 10000 completely divisible by 327, a number should be added to that number which would be divisible by 109 also.
So, $$(10000+137)=10137$$ is divisible by 3 as well as 109.
So,Option C is correct.
$$9\frac{3}{4}\div\left[2\frac{1}{6}+\left\{4\frac{1}{3}-\left(2\frac{1}{2}+\frac{3}{4}\right)\right\}\right]$$ is equal to:
The value of $$3\frac{5}{6}+\left[ 3\frac{2}{3}-\left\{ \frac{15}{4}\left( 5\frac{4}{5}\div 14\frac{1}{2}\right)\right\}\right]$$ is equal to:
If $$x-\frac{1}{x}=6$$, then $$x^3-\frac{1}{x^3}$$ is equal to:
The greatest number of four digits which is exactly divisible by 24, 36 and 54 is:
$$ 9936 = 12\times 12\times 23\times 3.$$
So, 24,36 and 54 , all of these numbers have the common factors in 9936.
But, numbers in other options don't have common factors.
So, Option C is correct.
$$\frac{5.75\times5.75\times5.75+3.25\times3.25\times3.25}{57.5\times57.5+32.5\times32.5-57.5\times32.5}$$ is equal to:
If $$x + \frac{1}{x} = 8$$,then $$x^2 + \frac{1}{x^2}$$ is equalto:
$$\left(x+\frac{1}{x}\right)^{2\ }=x^2+\frac{1}{x^2}+2x.\ \frac{1}{x}$$
$$64=x^2+\frac{1}{x^2}+2$$
$$64\ -\ 2=x^2+\frac{1}{x^2}$$
$$62=x^2+\frac{1}{x^2}$$
$$7-(4\times3-(-10)\times8\div(-4))$$ is equal to:
$$7-(4\times3-(-10)\times8\div(-4))$$
Using BODMAS
$$=7-(4\times 3-(-10)\times (-2))$$
$$=7-(12-20)$$
$$=7+8$$
$$=15.$$
D is correct choice.
If $$x^2 + \frac{1}{x^2} = 11$$, then $$x - \frac{1}{x}$$ is equal to:
If $$x - \frac{1}{x} = 4$$, then $$x^3 - \frac{1}{x^3}$$ is equal to:
The cube root of 3375 equal to.
$$3375=15\times 15\times 15.$$
So, cube root of 3375 is 15.
D is correct.
The value of $$\frac{1}{3} \div \frac{5}{6} \times \frac{-5}{8}$$ is equal to:
The sum of all the digits of the numbers from 1 to 100 is
Sum of first 'n' natural numbers = $$ \frac{n(n + 1)}{2} $$
here n =100
substituting,
$$ \frac{100(100 +1)}{2} = 5050 $$
$$10 - \left\{17 - 12 \div (59 + 9 \times 2 - 17)\right\}$$ is equal to:
$$\frac{3}{4}+\frac{5}{2}[\frac{1}{4}\times(\frac{8}{5}-\frac{4}{3})]$$ is equal to:
$$\ \frac{\ 3}{4}+\ \frac{\ 5}{2}\times\ \left(\frac{\ 1}{4}\times\ \left(\ \frac{\ 8}{5}\ -\ \frac{\ 4}{3}\right)\right)$$
$$=\ \frac{\ 3}{4}+\ \frac{\ 5}{2}\times\ \left(\frac{\ 1}{4}\times\ \left(\frac{\ 24\ -\ 20}{5\times\ 3}\right)\right)$$
$$=\ \frac{\ 3}{4}+\ \frac{\ 5}{2}\times\ \left(\frac{\ 1}{4}\times\ \left(\frac{\ 4}{5\times\ 3}\right)\right)$$
$$=\ \frac{\ 3}{4}+\ \frac{\ 5}{2}\times\ \left(\frac{\ 1}{15}\right)$$
$$=\ \frac{\ 3}{4}+\ \frac{\ 1}{6}$$
$$=\ \frac{\ 9+2}{12}$$
$$=\ \frac{\ 11}{12}.$$
D is correct choice.
Which two signs should be interchanged to make the given equation correct?
$$12 \times 8 \div 36 + 3 - 6 = 102$$
$$12 \times 8 + 36 \div 3 - 6 = 102$$
$$12 \times 8 + 12 - 6 = 102$$
$$96 + 12 - 6 = 102$$
$$102= 102$$
Henc option (b) is correct
Find out the two signs to be interchanged for making following equation correct.
$$18 - 2 \times 7 \div 6 + 10 = 67 $$
If
+ denotes —
— denotes *
* denotes /
/ denotes +
then what will be the value of
25 - 2 / 10 * 5 + 2 = ?
Which of the two signs should be interchanged in the following equation to make the given value correct?
$$15 + 5 - 10 \times 6 \div 12 = 6$$
The value of $$22.\overline{4} + 11.5\overline{67} - 33.5\overline{9}$$ is:
$$22.\overline{4} + 11.5\overline{67} - 33.5\overline{9}$$
= $$22.44444 + 11.56767 - 33.59999$$
= $$22.44444 + 11.56767 - 33.59999$$
= $$0.41212$$
= $$0.4\overline{12}$$
$$\threrefore$$ The correct answer is option D.
Four brothers P, Q, R and S go to a hotel. They book four hotel rooms numbered 301, 302, 303 and 304. Sum of room numbers of P and R is 603 and the sum of room numbers of R and S is 604. What is the sum of room numbers of P, Q and R?
How many perfect cubes are there between 1 and 100000 which are divisible by 7?
A perfect cube that is divisible by 7 ,when that number contain a cube of 7 or a perfect
multiple of 7's cube in following form , $$N=7^3\times k^3\ \left(where,\ k=1,2,3.....\right)$$
If we, put k=6 ,then the number become, $$N=7^3\times6^3=74088.$$
But , if we put k=7, then the number become, $$N=7^3\times7^3=117649.$$
117649 exceeds 100000 , So there are only 6 numbers(when, k=1,2,....,6) present between 1 and 100000 which are divisible by 7.
B is correct choice.
If 738A6A is divisible by 11, then the value of A is
Sum of digits at odd places is 7+8+6=21.
Sum of digits at even places is 3+2A.
Their difference = 21-(3+2A) = 18-2A
The number will be divisible by 11 if 18-2A is 11 or 0.
But to get to 11, 2A needs to be 7 where it will give a fraction as a digit.
So 18-2A = 0.
hence A = 9
Two pipes of length 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be
What is the sum of first 40 terms of 1 + 3 + 4 + 5 + 7 + 7 + 10 + 9 + ….?
The sequence has to be split into two with alternate terms:
S1=1+4+7+10+…(S1=1+4+7+10+…(AP with A1=1,D1=3
S2=3+5+7+9+...(S2=3+5+7+9+...(AP with A2=3,D2=2)
Sum of 40 terms of the original series = Sum of 20 terms of S1+ Sum of 20 terms of S2
S=N[2A1+(N−1)D1]/2+N[2A2+(N−1)D2]/2
⟹S=[20∗((2∗1)+(19∗3))]+[20∗((2∗3)+(19∗2)]/2
⟹S=10∗[59+44]=1030
Which two numbers should be interchanged to make the given equations correct?
$$6 \times 3 - 8 \div 2 + 5 = 8 \div 2 + 3 \times 5 - 6$$
$$A = \frac{(x^8 - 1)}{(x^4 + 1)}$$ and $$B = \frac{(y^4 - 1)}{(y^2 + 1)}$$. If $$x = 2$$ and $$y = 9$$, then what is the value of $$A^2 + 2AB + A(A+B)^2$$?
$$A = \frac{(x^8 - 1)}{(x^4 + 1)}$$ and $$B = \frac{(y^4 - 1)}{(y^2 + 1)}$$
$$A = (x^4 - 1)$$
$$B=(y^2 - 1)$$
For x=2 ,A=15
For y=9,B=80
$$A^2 + 2AB + A(A+B)^2$$=225+2400+(15)(9025)
=2625+135375
=138000
Find out the two signs to be interchanged to make the following equation correct.
$$13 + 26 \times 2 - 5 \div 3 = 11 $$
If $$A = 125$$ and $$B = 8$$, then what is the value of
$$(A + B)^3 - (A - B)^3 - 6B(A^2 - B^2)$$?
$$(A+B)^3-(A-B)^3-6B(A^2-B^2)$$
$$=\left(A+B-A+B\right)^3+3\left(A+B\right)\left(A-B\right)\left(A+B-A+B\right)-6B\left(A^2-B^2\right).$$
$$=\left(2B\right)^3+6\left(A^2-B^2\right)B-6B\left(A^2-B^2\right).$$
$$=\left(2\times8\right)^3=4096.$$
A is correct choice.
If '$$\div$$' means means '$$+$$', '$$-$$' means '$$\div$$' '$$\times$$' means '$$-$$' and '$$+$$' means '$$\times$$' then find the value of
$$\frac{(12 \times 4) - 2 \times 4}{2 + 8 \times 2 + 25 \div 1}$$
Find out the two signs to be interchanged to make the following equation correct.
$$25 + 5 \times 7 - 12 \div 3 = 26$$
The value of $$0.4\overline{7} + 0.5\overline{03} - 0.3\overline{9} \times 0.\overline{8}$$ is:
$$0.4\overline{7} + 0.5\overline{03} - 0.3\overline{9} \times 0.\overline{8}$$
= $$\frac{47 - 4}{90}+ \frac{503 - 5}{990} - \frac{39 - 3}{90} \times \frac{8}{9}$$
= $$\frac{43}{90}+ \frac{498}{990} - \frac{36}{90} \times \frac{8}{9}$$
= $$\frac{43}{90}+ \frac{498}{990} - \frac{32}{90}$$
= $$\frac{619}{990}$$
= $$0.6\overline{25}$$
Which two signs should be interchanged in the following equation to make it correct?
$$9-3+12\times8\div4=11$$
By Trial and Error method,
Option A
$$9+3-12\times8\div4=11$$
$$9+3-12\times2=11$$
$$9+3-24=11$$
$$-12=11$$
Hence option A is incorrect
Option B
$$9-3\times12+8\div4=11$$
$$9-3\times12+2=11$$
$$9-36+2=11$$
$$-25=11$$
Hence option B is incorrect
Option C
$$9\div3+12\times8-4=11$$
$$3+12\times8-4=11$$
$$3+96-4=11$$
$$95=11$$
Option D
$$9-3\div12\times8+4=11$$
$$9-\frac{1}{4}\times8+4=11$$
$$9-2+4=11$$
$$11=11$$
Hence, the correct answer is Option A
Find out the two signs to be interchanged to make the following equation correct.
$$21 + 5 \times 2 - 21 \div 3 = 12 $$
Find out the two signs to be interchanged to make the following equation correct.
$$30 + 28 \times 3 - 16 \div 4 = -50$$
Which two signs need to be interchanged to make the given equation correct?
$$20 \div 20 + 20 - 20 \times 20 = 20$$
Select the correct combination of mathematical signs to replace ‘* signs and to balance the given equation:
$$530*2*3*5*800$$
Which two signs should be interchanged to make the given equation correct?
$$20 + 5 \times 3 \div 3 - 1 = 14$$
Going by the options,
D) interchanging $$\times\ \ and \ +\ $$
$$20\ \times\ 5\ +\ 3\ \ \ $$ 3 ÷ 3$$\ -\ 1\ne\ 14$$
c) $$\times\ \ and\ \ -\ $$
$$20\ \ +\ 5\ -\ 3\ $$ ÷ $$3\times\ 1\ne\ 14$$
B) ÷ and $$\times\ $$
$$20\ +\ 5$$ ÷ $$3\times\ 3\ -\ 1\ne\ 14$$
A) ÷ and $$\ +\ $$
20 ÷ 5$$\ \times\ 3\ +\ 3\ -\ 1$$ = 14
(Explanation is required)
Hence option A is the correct answer
The expression $$\sqrt{10+2\left(\sqrt{6}-\sqrt{15}-\sqrt{10}\right)}$$ is equal to:
$$\sqrt{10+2\left(\sqrt{6}-\sqrt{15}-\sqrt{10}\right)}$$
= $$\sqrt{3 + 2 + 5 +2\left(\sqrt{3} \times \sqrt{2} - \sqrt{2} \times \sqrt{5} -\sqrt{5} \times \sqrt{2}\right)}$$
= $$\sqrt{(\sqrt{3})^2 + (\sqrt{2})^2 + (-\sqrt{5})^2 +2\left(\sqrt{3} \times \sqrt{2} - \sqrt{2} \times \sqrt{5} -\sqrt{5} \times \sqrt{2}\right)}$$
= $$\sqrt{(\sqrt{3} + \sqrt{2} -\sqrt{5})^2}$$
= $$\sqrt{3} + \sqrt{2} -\sqrt{5}$$
A's income is Rs 140 more than B's income and C's income is Rs 80 more than D's. If the ratio of A's and C's income is 2:3 and the ratio of B's and D's income is 1:2, then the incomes of A, B, C and D are respectively
By interchanging which two signs the equation will be correct?
$$6 + 9 \times 2 - 3 \div 4 = 8$$
$$6 + 9 \times 2 - 3 \div 4 = 8$$
this results in a fraction so in order to get a whole number which is 8 it is important to place divide symbol such that a whole number is obtained
now if $$- and \div$$ is interchanged 9 gets divided by 3 thus resulting in a whole number
$$6 + 9 \times 2\div 3- 4 $$ (using BODMAS rule)
$$ 6 + \frac{ 9 \times 2}{ 3} - 4 $$
= 6+ 6 - 4 = 8
If '$$+$$' is '$$\times$$', '$$-$$' is '$$+$$', '$$\times$$' is '$$\div$$' and '$$\div$$' is '$$-$$',then what will be the value of the following expression?
$$6 + \frac{2}{3} - \frac{1}{2} \div \frac{3}{4} \times 9$$
By interchanging which two signs the equation will be correct?
$$11 + 16 \times 12 \div 4 - 2 = 21$$
Given, 11+16 $$\times$$ 12 $$ $$ $$\div$$ 4 $$ $$ - 2 = 21
These type of questions can be quickly solved by checking options.
So,from the options we get option A would be correct.
On solving,11+16-12 $$\div $$ 4 $$ $$ $$\times$$2 $$ $$
$$\Rightarrow$$ 27 - 6 = 21.
From option (b), we will get the negative value which is not possible.
From options (c) and (d), we will get the fractional values which is not possible.
By interchanging the given signs which of the following equations will be correct?
$$+ and \times$$
Option (a) $$9 \times 5 \div 10 + 30 = 24$$
$$9 + 5 \div 10 \times 30 = 24$$
$$9+\frac{5}{10}\times30=24$$
9+15 = 24
24 = 24
Here the equation is satisfied. So this will be correct answer.
Option (b) $$11 + 13 \div 6 \times 12 = 37$$
$$11\times13\div6+12=37$$
Here the value of equation is in fraction and does not satisfy the given equation. So this will not be correct answer.
Option (c) $$5 + 11 - 6 \times 3 = -2$$
$$5 \times 11 - 6 + 3 = -2$$
$$55 - 6 + 3 = -2$$
$$52\ne-2$$
Here the value of the equation is not satisfying the equation. So this will not be the correct answer.
Option (d) $$16 + 32 \times 19 \div 38 = 32$$
$$16 \times 32 + 19 \div 38 = 32$$
Here the value of the equation is in decimal and does not satisfy the given equation. So this will not be the correct answer.
Which of the following interchanges of signs and numbers would make the given equation correct?
$$12 \times 18 \div 3 - 6 + 4 = 5$$
Which two signs should be interchanged to make the given equation correct?
$$14 + 4 \div 5 - 18 \times 2 = 25$$
Which sequence of mathematical symbols can replace * in the given equation:
8 * 5 * 9 * 31
Option (a) $$\times, -, =$$
$$8 \times 5 - 9 = 31$$
40-9 = 31
31 = 31
The given equation is satisfied. So this is the correct answer.
Option (b) $$-, =, \times$$
$$8 - 5 = 9 \times 31$$
$$3\ne\ 279$$
The given equation is not satisfied. So this is not the correct answer.
Option (c) $$=, \times, -$$
$$8 = 5 \times 9 - 31$$
8 = 45-31
$$8\ne14$$The given equation is not satisfied. So this is not the correct answer.
Option (d) $$-, \times, =$$
$$8 - 5 \times 9 = 31$$
8-45 = 31
$$37\ne\ 31$$
The given equation is not satisfied. So this is not the correct answer.
A General of an Army wants to create a formation of square from 36562 army men. After arrangement, he found some army men remained unused. Then the number of such army men remained unused was
f the sum of the digits of a three digit numberis subtracted from that number, then it will always be divisible by
Let the three digit number be xyz.
(100x + 10y +z) -(x + y +z) = 99x - 9y , which is divisible by both 3 and 9.
So, the answer would be option c)both 3 and 9
Select the correct set of symbols which will fit in the given equation?
8 0 3 9 = 35
What is the value of $$\frac{1}{0.2} + \frac{1}{0.02} + \frac{1}{0.002} +....$$ upto 9 terms?
we have
$$\frac{10}{2}+\frac{100}{2}+\frac{1000}{2}+......\ 9\ terms$$
= 5+50+500 +..... 9 terms
this is a geometric progression with first term =5 and common ratio =10
So we get sum = $$\frac{5}{9}\left(10^9-1\right)$$
We get sum as 555555555
What is the value of $$\frac{5.6 \times 0.36 + 0.42 \times 3.2}{0.8 \times 2.1}$$?
=$$\frac{5.6 \times 0.36 + 0.42 \times 3.2}{0.8 \times 2.1}$$
= $$\frac{2.016 + 1.3444}{1.68}$$
=$$\frac{3.36}{1.68}$$
=2
Which two numbers should be interchanged to make the given equation correct?
$$9+4\div2-6\times3=4+3\times6-9+1$$
By interchanging which two numbers, the value obtained after solving the given equation will be ’13’?
$$7 + 8 \div 4 \times 3$$
going by the options
A) 8 and 3
$$7 + 3 \div 4 \times 8$$= $$7 + \frac{8}{4}\times 3$$ = 7 + 6 = 13 (Option A is correct )
B) 8 and 4
$$7 + 4 \div 8 \times 3$$ = $$7 + \frac{4}{8}\times 3$$ = 7 + $$\frac{3}{2}$$= $$\frac{17}{2}$$ (option B is incorrect)
c) 7 and 3
$$3 + 8 \div 4 \times 7$$ = 3+$$ \frac{8}{4}\times 7$$ = 3 +14 = 17 (option C is incorrect)
d) 3 and 4
$$7 + 8 \div 3 \times 4$$ = 7+ $$ \frac{8}{3}\times 4$$ = 7 +$$ \frac{32}{3}$$ = $$ \frac{53}{3}$$ (option D is incorrect)
Find out the two signs to be interchanged for making following equation correct.
$$5 + 3 \times 4 - 12 \div 2 = -1$$
If '$$\div$$' means '$$+$$', '$$-$$' means '$$\div$$', '$$\times$$' means '$$-$$', and '$$+$$' mean '$$\times$$' then find the value of
$$\frac{24 - 8 \div 6 + 4 \times 7}{8 + 3 \times 19}$$
Which two signs should be interchanged to make the given equation correct?
$$15 - 18 + 14 \times 3 \div 3 = 19$$
Option (a) $$'\times'\ and\ '-'$$
$$15 \times 18 + 14 - 3 \div 3 = 19$$
$$270 + 14 - 1 = 19$$
$$283\ne19$$
The given equation is not satisfied. So this is not the correct answer.
Option (b) $$'+'\ and\ '-'$$
$$15 + 18 - 14 \times 3 \div 3 = 19$$
$$15 + 18 - 14 \times 1 = 19$$
$$33 - 14 = 19$$
19 = 19
The given equation is satisfied. So this is the correct answer.
Option (c) $$'\times'\ and\ '+'$$
$$15 - 18 \times 14 + 3 \div 3 = 19$$
$$15 - 18 \times 14 + 1 = 19$$
The given equation is not satisfied. Because it will give the negative values. So this is not the correct answer.
Option (d) $$'+'\ and\ '\div'$$
$$15 - 18 \div 14 \times 3 + 3 = 19$$
The given equation is not satisfied. Because it will give the fractional values. So this is not the correct answer.
After interchanging the given two numbers, what will be the value of $$6 + 7 \times 3 - 8 \div 4$$ ?
3 and 6
Expression : $$6 + 7 \times 3 - 8 \div 4$$ ?
After interchanging 3 and 6, we get :
= $$3+7\times6-8\div4$$
= $$3+42-2=43$$
=> Ans - (C)
By interchanging which two numbers the equation will be correct?
$$9 - 2 \times 4 \div 6 = -3$$
$$9 - 2 \times 4 \div 6 = -3$$
By option (b) 6 and 2, on interchanging we get, $$9 - 6 \times 4 \div 2 = -3$$
Using BODMAS rule, we get, $$9 - 6 \times 2 = -3$$
9 - 12 = -3
-3 = -3
Hence LHS = RHS.
By options (a) and (d), we will get fractional values that are not possible.
By options (c), we will get 1 which will not satisfy the equation.
By interchanging which two signs the equation will be correct?
$$11 + 9 - 4 \times 12 \div 6 = 32$$
Option (a) $$\div and -$$
$$11 + 9 \div 4 \times 12 - 6 = 32$$
$$11+\frac{9}{4}\times12-6=32$$
$$11+9\times3-6=32$$
$$11+27-6=32$$
32=32
The given equation is satisfied. So this is the correct answer.
Option (b) $$- and +$$
$$11 - 9 + 4 \times 12 \div 6 = 32$$
$$11-9+4\times2=32$$
$$2+8=32$$
$$10\ne\ 32$$The given equation is not satisfied. So this is not the correct answer.
Option (c) $$\times and +$$
$$11 \times 9 - 4 + 12 \div 6 = 32$$
$$99 - 4 + 2 = 32$$
$$97\ne\ 32$$
The given equation is not satisfied. So this is not the correct answer.
Option (d) $$\times and \div$$
$$11 + 9 - 4 \div 12 \times 6 = 32$$
$$11+9-\frac{4}{12}\times6=32$$
$$11+9-\frac{24}{12}=32$$
$$11+9-2=32$$
$$18\ne\ 32$$
The given equation is not satisfied. So this is not the correct answer.
Find out the two signs to be interchanged for making following equation correct:
$$27 + 13 \times 12 - 6 \div 3 = 50$$
The value of $$\frac{(253)^3 + (247)^3}{25.3 \times 25.3 - 624.91 + 24.7 \times 24.7}$$ is $$50 \times 10^k$$, where the value of k is:
$$\frac{(253)^3 + (247)^3}{25.3 \times 25.3 - 624.91 + 24.7 \times 24.7}$$ = $$50 \times 10^k$$
$$\frac{(253 + 247)(253)^2 + (247)^2 - 253 \times 247)}{\frac{1}{100}[(253)^2 - 253 \times 247 + (247)^2] }$$ = $$50 \times 10^k$$
50000 = $$50 \times 10^k$$
$$50 \times 10^3$$ = $$50 \times 10^k$$
k = 3
Which two signs should be interchanged to make the given equation correct?
$$4 + 8 \times 12 \div 6 - 4 = 8$$
If the two signs, '$$\times$$ and $$\div$$' are interchanged, which of the following equations will be correct?
If we interchange '$$\times$$ and $$\div$$' then-
14 + 9 $$ \times $$ 24 $$ \div $$ 3
= 14+72
= 86
After interchanging the given two signs, what will be the value of $$9 + 143 \div 13 \times 11 - 160 = ?$$
$$\times and \div$$
As per the given question, $$\div$$ and $$\times$$ will be interchanged which is given below in the equation.
= $$9 + 143 \times 13 \div 11 - 160$$
= $$9+143\times\frac{13}{11}-160$$
$$=9+13\times13-160$$
$$=9+169-160$$
= 9+9
= 18
By interchanging the given two signs which of the following equation will be correct?
$$\times$$ and $$+$$
On interchanging the two signs $$ +$$ and $$\times $$
we get the equation as
$$ 11+6 \div 18\times 54 $$
or $$11+1\div 3\times 54 =29$$
$$ 29=29 $$ which is true
Which two numbers need to be interchanged to make the given equation correct?
$$96 \times 6 - 8 \div 2 + 3 = 768$$
Option (a) 6, 8
$$96 \times 8 - 6 \div 2 + 3 = 768$$
768 - 3 + 3 = 768
768 = 768
The given equation is satisfied. So this is the correct answer.
Option (b) 6, 3
$$96 \times 3 - 8 \div 2 + 6 = 768$$
288 - 4 + 6 = 768
$$290\ne\ 768$$
The given equation is not satisfied. So this is not the correct answer.
Option (c) 2, 3
$$96 \times 6 - 8 \div 3 + 2 = 768$$
The given equation is not satisfied. Because it will give values in fraction. So this is not the correct answer.
Option (d) 96, 8
$$8 \times 6 - 96 \div 2 + 3 = 768$$
$$48 - 48 + 3 = 768$$
$$3\ne\ 768$$
The given equation is not satisfied. So this is not the correct answer.
After interchanging which two numbers, the value of the given equation will be ‘4’?
6 + 3 $$\div$$ 9 $$\times$$ 7 - 5
Option (a) 7 and 6
7 + 3 $$\div$$ 9 $$\times$$ 6 - 5
$$7+\frac{3}{9}\times6-5$$
7+2-5
4
We can obtain the required value from this option.
Option (b) 3 and 5
6 + 5 $$\div$$ 9 $$\times$$ 7 - 3
From this, we will get the fractional value which is not possible.
Option (c) 5 and 6
5 + 3 $$\div$$ 9 $$\times$$ 7 - 6
$$5+3\div9\times7-6$$
From this, we will get the fractional value which is not possible.
Option (d) 9 and 5
6 + 3 $$\div$$ 5 $$\times$$ 7 - 9
From this, we will get the fractional value which is not possible.
By interchanging which two signs the equation will be correct?
$$9 \times 11 \div 31 + 62 - 13 = 18$$
Option (a) $$\times\ and\ \div$$
$$9 \div 11 \times 31 + 62 - 13 = 18$$
The given equation is not satisfied. Because it will give the values in fraction which is not possible.
Option (b) $$-\ and\ \times$$
$$9 - 11 \div 31 + 62 \times 13 = 18$$
The given equation is not satisfied. Because it will give the values in fraction which is not possible.
Option (c) $$\div\ and\ +$$
$$9 \times 11 + 31 \div 62 - 13 = 18$$
The given equation is not satisfied. Because it will give the values in decimal which is not possible.
Option (d) $$+\ and\ \times$$
$$9 + 11 \div 31 \times 62 - 13 = 18$$
$$9+\frac{11}{31}\times62-13=18$$
$$9+11\times2-13=18$$
$$9+22-13=18$$
18=18
The given equation is satisfied. So this is the correct answer.
Which two numbers need to be interchanged to make the given equation correct?
$$16 \times 1792 \div 7 + 9 - 15 = 778$$
Option (a) 15, 9
$$16\times1792\div7+15-9=778$$
$$16\times256+6=778$$
4096+6=778
$$4102\ne778$$
The given equation is not satisfied. So this will not be the correct answer.
Option (b) 16, 7
$$7 \times 1792 \div 16 + 9 - 15 = 778$$
$$7\times\frac{1792}{16}+9-15=778$$
$$7\times112+9-15=778$$
784-6=778
778=778
The given equation is satisfied. So this will be the correct answer.
Option (c) 16, 15
$$15 \times 1792 \div 7 + 9 - 16 = 778$$
$$15 \times 256 + 9 - 16 = 778$$
3840-7 = 778
$$3833\ne\ 778$$
The given equation is not satisfied. So this will not be the correct answer.
Option (d) 16, 9
$$9 \times 1792 \div 7 + 16 - 15 = 778$$
$$9 \times 256 + 16 - 15 = 778$$
2304+1 = 778
$$2305\ne\ 778$$
The given equation is not satisfied. So this will not be the correct answer.
After interchanging the given two numbers, what will be the value of $$3 + 2 \div 1 \times 4 - 7$$?
4 and 7
given 3 + 2 ÷ 1 × 4 - 7
on interchanging 4 and 7
BODMAS rule{ brackets > of > division > multiplication > addition > subtraction }
we get 3 + 2 ÷ 1 × 7 - 4 ( using BODMAS rule)
3+$$\frac{2}{1} \times$$ 7 -4 = 3 + 2 $$\times$$ 7 - 4 = 3 + 14 - 4 = 13
By interchanging which two signs the equation will be correct?
$$19 + 63 \div 7 - 8 \times 12 = 79$$
For this question we have to go by option, so when we replace $$- and \times$$ as per option A,
$$19 + 63 \div 7 \times 8 - 12 = 79$$
$$19 + {\frac{63}{7}}\times 8 - 12 = 79$$
$$19 + {9\times8} - 12 = 79$$
$$19 + 72 - 12 = 79$$
$$79 = 79$$
Therefore option A is the answer.
If $$+$$ means ‘$$\div$$’, $$-$$ means ‘$$+$$’, $$\times$$ means ‘$$-$$’ and $$\div$$ means ‘$$\times$$' , then what will be the value of the following expression?
$$18 \div 6 - 27 + 3 \times 12 = ?$$
After interchanging the given signs, what will be the value of $$16 + 19 \times 51 \div 153 - 12 ?$$
$$\times and \div$$
On interchanging the signs $$\times and \div$$
we get the equation as
$$ 16+19\div 51 \times 153 -12 $$
or $$ 16+19 \times 3-12$$
16+57-12=61
Select the correct combination of mathematical signs to replace * signs and to balance the given equation:
28 * 4 * 9 * 16
Option (a) $$-=\times$$
$$28 - 4 = 9 \times 16$$
$$24\ne1444$$
The given equation is not satisfied. So this is not the correct answer.
Option (b) $$-\times+$$
The given set of signs is not the correct combination. Because here '=' sign is missing. So this is not the correct answer.
Option (c) $$\div+=$$
$$28 \div 4 + 9 = 16$$
$$7 + 9 = 16$$
16 = 16
The given equation is satisfied. So this is the correct answer.
Option (d) $$+\div=$$
$$28 + 4 \div 9 = 16$$
The given equation is not satisfied. Because it will give the values in fractions. So this is not the correct answer.
If the two signs, '$$+$$' and '$$\div$$ ' are interchanged, which of the following equations will be correct?
If we exchange '$$+$$' and '$$\div$$'
(A) : $$16 \div 9 + 4 \times 8 = 34$$
L.H.S. $$\equiv16+9\div4\times8$$
= $$16+(9\times2)=34=$$ R.H.S.
=> Ans - (A)
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder. The sum of digits of x is
Given that , Let x be the least number, which when divided by 5, 6, 7 and & leaves a remainder 3. Not sure what & represents.
Please provide correct data.
The value of $$\frac{(0.545)(0.081)(0.51)(5.2)}{\left(0.324\right)^3+\left(0.221\right)^3-\left(0.545\right)^3}$$ is:
$$\frac{(0.545)(0.081)(0.51)(5.2)}{\left(0.324\right)^3+\left(0.221\right)^3-\left(0.545\right)^3}$$
= $$\frac{(0.545)(0.081)(0.51)(5.2)}{3(0.324)(0.221)(0.545)}$$
$$(\because (a + b)^3 = a^3 + b^3 + 3ab(a + b))$$
= $$\frac{(0.081)(0.51)(5.2)}{3(0.324)(0.221)}$$ = 1
Which of the following equations will be correct if numbers 3 and 6 and signs $$+$$ and $$\times$$ are interchanged?
If $$A = \frac{0.216 + 0.008}{0.36 + 0.04 - 0.12}$$ and $$B = \frac{0.729 - 0.027}{0.81 + 0.09 + 0.27}$$, then what is the value of $$(A^2 + B^2)^2?$$
$$A = \frac{0.216 + 0.008}{0.36 + 0.04 - 0.12}$$
$$A = \frac{0.224}{0.28}$$
=0.8
$$B = \frac{0.729 - 0.027}{0.81 + 0.09 + 0.27}$$
$$B=\frac{0.702}{1.17}$$
=0.6
$$(A^2 + B^2)^2$$=0.36+0.64=1
The smallest number, which should be added to 756896 so as to obtain a multiple of 11, is
The value of is $$\frac{(81)^{3.6}\times(9)^{2.7}}{(81)^{4.2}\times3}$$
The value of $$\sqrt{28+10\sqrt{3}}-\sqrt{7-4\sqrt{3}}$$ is closest to:
$$\sqrt{28+10\sqrt{3}}-\sqrt{7-4\sqrt{3}}$$
= $$\sqrt{(5)^2 + (\sqrt{3})^2 + 2\times 5 \sqrt{3}}-\sqrt{(2)^2 + (\sqrt{3})^2 - 2 \times 2 \sqrt{3}}$$
= $$\sqrt{(5 + \sqrt{3})^2 } - \sqrt{(2 - \sqrt{3})^2}$$
= $$5 + \sqrt{3} -2 + \sqrt{3}$$
= $$3 + 2\sqrt{3}$$
= 3 + 2$$\times$$ 1.732
= 3 + 3.464
= 6.464 ~ 6.5
Which of the four changes given in the options would make the following equation correct?
$$30 \times 3 - 3 = 13$$
Which of the following interchanges of signs and numbers would make the flowing equation correct?
$$18 - 8 \div 12 \times 6 + 10 = 12$$
Which two numbers should be interchanged to make the given equation correct?
$$64 - 17 + 55 \times 65 \div 5 = 230$$
Here we need to check each of the option to get the correct answer.
Option (a) 55 and 65
$$64 - 17 + 65 \times 55 \div 5 = 230$$
$$64 - 17 + 65 \times 11 = 230$$
$$47 +715 = 230$$
$$762\ne\ 230$$
This option is not satisfying the given equation. So this will not be answer.
Option (b) 17 and 55
$$64 - 55 + 17 \times 65 \div 5 = 230$$
$$64 - 55 + 17 \times 13 = 230$$
$$64 - 55 + 221 = 230$$
230 = 230
This option is satisfying the given equation. So this will be answer.
Option (c) 64 and 17
$$17 - 64 + 55 \times 65 \div 5 = 230$$
$$17 - 64 + 55 \times 13 = 230$$
$$17 - 64 + 715 = 230$$
$$668\ne\ 230$$
This option is not satisfying the given equation. So this will not be answer.
Option (d) 17 and 65
$$64 - 65 + 55 \times 17 \div 5 = 230$$
$$64-65+55\times\frac{17}{5}=230$$
$$-1+11\times17=230$$
$$-1+187=230$$
$$186\ne\ 230$$
This option is not satisfying the given equation. So this will not be answer.
A cube is placed inside a cone of radius 20 cm and height 10 cm, one of its face being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm) of side of the cube?
Which two signs need to be interchanged to make the given equation correct?
$$27 - 3 \times 2 \div 13 + 9 = 14$$
Option (a) $$\div, +$$
$$27 - 3 \times 2 + 13 \div 9 = 14$$
$$27-6+\frac{13}{9}=14$$
This is the not correct answer. Because the given equation is not satisfied and gives fractional values.Option (b) $$\times, \div$$
$$27 - 3 \div 2 \times 13 + 9 = 14$$
$$27-\frac{3}{2}\times13+9=14$$
This is the not correct answer. Because the given equation is not satisfied and gives fractional values.
Option (c) $$-, \div$$
$$27 \div 3 \times 2 - 13 + 9 = 14$$
$$\frac{27}{3}\times2-13+9=14$$
$$9\times2-13+9=14$$
18-13+9=14
5+9=14
14=14
This is the correct answer. Becasue the given equation is satisifed.
Option (d) $$-, \times$$
$$27 \times 3 - 2 \div 13 + 9 = 14$$
This is the not correct answer. Because the given equation is not satisfied and gives fractional values.
By interchanging the given two signs which of the following equation will be correct?
$$+ and -$$
By interchanging '$$+$$' and '$$-$$'
(A) : $$13 - 14 \times 3 + 7 = 48$$
L.H.S. $$\equiv13+14\times3-7$$
= $$13+42-7=48=$$ R.H.S.
=> Ans - (A)
If the two signs, ' $$\div$$ and $$\times$$' and two numbers '2 and 8' are interchanged, then what will be the value of the following equation?
$$4 \times 8 \div 2 = ?$$
= $$4 \div2\times8$$
= $$\frac{4}{2}\times8$$
= $$2\times8$$
= 16
In the following question, which of the two signs will be interchanged to get the correct equation?
$$119 - 21 \div 7 + 117 \times 3 = 11$$
Option (a) $$\div\ and\ \times$$
$$119 - 21 \times 7 + 117 \div 3 = 11$$
119 - 147 + 39 = 11
11 = 11
The given equation is satisfied. So this is the correct answer.
Option (b) $$-\ and\ \times$$
$$119 \times 21 \div 7 + 117 - 3 = 11$$
$$119 \times 3 + 114 = 11$$
357 + 114 = 11
$$471\ne\ 11$$
The given equation is not satisfied. So this is not the correct answer.
Option (c) $$-\ and\ +$$
$$119 + 21 \div 7 - 117 \times 3 = 11$$
$$119 + 3 - 351 = 11$$
$$-229\ \ne\ 11$$
The given equation is not satisfied. So this is not the correct answer.Option (d) $$\div\ and\ +$$
$$119 - 21 + 7 \div 117 \times 3 = 11$$
The given equation is not satisfied. Becasue it will give the values in fraction. So this is not the correct answer.
Which two signs and two numbers should be interchanged to make the given equation correct?
$$54 - 45 \div 9 + 7 \times 11 = 14$$
We can check each of the options to get the correct answer.
Option (a) $$7\ and\ 54\ ,+\ and\ -$$
$$7 + 45 \div 9 - 54 \times 11 = 14$$
$$7 + 5 - 54 \times 11 = 14$$
This will not be the correct option. Because the given equation is not satisfied and get the negative value.
Option (b) $$9\ and\ 11,-\ and\ \div$$
$$54 \div 45 - 11 + 7 \times 9 = 14$$
This will not be the correct option. Because the given equation is not satisfied and get the fractional value.
Option (c) $$54\ and\ 45,+\ and\ \times$$
$$45 - 54 \div 9 \times 7 + 11 = 14$$
$$45-6\times7+11=14$$
$$45-42+11=14$$
3+11 = 14
This will be the correct answer. Because the given equation is satisfied.
Option (d) $$45\ and\ 11,\div\ and\ \ \times\ $$
$$54 - 45 \times 9 + 7 \div 11 = 14$$
This will not be the correct option. Because the given equation is not satisfied and gets the fractional value.
If 'A' is replaced by '$$+$$'; if 'B' is replaced by '$$-$$': 'C' is replaced by '$$\div$$' and 'D' replaced by '$$\times$$'. find the value of the following equation.
45C15B7A5D23
After interchanging the given two signs, what will be the value of $$11 \div 9 - 63 + 7 \times 2$$ ?
$$\div and +$$
$$11 \div 9 - 63 + 7 \times 2$$
= $$11 + 9 - 63 \div 7 \times 2$$
= $$11 + 9 - 9 \times 2$$
= 11 - 9 =2
So , the answer would be option a )2.
Find out the two signsto be interchanged for making following equation correct:
$$6 \div 5 + 12 \times 4 - 7 = 26$$
Option (a) $$\div\ and\ \times$$
$$6 \times 5 + 12 \div 4 - 7 = 26$$
$$30 + 3 - 7 = 26$$
33-7 = 26
26 = 26
The given equation is satisfied. So this will be the correct answer.
Option (b) $$\div\ and\ -$$
$$6 - 5 + 12 \times 4 \div 7 = 26$$
The given equation is not satisfied. Because it will give the values in fraction which is not possible. So this will not be the correct answer.
Option (c) $$+\ and\ -$$
$$6 \div 5 - 12 \times 4 + 7 = 26$$
The given equation is not satisfied. Because it will give the values in fraction which is not possible. So this will not be the correct answer.
Option (d) $$+\ and\ \times$$
$$6 \div 5 \times 12 + 4 - 7 = 26$$
The given equation is not satisfied. Because it will give the values in fraction which is not possible. So this will not be the correct answer.
Which of the following interchanges of signs and numbers would make the given equation correct?
$$8 \div 2 - 6 \times 4 + 3 = 13$$
If the given two numbers are interchanged, which of the following equations will become correct?
3 and 5
if we interchange 3 and 5 then-
6 + 3 $$\times$$ 2 - 5
= 6+6-5
=7
There is a number consisting of two digits, the digit in the units place is twice that in the tens place and if 2 be subtracted from the sum of the digits, the difference is equal to$$ \frac{1}{6}$$ thof the number. The number is
Let the two digit number be ab,
Where ab = 10a + b, and b = 2*a,
According to the Question,
a+b - 2 = 1/6(10a+b)
Multiply both side by 6,
6a + 6b - 12 = 10a + b
5b = 4a + 12,
Subtracting (b + 6a - 12 ) on both sides,
Substituting b = 2*a,
5(2a) = 4a + 12,
10a = 4a + 12,
Subtract 4a on both sides,
6a = 12,
Divide 6 on both sides,
a = 2,
b = 2*2 = 4,
Therefore , the number is 24
Which two numbers should be interchanged to make the below equation mathematically correct?
$$144 + 108 \div 12 - 16 \times 6 = 24$$
Option (a) 12, 6
$$144 + 108 \div 6 - 16 \times 12 = 24$$
$$144 + 18 - 192 = 24$$
$$-30\ne24$$
The given equation is not satisfied. So this is not the correct answer.
Option (b) 108, 144
$$108 + 144 \div 12 - 16 \times 6 = 24$$
$$108 + 12 - 96 = 24$$
120 - 96 = 24
24 = 24
The given equation is satisfied. So this is the correct answer.
Option (c) 108, 6
$$144 + 6 \div 12 - 16 \times 108 = 24$$
The given equation is not satisfied. Because it will give the values in fractions. So this is not the correct answer.
Option (d) 12, 16
$$144 + 108 \div 16 - 12 \times 6 = 24$$
The given equation is not satisfied. Because it will give the values in fractions. So this is not the correct answer.
Which two signs should be interchanged to make the following equation correct?
$$10 - 15 \times 9 + 6 \div 3 = 9$$
$$\frac{\sqrt{7}}{\sqrt{16+6\sqrt{7}}-\sqrt{16-6\sqrt{7}}}$$ is eual to
After interchanging the signs '$$\times$$ and $$\div$$', what will be the value of the given equation?
$$11 + 13 - 24 \times 3 \div 2 = ?$$
= $$11 + 13 - 24 \times 3 \div 2$$
Interchanging the signs '$$\times$$ and $$\div$$'.
= $$11 + 13 - 24 \div 3 \times 2$$
= $$11+13-8\times2$$
= 24-16
= 8
The value of $$24 \times 2 \div 12 + 12 \div 6 of 2 \div (15 \div 8 \times 4) of (28 \div 7 of 5)$$ is:
$$24 \times 2 \div 12 + 12 \div 6 of 2 \div (15 \div 8 \times 4) of (28 \div 7 of 5)$$
Solve using by BODMAS rule,
$$24 \times 2 \div 12 + 12 \div 12 \div (15 \div 8 \times 4) of (28 \div 35)$$
= $$24 \times 2 \div 12 + 12 \div 12 \div 7.5 of 0.8$$
= $$24 \times 2 \div 12 + 12 \div 12 \div 6$$
= 4 + 1/6 = $$4\frac{1}{6}$$
Which two signs should be interchanged to make the given equation correct?
$$9 + 12 \div 6 \times 8 - 4 = 14$$
By interchanging the given two signs which of the following equation will be incorrect?
÷ and +
Option (a) 12$$\div$$9$$\times$$31+3=105
$$12+9\times31\div3=105$$
$$12+9\times\frac{31}{3}=105$$
$$12+3\times31=105$$
12+93 = 105
105 = 105
The given equation is correct.
Option (b) 7$$\times$$16+4$$\div$$5=33
$$7\times16\div4+5=33$$
$$7\times4+5=33$$
$$28+5=33$$
33 = 33
The given equation is correct.
Option (c) 9$$\div$$11$$+11\times$$2=9
$$9+11\div11\times2=9$$
$$9+1\times2=9$$
$$11\ne\ 9$$
The given equation is not correct.
Option (d) 6$$\times$$11+2$$\div$$5=38
$$6\times11\div2+5=38$$
$$6\times\frac{11}{2}+5=38$$
$$3\times11+5=38$$
33+5 = 38
38 = 38
The given equation is correct.
A boy found the answer for the question "Subtract the sum of $$\frac{1}{4}$$ and $$\frac{1}{5}$$ from unity and express the answer in decimals" as 0.45. The percentage of error in his answer was
Select the option that is related to the third term in the same way as the second term is related to the first term.
6 : 18 :: 14 : .......
If digit 3 is interchanged with digit 1, then what will be the value of the following equation?
$$6 + 9 \div 1 \times 3 - 2 = ?$$
Which two signs need to be interchanged to make the given equation correct?
$$104 \div 8 + 6 - 9 \times 3 = 34$$
Option (a) $$+, -$$
$$104 \div 8 - 6 + 9 \times 3 = 34$$
$$13 - 6 + 27 = 34$$
7+ 27 = 34
34 = 34
The given equation is satisfied. So this is the correct answer.
Option (b) $$\div, +$$
$$104 + 8 \div 6 - 9 \times 3 = 34$$
The given equation is not satisfied. Because it will give the values in fraction which is not possible. So this is not the correct answer.
Option (c) $$-, \times$$
$$104 \div 8 + 6 \times 9 - 3 = 34$$
$$13 + 54 - 3 = 34$$
$$64\ne\ 34$$
The given equation is not satisfied. So this is not the correct answer.
Option (d) $$+, \times$$
$$104 \div 8 \times 6 - 9 + 3 = 34$$
$$13 \times 6 - 9 + 3 = 34$$
$$78 - 9 + 3 = 34$$
$$72\ne\ 34$$
The given equation is not satisfied. So this is not the correct answer.
Simplify : $$5 - 6.5 \div 13 + 2.3 \times 0.8 + 0.4$$
=$$5 - 6.5 \div 13 + 2.3 \times 0.8 + 0.4$$
=$$5 - 0.5 + 2.3 \times 0.8 + 0.4$$
=$$5 - 0.5 + 1.84 + 0.4$$
=$$4.5 1.84 + 0.4$$
=6.74
What is the value of $$\left[6\frac{1}{5}\times\frac{5}{6}of\left(\frac{2}{5}-\frac{16}{62}+\frac{11}{62}\right)\right]$$?
Expression : $$\left[6\frac{1}{5}\times\frac{5}{6}of\left(\frac{2}{5}-\frac{16}{62}+\frac{11}{62}\right)\right]$$
= $$(\frac{31}{5}\times\frac{5}{6})\times(\frac{2}{5}-\frac{5}{62})$$
= $$\frac{31}{6}\times\frac{99}{310}$$
= $$\frac{99}{60}=\frac{33}{20}$$
=> Ans - (B)
What is the value of $$\left[\left(\frac{1}{2}\div\frac{1}{4}-4\times\frac{1}{2}\times\frac{1}{3}\right)of\left(\frac{2}{3}\div\frac{4}{3}+\frac{1}{2}\right)\right]$$ ?
Expression : $$\left[\left(\frac{1}{2}\div\frac{1}{4}-4\times\frac{1}{2}\times\frac{1}{3}\right)of\left(\frac{2}{3}\div\frac{4}{3}+\frac{1}{2}\right)\right]$$
= $$\left[\left(\frac{1}{2}\times4-4\times\frac{1}{2}\times\frac{1}{3}\right)\times\left(\frac{2}{3}\times\frac{3}{4}+\frac{1}{2}\right)\right]$$
= $$[(2-\frac{2}{3})\times(\frac{1}{2}+\frac{1}{2})]$$
= $$(\frac{6-2}{3})\times1$$
= $$\frac{4}{3}$$
=> Ans - (D)
What is the value of x so that the seven digit number 5656x52 is divisible by 72?
To be divisible by 72 it should be divisible by 8 and 9
8 division rule is last 3 digits should be divisible by 8.
9 division rule is sum all the digits should be divisible by 9.
Only option satisfying is 7
For what value of x is the seven digit number 46393x8 divisible by 11 ?
Divisibility rule of 11 : If the difference of the alternating sum of digits of NN is 0 or a multiple of 11 , then N is divisible by 11.
46393x8
4 - 6 + 3 - 9 + 3 - x + 8 = 3 - x
So , value of x should be Option A) 3
If the 8-digit number is 789x531y is divisible by 72, then the value of (5x — 3y) is:
As per the given question,
789x531y is divisible by 72
The given number will be divisible by 72, if it is individually divisible by 8 and 9.
Divisibility by 8-Any number is divisible by 8if the last three digit of that number is divisible by 8.
last 3 digit is 31y, it will be divisible by 8 if y=2
Divisibility by 9-Any number is always divisible by 9 if the sum of the digit of any number is evenly divisible by 9.
Hence, the required number $$= 7+8+9+x+5+3+1+y=33+x+y$$
Now, y=2
the required number $$=33+x+2=35+x$$
if x=1, then it will be divisible.
Hence the value of $$5x-3y=5\times 1-3\times 2=5-6 =-1$$
What is the value of $$512 \div 16 + 4 \times \dfrac{5}{2} of \left(\dfrac{1}{8}+ \dfrac{1}{3}\right)$$?
$$512 \div 16 + 4 \times \dfrac{5}{2} of \left(\dfrac{1}{8}+ \dfrac{1}{3}\right) = \dfrac{512}{16} + 4 \times \dfrac{5}{2} \times \dfrac{11}{24} = 32 + \dfrac{55}{12} = \dfrac{384+55}{12} = \dfrac{439}{12}$$
What is the value of the square root of:
$$[\left\{(100 of 0.9 \times 0.8 - 7 \times 1.2 \div 0.2 + 5 \times 4 - 3 \times 2)\right\}\div 10 + 1.85]$$
= $$[\left\{(100\ of\ 0.9\times0.8-7\times1.2\div0.2+5\times4-3\times2)\right\}\div10+1.85]$$
= $$[\left\{(90\times0.8-7\times6+20-6)\right\}\div10+1.85]$$
= $$[\left\{(72-42+20-6)\right\}\div10+1.85]$$
= $$[\left\{44\right\}\div10+1.85]$$
= $$[4.4+1.85]$$
= 6.25
value of the square root of 6.25 = 2.5
What should come in place of the question mark (?) in the following question?
$$[((16\div4)\times4)\div4]=?$$
Using BODMAS rule,
$$[((16\div4)\times4)\div4]$$
$$[(4\times4)\div4]=4$$
Option C is correct.
A is the smallest three-digit number which when divided by 3, 4 and 5 leaves remainders 1, 2 and 3 respectively. What is the sum of the digits of A?
Here the LCM of 3, 4 and 5 is 60.
We need the smallest three-digit number. so we can multiply 60 by 2. So $$60\times\ 2$$ = 120.
The number is divided by 3, 4 and 5 respectively, and leaves 1, 2, and 3 as a remainder.
So 3-1 = 2, 4-2 = 2, 5-3 = 2
Hence 120 will be subtracted by 2.
So the smallest three-digit number = A = 120-2 = 118
Sum of the digits of A = 1+1+8 = 10
We can also obtain the value 'A' by checking the random number starting from the smallest one. In this (A-3) will be the multiple of five. The numbers can be 103, 108, 113, 118 etc.. Now 113 and 108, when subtracted by 1, then it will not be divisible by 3. Now 103 and 118 are remaining. 103 when subtracted by 2, then it will not be divisible by 4. Hence we are left with 118 which is following all the given conditions.
DIRECTIONS: What should come in place of question mark (?) in the following questions?
1072 + [{8240 + (-9213)} - {(2863 - (4329 - 2143)}] = ?
1072 + [{8240 + (-9213)} - {(2863 - (4329 - 2143)}]
=1072 + [{8240 + (-9213)} - {(2863 - 2186}]
=1072 + [{8240 + (-9213)} - 677]
=1072-1650
=-578
If $$3\sqrt{3}x^3 - 2\sqrt2 y^3 = (\sqrt3 x - \sqrt2 y)(Ax^2 + By^2 + Cxy)$$, then the value of $$(A \times B) \div C$$ is:
If 40% of $$\frac{2}{5}$$ of a number is 24, then the number is:
$$\frac{40}{100}\times\ \frac{2}{5}\times\ X=24$$
$$\frac{2}{5}\times\ \frac{2}{5}\times\ X=24$$
$$\frac{4}{25}\times\ X=24$$
$$X=150$$
The value of $$[0.08 \div 1.2 of (3.4 - 2.6) \times 0.8 of 3.2] of \frac{9}{16}$$ lies between:
=$$[0.08 \div 1.2 of (3.4 - 2.6) \times 0.8 of 3.2] of \frac{9}{16}$$
=$$[0.08 \div 1.2 of 0.8 \times 0.8 of 3.2] of \frac{9}{16}$$
=$$[0.08 \div 0.96 \times 2.56] \times \frac{9}{16}$$
=$$[(1/12) \times 2.56] \times \frac{9}{16}$$
=$$(16/75) \times \frac{9}{16}$$
=9/75
=0.12
What is the sum of digits of the least number which when divided by 21, 28, 30 and 35 leaves the same remainder 10 in each case but is divisible by 17?
L.C.M. (21,28,30,35) = 420
Least number that will leave remainder 10 will be of the form = $$420n+10$$
Now, if $$n=1$$, number = 430, which is not divisible by 17
But, when $$n=2$$, number = 850, which is divisible by 17
Thus, sum of digits of number 850 = $$8+5+0=13$$
=> Ans - (B)
What is the value of $$\left(24 \div 4 - \frac{2}{3} of \frac{21}{8} \div \frac{1}{4}\right)$$?
$$\left(24 \div 4 - \dfrac{2}{3} of \dfrac{21}{8} \div \dfrac{1}{4}\right) = \dfrac{24}{4} - \dfrac{2}{3} \times \dfrac{21}{8} \times 4 = 6 - 7 = -1$$
The value of $$56 + (4)^3 - 3 \times (3)^2$$ is:
$$56+4^3\ -3\times\ 9$$
$$56+64-27$$
120-27 =93
What approximate value should come in place of the question mark (?) in the following questions?
$$21 + 68 \div 17 = ? $$
By applying BODMAS we have
=$$21+(68\div17)$$
=21+4
=25
Find the value of:
$$(7 \times 6 + 5 - 15) \div 4 + 6 \div 3 - 4 + 18 \div 3$$
$$(7 \times 6 + 5 - 15) \div 4 + 6 \div 3 - 4 + 18 \div 3 = \dfrac{32}{4} + \dfrac{6}{3} - 4 + \dfrac{18}{3} = 8 + 2 - 4 + 6 = 12$$
Find the value of the following expression.
$$51 \div 3 \times 15 = ?$$
By simplification we get 17*15=255
The value of $$[12 \times 5 - \left\{200 - (501 + 247 - 386)\right\}] \div 2$$ is:
(60-(200-(501+247-386)))/2
(60+162)/2
222/2
111
The value of $$\frac{1}{3}+\frac{6}{7}\div\frac{6}{3}+\frac{8}{9}-\frac{2}{3}\times\frac{4}{3}$$ is:
$$\dfrac{1}{3}+\dfrac{6}{7}\div\dfrac{6}{3}+\dfrac{8}{9}-\dfrac{2}{3}\times\dfrac{4}{3} $$
$$= \dfrac{1}{3} + \dfrac{6}{7}\times\dfrac{3}{6}+\dfrac{8}{9}-\dfrac{8}{9}$$
$$= \dfrac{1}{3} + \dfrac{3}{7} = \dfrac{7+9}{21}$$
$$= \dfrac{16}{21}$$
What is the value of $$10 - [6 - 4 - (2\div 1 - 2)]$$?
$$10 - [6 - 4 - (2\div 1 - 2)] = 10 - [2 - (2 - 2)] = 10 - [2 - 0] = 10-2 = 8$$
What is the value of $$(6 of 4 \div 16 \times 48) \div 8 \times 4 + 2 \times 3 \div 6 + 5(6 - 2)$$ ?
$$=(6\times\frac{4}{16}\times48)\div8\times4+2\times3\div6+5\times4$$
$$=(6\times4\times3)\div8\times4+2\times\frac{3}{6}+20$$
$$=\frac{72}{8}\times4+1+20$$
$$=36+1+20$$
= 57
What is the value of $$7\frac{1}{4} + [6 + (5 - 8 \div 4) - 1]$$?
$$7\frac{1}{4} + [6 + (5 - 8 \div 4) - 1] = \dfrac{29}{4} + [6+(5-\dfrac{8}{4})-1]$$
$$= \dfrac{29}{4} + [6+5-2-1] = \dfrac{29}{4} + 8$$
$$= \dfrac{29+32}{4} = \dfrac{61}{4}$$
$$\frac{4^2+4}{5}+5\times2-3$$ of $$4$$ is:
$$\frac{4^2+4}{5}+5\times2-3$$ of $$4$$
=$$\frac{20}{5}+5\times2-12$$
=$$4+5\times2-12$$
=4+10-12
=14-12
=2
Simplify: $$8+3-\left(\frac{5}{2}\times\frac{1}{3}\right) of \frac{12}{5}+\frac{4}{3}\times\frac{3}{8}$$
=$$8+3-\left(\frac{5}{2}\times\frac{1}{3}\right) of \frac{12}{5}+\frac{4}{3}\times\frac{3}{8}$$
=$$8+3-2+\frac{4}{3}\times\frac{3}{8}$$
=$$8+3-2+\frac{1}{2}$$
=9.5
What is the value of $$(1 \times 2 + 2 \times 3 - 3 \times 4 + 4 \times 5 - 5 \times 6 + 6 \times 7)$$?
= $$(1 \times 2 + 2 \times 3 - 3 \times 4 + 4 \times 5 - 5 \times 6 + 6 \times 7)$$
= (2+6-12+20-30+42)
= (2+6+20+42-12-30)
= (70-42)
= 28
What is the value of $$80 \div 40 - 10 - 5 \times 4 of \left(\frac{1}{3} \div \frac{10}{3}\right)$$?
$$80 \div 40 - 10 - 5 \times 4 of \left(\frac{1}{3} \div \frac{10}{3}\right) = \dfrac{80}{40} - 10 - 5 \times 4 \times (\dfrac{1}{3}\times\dfrac{3}{10})$$
= $$2 - 10 - 5\times4\times\dfrac{1}{10} = 2 - 10 - 2 = -10$$
What is the value of $$\left[22\frac{3}{4}\div\frac{14}{3}of\left(8-\frac{1}{5}+4-2\div\frac{1}{2}\right)\right]$$?
$$\left[22\frac{3}{4}\div\frac{14}{3}of\left(8-\frac{1}{5}+4-2\div\frac{1}{2}\right)\right] = \dfrac{91}{4} \times \dfrac{3}{14} \times \dfrac{5}{39} = \dfrac{5}{8}$$
What should come in place of question mark (?) in the following questions?
$$383\div25\times2.5+12=?$$
If $$A = 7 \times 3 \div (2 + 4) + 4 - 2, B = 3 \div 6 \times 4 + 2 - 2 of 3$$ and $$C = 6 \div 2 + 4 \times 3 - 2$$. What is the value of $$(A + B - C)$$?
A =$$ 7 \times 3 \div (2 + 4) + 4 - 2 $$
= $$ 7 \times 3 \div 6 + 4 - 2 $$
= $$ 7 \times \frac{1}{2} + 4 - 2 $$
= $$ \frac{7}{2} + 2 $$
= $$ \frac{11}{2} $$
B = $$ 3 \div 6 \times 4 + 2 - 2 of 3 $$
= $$ 3 \div 6 \times 4 + 2 - 6 $$
= $$ \frac{1}{2} \times 4 + 2 - 6 $$
= -2
C =$$ 6 \div 2 + 4 \times 3 - 2 $$
= $$ 3 + 4 \times 3 - 2 $$
= $$ 3 + 12 - 2 $$
= 13
$$ (A + B - C) = \frac{11}{2} - 2 - 13 = \frac{-19}{2} $$
If $$\sqrt{7\sqrt{7\sqrt{7\sqrt{7....}}}} = (343)^{y - 1}$$, then y is equal to
$$ \sqrt{7\sqrt{7\sqrt{7\sqrt{7....}}}} = x $$
$$ x = \sqrt{7}x $$
$$ x^2 = 7x $$
$$ x^2 - 7x = 0 $$
x=0,7
neglect 0 x = 7
now $$ 7 = (343)^{y-1} $$
$$ (343)^{\frac{1}{3}} = (343)^{y-1} $$
$$ \frac{1}{3} = y - 1 $$
$$ y = \frac{4}{3} $$
If the six digit number 4x573y is divisible by 72 then the value of (x + y) is:
4x573y will be divisible by 72
to divide that no it should be divided by 9 and 8 both
The value of $$4 \times 2 \div 4 of (4 + 4 \div 4 of 4) - (4 \div 4 of 2 \times 4)$$ is:
= $$4\times2\div4\ of\ (4+4\div4\ of\ 4)-(4\div4\ of\ 2\times4)$$
= $$4\times2\div4\ of\ (4+4\div16)-(4\div8\times4)$$
= $$4\times2\div4\ of\ (4+\frac{1}{4})-\left(\frac{1}{2}\times4\right)$$
= $$4\times2\div4\ of\ (\frac{17}{4})-2$$
= $$4\times2\div17-2$$
= $$4\times\frac{2}{17}-2$$
= $$\frac{8}{17}-2$$
= $$\frac{8}{17}-\frac{34}{17}$$
= $$-\frac{26}{17}$$
What is the value of $$(3 \times 1500 \div 40 + 5 \div \frac{2}{7} of 70)$$?
Expression : $$(3 \times 1500 \div 40 + 5 \div \frac{2}{7} of 70)$$
= $$(3 \times \frac{1500}{40}) + (5 \div 20)$$
= $$\frac{450}{4}+\frac{1}{4}=\frac{451}{4}$$
=> Ans - (C)
What is the value of:
$$\dfrac{\left(1 - \dfrac{3}{4}\right) + \dfrac{1}{2} of \dfrac{6}{10}}{\dfrac{2}{3} \div \dfrac{4}{10} + \left(1 - \dfrac{1}{5}\right) of \dfrac{25}{16}}$$?
= $$\dfrac{\left(1 - \dfrac{3}{4}\right) + \dfrac{1}{2} of \dfrac{6}{10}}{\dfrac{2}{3} \div \dfrac{4}{10} + \left(1 - \dfrac{1}{5}\right) of \dfrac{25}{16}}$$
= $$\frac{\left(\frac{4}{4}-\frac{3}{4}\right)+\frac{1}{2}of\frac{3}{5}}{\frac{2}{3}\div\frac{2}{5}+\left(\frac{5}{5}-\frac{1}{5}\right)of\frac{25}{16}}$$
= $$\frac{\frac{1}{4}+\frac{3}{10}}{\frac{2}{3}\times\frac{5}{2}+\left(\frac{4}{5}\right)of\frac{25}{16}}$$
= $$\frac{\frac{5}{20}+\frac{6}{20}}{\frac{5}{3}+\frac{5}{4}}$$
= $$\frac{\frac{11}{20}}{\frac{20}{12}+\frac{15}{12}}$$
= $$\frac{\frac{11}{20}}{\frac{35}{12}}$$
= $$\frac{11}{20}\times\ \frac{12}{35}$$
= $$\frac{11}{5}\times\ \frac{3}{35}$$
= $$\frac{33}{175}$$
What should come in place of question mark (?) in the following questions?
$$(140+80\times2-24)\div(80+20\times3-40)=?$$
$$(140+80\times2-24) = 140+160-24 = 276$$
$$(80+20\times3-40) = 80+60-40 = 100$$
Therefore, $$(140+80\times2-24)\div(80+20\times3-40) = \dfrac{276}{100} = 2.76$$
The value of:
$$4 \div 2 + 3 \times 6 - 7$$ is:
$$4 \div 2 + 3 \times 6 - 7 = 2+18-7 = 13$$
What is the least number which when increased by 8 is exactly divisible by 4, 5, 6 and 7?
LCM of 4, 5, 6 and 7 $$=420$$
Therefore the required number is $$=420-8=412$$
Option C is correct.
What is the value of $$1040 \div 65 - 8 \times \frac{1}{2} of \left(\frac{1}{2} - \frac{1}{3}\right)$$?
$$1040 \div 65 - 8 \times \frac{1}{2} of \left(\frac{1}{2} - \frac{1}{3}\right) = \dfrac{1040}{65} - 8 \times \dfrac{1}{2} \text{of} \dfrac{1}{6} = \dfrac{1040}{65} - 8 \times \dfrac{1}{12} = 16 - \dfrac{2}{3} = \dfrac{48-2}{3} = \dfrac{46}{3}$$
What is the value of $$(14 \div 49 - 3 \div \frac{7}{2} of 5)$$?
$$(14 \div 49 - 3 \div \frac{7}{2} of 5) = (\dfrac{14}{49} - 3 \div \dfrac{35}{2}) = \dfrac{2}{7} - 3 \times \dfrac{2}{35} = \dfrac{2}{7} - \dfrac{6}{35} = \dfrac{10-6}{35} = \dfrac{4}{35}$$
What is the value of $$3 \div 3 of 3 + 2 \div 4 + (4 \times 2 - 2) \div 12 + 4$$?
= $$3\div3\ of\ 3+2\div4+(4\times2-2)\div12+4$$
= $$\frac{3}{9}+\frac{2}{4}+(8-2)\div12+4$$
= $$\frac{1}{3}+\frac{1}{2}+\frac{6}{12}+4$$
= $$\frac{1}{3}+\frac{1}{2}+\frac{1}{2}+4$$
= $$\frac{1}{3}+1+4$$
= $$5\frac{1}{3}$$
= $$\frac{16}{3}$$
If the 8-digit number 179x091y is divisible by 88, the value of (5x — 8y) is:
Given that,
179x091y is divisible by 88.
We know that $$88=11\times 8$$
The given number will be divisible by 88, if it is individually divisible by 11 and 8.
Divisibility by 8 - Any number is divisible by 8, if the last 3 digit of that number is divisible by 8.
So, last 3 digit is 91y,
91y will be divisible by 8 if, y=2,
Divisibility by 11- Any number is divisible by 11, if the difference between the sum of odd place digit and sum of even place digit is
divisible by 11.
179x091y will be divisible by 11 if $$y+9+x+7-1-0-9-1=y+x+5=x+7$$
From the above, if x=4, then it will be divisible by 11.
Hence the value of x and y will be 4 and 2.
Hence,$$ (5x — 8y)=5\times4-8\times 2=20-16=4$$
Let x be the least number which when divided by 12, 15, 18, 20 and 27, the remainder in each case is 2, but x is divisible by 23. If x is divided by the sum of its digits then the quotient is:
L.C.M. (12,15,18,20,27) = 540
Least number which when divided by 12, 15, 18, 20 and 27, the remainder in each case is 2 = $$x=540n+2$$, where $$n$$ is any natural number.
Also, $$x$$ is divisible by 23, thus by hit and trial, we get $$n=4$$ and $$x=2162$$
Now, when $$2162$$ is divided by $$(2+1+6+2)=11$$, quotient = $$2162=11\times196+6$$
$$\therefore$$ Quotient = 196
=> Ans - (A)
The missing term in the sequence 2, 3, 5, 7,11, ... 17, 19 is
2, 3, 5, 7,11, 13,17, 19
all are consecutive prime numbers
What should come in place of question mark (?) in the following questions?
$$? = (45 \times 11) \div 3$$
By applying BODMAS we have $$(45 \times 11) \div 3$$
=$$15\times11$$
=165
The product of two numbers is 48. If one number equals "The number of wings of a bird plus 2 times the number of fingers on your hand divided by the number of wheels of a Tricycle". Then the other number is
A student was asked to find the value of $$9\frac{4}{9}\div11\frac{1}{3} of \frac{1}{6} + \left(1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}\right) \times 2\frac{1}{6} of \frac{2}{3} \div \frac{4}{3} of \frac{2}{3}$$. His answer was $$19\frac{1}{4}$$. What is the difference between his answer and the correct answer
$$9\frac{4}{9}\div11\frac{1}{3} of \frac{1}{6} + \left(1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}\right) \times 2\frac{1}{6} of \frac{2}{3} \div \frac{4}{3} of \frac{2}{3}$$
$$\frac{85}{9}\div\frac{34}{3} of \frac{1}{6} + \left(\frac{4}{3} \times \frac{9}{5} \div \frac{3}{5}\right) \times \frac{13}{6} of \frac{2}{3} \div \frac{4}{3} of \frac{2}{3}$$
$$\frac{85}{9}\div\frac{34}{18} + 4 \times \frac{13}{9} \div \frac{8}{9}$$
$$\frac{85}{9}\div\frac{34}{18} + \frac{13}{2}$$
$$ 5\frac{13}{2} = \frac{23}{2}$$
Answer of the student = $$19\frac{1}{4} = \frac{77}{4}$$
Difference = $$\frac{77}{4} - \frac{23}{2} = \frac{31}{4} = 7\frac{3}{4}$$
$$\frac{4}{5}\div\frac{4}{5}$$ of $$\frac{1}{10}\times\frac{1}{10}= ?$$
$$\dfrac{4}{5}\div\dfrac{4}{5}$$ of $$\dfrac{1}{10}\times\dfrac{1}{10}= \dfrac{4}{5} \times \dfrac{50}{4} \times \dfrac{1}{10}$$
$$= 10\times \dfrac{1}{10} = 1$$
If a nine-digit number 985x3678y is divisible by 72. then the value of (4x — 3y) is:
985x3678y is divisible by 72 , so it is divisible by both 9 & 8.
Divisibility rule of 8 : Last 3 digits of a whole number should be divisible by 8.
So y = 4
Divisibility rule of 9 : Sum of all the digits in whole number should be divisible by 9.
Sum = 50 + x
x = 4
4x - 3y = 4 $$\times$$ 4 - 3$$\times$$ 4 = 4
So , the answer would be option b)4.
The value of x in the given equation $$(5)^2 + (6)^2 + (30)^2 = (x)^2$$ is:
$$5^2+6^2+30^2=X^2$$
$$25+36+900=X^2$$
$$X^2=961$$
$$X^{ }=\sqrt{961}$$
$$X^{ }=31$$
The wrong number in the sequence 8, 13, 21, 32, 47, 63, 83 is
8, 13, 21, 32, 47, 63, 83
8 + 5 = 13
13 + 8 = 21 (5 + 3 = 8)
21 + 11 = 32 (8 + 3 = 11)
32 + 14 = 46 (11 + 3 = 14)
46 + 17 = 63 (14 + 3 =17)
63 + 20 = 83 (17 + 3 = 20)
Here wrong term is 47
What is the value of $$2 of 16 \div 48 \times 12 + 4 \div 8 \times 16 + (7 - 2) \times 25 \div 15?$$
= $$2 of 16 \div 48 \times 12 + 4 \div 8 \times 16 + (7 - 2) \times 25 \div 15$$
= $$2\times\frac{16}{48}\times12+\frac{4}{8}\times16+5\times\frac{25}{15}$$
= $$2\times\frac{16}{4}+\frac{1}{2}\times16+5\times\frac{5}{3}$$
= $$8+8+\frac{25}{3}$$
= $$16+\frac{25}{3}$$
= $$\frac{48+25}{3}$$
= $$\frac{73}{3}$$
What is the value of $$\left(5 \div \frac{1}{5} of \frac{25}{4} + \frac{20}{3} \div \frac{100}{9}\right)$$?
$$\left(5 \div \frac{1}{5} of \frac{25}{4} + \frac{20}{3} \div \frac{100}{9}\right)$$
$$= 5 \div \dfrac{1}{5}\times\dfrac{25}{4} + \dfrac{20}{3} \times \dfrac{9}{100}$$
$$= 5 \div \dfrac{5}{4} + \dfrac{3}{5} = \dfrac{5}{5}\times4 + \dfrac{3}{5} = 4+\dfrac{3}{5} = \dfrac{20+3}{5} = \dfrac{23}{5}$$
What is the value of $$\left[88 - 44 \div (22 \times 4) of \left(\frac{1}{2} - \frac{1}{4} \div \frac{1}{8}\right)\right]$$?
$$\left[88 - 44 \div (22 \times 4) of \left(\frac{1}{2} - \frac{1}{4} \div \frac{1}{8}\right)\right] = [88 - 44 \div (22 \times 4) of (\dfrac{1}{2} - 2)]$$
= $$88 - 44 \div 88 of \dfrac{(-3)}{2} = 88 - 44 \div (-132) = 88 + \dfrac{1}{3} = \dfrac{264+1}{3} = \dfrac{265}{3}$$
What is the value of x so that the seven digit number 6913 x 08 is divisible by 88?
Given that,
6913 x 08
The given number will be divisible by 88 if it will be individually divisible by 11 and 8.
Divisibility of 8:
Any number is divisible by 8 if the last three digits of that number will be divisible by 8.
the minimum possible value for which it is divisible by 8 is x=0,2,4,6,8
Divisibility by 11:
A number is divisible by 11 if we subtract and then add the digits in an alternate pattern from left to right, if it is either 0 or 11, then it will be divisible by 11 otherwise not.
$$\Rightarrow 6913 x 08$$
$$\Rightarrow (8+x+1+6) - (0+3+9)=15-12+x=3+x $$
There is only one value for which both are satisfying the condition, which is x=8.
Hence, the number will be 6913808.
Hence, the minimum value of x should be 8.
$$\frac{4}{7} of \frac{8}{9} \div \frac{8}{7} \times 180 of \frac{1}{9} = ?$$
By using BODMAS we have
=$$(32/63)\div(8/7)\times20$$
=$$(32/63)\times(7/8)\times20$$
=$$(4/9)\times20$$
=80/9
If the 8-digit number 2074x4y2 is divisible by 88, then the value of (4x + 3y) is:
Given that 2074x4y2 is divisible by 88,
This will be divisible by 88 if, it is individually divisible by 11 and 8.
Divisibility by - Any number is divisible by 8, if the last 3 digit of that number is divisible by 8.
4y2 it will be divisible by 8 if, y=3 or y=7
Divisibility by 11- Any number is divisible by 11 if the difference between the sum of odd place digit and sum of even place digit is divisible by 11.
$$2+4+4+0-x-y-7-2=1-x-y$$
Now y=3 then x=9
if y=7 then x=5
Now, substituting the values in the equation,
if x=9 and y=3 then $$ (4x + 3y)=4\times 9+3\times 3=36+9=45 $$
if x=5 and y=7 then$$ (4x + 3y)=4\times 5+3\times 7=20+21=41$$
The value of
$$1\frac{2}{3} \div \left\{\frac{3}{7} of \frac{14}{5} \times 1\frac{2}{3} - \left(3\frac{1}{2} - 2\frac{1}{6} \right)\right\} + \frac{1}{2} \div \frac{3}{2} of \frac{1}{2}$$ is:
Given Equation :
$$1\frac{2}{3} \div \left\{\frac{3}{7} of \frac{14}{5} \times 1\frac{2}{3} - \left(3\frac{1}{2} - 2\frac{1}{6} \right)\right\} + \frac{1}{2} \div \frac{3}{2} of \frac{1}{2}$$ is
Lets solve it as per the rule of BODMAS :
= $$\frac{5}{3}\div\left\{\frac{3}{7}of\frac{14}{5}\times\frac{5}{3}-\left(\frac{5}{2}-\frac{13}{6}\right)\right\}+\frac{1}{2}\div\frac{3}{2}of\frac{1}{2}$$
= $$\frac{5}{3}\div\left\{\frac{3}{7}of\frac{14}{5}\times\frac{5}{3}-\left(\frac{4}{3}\right)\right\}+\frac{1}{2}\div\frac{3}{2}of\frac{1}{2}$$
= $$\frac{5}{3}\div\left\{2-\frac{4}{3}\right\}+\frac{1}{2}\div\frac{3}{2}of\frac{1}{2}$$
= $$\frac{5}{3}\div\frac{2}{3}+\frac{1}{2}\div\frac{3}{2}of\frac{1}{2}$$
= $$\frac{5}{3}\times\ \frac{3}{2}+\frac{1}{2}\div\frac{3}{4}$$
= $$\frac{5}{3}\times\ \frac{3}{2}+\frac{1}{2}\times\frac{4}{3}$$
= $$\frac{5}{2}+\frac{2}{3}$$
= $$\frac{19}{6}$$
= $$3\frac{1}{6}$$
Hence, Option A is correct.
The value of
$$3 \div 21 of 3 \times 7 + 24 \times 6 \div 18 - 3 \div 2 + 3 - 2 + 2 \times 3 \div 6$$ is:
$$3\div63\times7+24\times\frac{1}{3}-\frac{3}{2}+3-2+2\times\frac{1}{2}$$
$$\frac{1}{21}\times7+8-\frac{3}{2}+3-2+1$$
$$\frac{1}{3}+8-\frac{3}{2}+3-2+1$$
$$10+\frac{1}{3}-\frac{3}{2}$$
$$10+\frac{2}{6}-\frac{9}{6}$$
$$10-\frac{7}{6}$$
$$\frac{53}{6}$$
$$8\frac{5}{6}$$
What is the value of $$\left(2000 \div \frac{1}{2} of \frac{25}{2} \times \frac{5}{2} of \frac{4}{25} - 5\right)$$?
$$\left(2000 \div \dfrac{1}{2} of \dfrac{25}{2} \times \dfrac{5}{2} of \dfrac{4}{25} - 5\right) = 2000 \div \dfrac{25}{4} \times \dfrac{2}{5} - 5 = \dfrac{2000}{25}\times4 \times \dfrac{2}{5} - 5 = 128 - 5 = 123$$
Find the value of $$5\frac{1}{2} - \left[3\frac{1}{4} + 6 - 4 \div 2\right]$$
$$5\frac{1}{2} - \left[3\frac{1}{4} + 6 - 4 \div 2\right] = \dfrac{11}{2} - [\dfrac{13}{4} + 6 - \dfrac{4}{2}]$$
$$= \dfrac{11}{2} - [\dfrac{13}{4} + 6 - 2] = \dfrac{11}{2} - [\dfrac{13}{4} + 4] = \dfrac{11}{2} - \dfrac{29}{4} = \dfrac{22-29}{4} = \dfrac{-7}{4}$$
If x=$$a^{\frac{1}{2}}+a^{\frac{-1}{2}}$$, y=$$a^{\frac{1}{2}}-a^{\frac{-1}{2}}$$ then the value of$$ (x^{4}-x^{2}y^{2}-1)+(y^{4}-x^{2}y^{2}+1)$$
The difference between upper limit and lower limit of the class interval is called as:
The difference between upper limit and lower limit of the class interval is called as Class Size.
Class Size = Upper Limit $$-$$ Lower Limit
Option D is correct.
What is the value of $$24 - [48 \div \left\{48 \times (48 \div (24 \times 24))\right\}]$$?
$$24 - [48 \div \left\{48 \times (48 \div (24 \times 24))\right\}] = 24 - [48 \div {48 \times \dfrac{1}{12}}] = 24 - [48 \div 4] = 24 - 12 = 12$$
What is the value of $$\left[4+200\div 50 + \frac{3}{2} of\left(\frac{1}{5} - \frac{1}{4}\right)\right]$$?
Expression : $$\left[4+200\div 50 + \frac{3}{2} of\left(\frac{1}{5} - \frac{1}{4}\right)\right]$$
= $$[4+4+(\frac{3}{2}\times\frac{-1}{20})]$$
= $$8-\frac{3}{40}$$
= $$\frac{320-3}{40}=\frac{317}{40}$$
=> Ans - (A)
What is the value of $$\left[\frac{4}{5} \div \frac{5}{8} - \frac{7}{5} + \frac{2}{15} of \left(\frac{3}{2} \div \frac{4}{5}\right)\right]$$?
$$\left[\dfrac{4}{5} \div \dfrac{5}{8} - \dfrac{7}{5} + \dfrac{2}{15} of \left(\dfrac{3}{2} \div \dfrac{4}{5}\right)\right]$$
$$= \dfrac{4}{5}\times\dfrac{8}{5} - \dfrac{7}{5} + \dfrac{2}{15} \times \dfrac{3}{2} \times \dfrac{5}{4} $$
$$= \dfrac{32}{25} - \dfrac{7}{5} + \dfrac{1}{4} = \dfrac{128-140+25}{100} = \dfrac{13}{100}$$
0.15% of $$33\frac{1}{3}\%$$ of 180000 is:
Given Equation : 0.15% of $$33\frac{1}{3}\%$$ of 180000
Lets solve it as per the rule of BODMAS :
$$\frac{0.15}{100}\times\ \frac{100}{3\times\ 100}\times\ 180000$$
$$=90$$
Hence, Option B is correct.
What is the value of
$$\frac{5}{4} of \frac{12}{5} \div \frac{4}{25} + \frac{1}{2} \times \frac{3}{4}$$?
$$\dfrac{5}{4} of \dfrac{12}{5} \div \dfrac{4}{25} + \dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{5}{4} \times \dfrac{12}{5} \times \dfrac{25}{4} + \dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{75}{4} + \dfrac{3}{8} = \dfrac{150+3}{8} = \dfrac{153}{8}$$
$$11^2 + 11^4 \div 11^3 of 11 - 11 $$= ?
By simplifying we get 121+1-11
=122-11
=111
If 10-digit number 67127y76x2 is divisible by 88, then the value of (7x- 2y)is:
Given, 10-digit number 67127y76x2 is divisible by 88 then the number must be divisible by 8 and 11.
If the number is divisible by 8, then the last three digits should be divisible by 8
$$\Rightarrow$$ 6x2 is divisible by 8
$$\Rightarrow$$ x = 3
If the number is divisible by 11 then,
Sum of digits at even place - Sum of digits at odd place = 0 or multiple of 11
$$\Rightarrow$$ (7+2+y+6+2)-(6+1+7+7+x) = 0 or multiple of 11
$$\Rightarrow$$ 17 + y - 21 - x = 0 or multiple of 11
$$\Rightarrow$$ 17 + y - 21 - 3 = 0 or multiple of 11
$$\Rightarrow$$ y - 7 = 0 or multiple of 11
The only possibility is y - 7 = 0
$$\Rightarrow$$ y = 7
$$\therefore\ $$7x - 2y = 7(3) - 2(7) = 21 - 14 = 7
Hence, the correct answer is Option B
$$\sqrt{729} \times 56 \div 8 = ?$$
The approximate value of $$(4488 \div 11.01 - 7.98) \div 15.99$$ is:
$$\ \frac{\frac{4488}{11.01}-7.98\ }{15.99}$$
$$\ \frac{\frac{4488}{11}-8}{16}$$
$$\ \frac{408-8}{16}$$
$$\ \frac{400}{16}$$
$$\ 25$$
The value of $$64 \div 2 \times (9 \div 3) \times 3 \div 9 - 32$$ is:
$$64 \div 2 \times (9 \div 3) \times 3 \div 9 - 32 = \dfrac{64}{2} \times 3 \times \dfrac{3}{9} - 32 = 32-32 = 0$$
What is the value of $$\left[100 \div 50 - 25 - 55 of \left(\frac{1}{3}\times\frac{11}{9}\right)\right]$$ ?
Expression : $$\left[100 \div 50 - 25 - 55 of \left(\frac{1}{3}\times\frac{11}{9}\right)\right]$$
= $$\left[(\frac{100}{50}) - 25 - \left(55 \times \frac{11}{27}\right)\right]$$
= $$(2-25)-\frac{605}{27}$$
= $$\frac{-621-605}{27}=\frac{-1226}{27}$$
=> Ans - (D)
$$12^2+16\ of\ 3-20\div4=?$$
= $$12^2+16\ of\ 3-20\div4$$
= $$144+48-\frac{20}{4}$$
= $$144+48-5$$
= 187
If the six digit number 6x2904 is divisible by 88, then the value ofx is:
It will be divisible by 11
so using divisibility of 11
we get 13+x-8 =0 or 11k
so it cannot be 0
it will be 11 and we get x =6
Let x be the least multiple of 29 which when divided by 20, 21, 22, 24 and 28 then the remainders are 13, 14, 15, 17 and 21 respectively. What is the sum of digits of x?
Since, the difference between the all the numbers are : (20-13), (21-14) = 7
Thus, L.C.M. (20,21,22,24,28) = 9240
Hence, required number will be of the form = $$9240k-7=$$ multiple of 29
By hit and trial, we see that $$k=2$$ satisfy above equation, thus required number = $$(9240\times2)-7=18473$$
=> Sum of digits = 23
=> Ans - (D)
$$\sqrt{\frac{25.60}{72.90}} + \sqrt{\frac{0.10}{8.10}} = ?$$
$$\sqrt{\ \frac{25.60}{72.90}\cdot\frac{10}{10}}+\sqrt{\ \frac{0.10}{8.10}\cdot\frac{10}{10}\ \ \ }$$
(16/27)+(1/9)
(16+3)/27
19/27
The value of $$99\frac{95}{99} \times 99 - 95$$ is:
= $$99\frac{95}{99} \times 99 - 95$$
= $$\frac{\left(99\times\ 99\right)+95}{99}\times99-95$$
= $$\left(99\times\ 99\right)+95-95$$
= $$\left(99\times\ 99\right)+0$$
= 9801
The value of
$$\frac{1}{4} \times \frac{3}{4} \div 1\frac{1}{4} of \frac{2}{5} - \left[\frac{1}{6} \div \left\{\frac{3}{7} of \frac{14}{5} \times 1\frac{2}{3} - \left(3\frac{1}{2} - 2\frac{1}{6}\right) \right\}\right]$$ is:
= $$\frac{1}{4} \times \frac{3}{4} \div 1\frac{1}{4} of \frac{2}{5} - \left[\frac{1}{6} \div \left\{\frac{3}{7} of \frac{14}{5} \times 1\frac{2}{3} - \left(3\frac{1}{2} - 2\frac{1}{6}\right) \right\}\right]$$
= $$\frac{1}{4}\times\frac{3}{4}\div\frac{5}{4}of\frac{2}{5}-\left[\frac{1}{6}\div\left\{\frac{3}{7}of\frac{14}{5}\times\frac{5}{3}-\left(\frac{7}{2}-\frac{13}{6}\right)\right\}\right]$$
= $$\frac{1}{4}\times\frac{3}{4}\div\frac{10}{20}-\left[\frac{1}{6}\div\left\{2-\left(\frac{21}{6}-\frac{13}{6}\right)\right\}\right]$$
= $$\frac{1}{4}\times\frac{3}{4}\times\frac{2}{1}-\left[\frac{1}{6}\div\left\{2-\left(\frac{8}{6}\right)\right\}\right]$$
= $$\frac{3}{8}-\left[\frac{1}{6}\div\left\{2-\left(\frac{4}{3}\right)\right\}\right]$$
= $$\frac{3}{8}-\left[\frac{1}{6}\div\left\{\frac{6-4}{3}\right\}\right]$$
= $$\frac{3}{8}-\left[\frac{1}{6}\div\left\{\frac{2}{3}\right\}\right]$$
= $$\frac{3}{8}-\left[\frac{1}{6}\times\frac{3}{2}\right]$$
= $$\frac{3}{8}-\frac{1}{4}$$
= $$\frac{3}{8}-\frac{2}{8}$$
= $$\frac{1}{8}$$
The value of $$\frac{1\frac{2}{3} + \left[16\frac{1}{2} - \left\{1\frac{1}{10}\left(3\frac{1}{3} + 5\right)\right\}\right]}{\frac{1}{4} of 2\frac{1}{2} \div \frac{3}{5} \times 4\frac{4}{5}}$$ is:
=$$\frac{1\frac{2}{3} + \left[16\frac{1}{2} - \left\{1\frac{1}{10}\left(3\frac{1}{3} + 5\right)\right\}\right]}{\frac{5}{8} \div \frac{3}{5} \times 4\frac{4}{5}}$$
=$$\frac{\frac{5}{3} + \frac{33}{2} - \frac{55}{6}}{\frac{5}{8} \div \frac{3}{5} \times 4\frac{4}{5}}$$
=$$\frac{\frac{5}{3} + \frac{33}{2} - \frac{55}{6}}{\frac{25}{24} \times \frac{24}{5}}$$
=$$\frac{\frac{54}{6}}{5}$$
=9/5
=$$1\frac{4}{5}$$
The value of:
$$\frac{3}{8} of \frac{4}{5} \div 1\frac{1}{5} + \frac{3}{7} of \frac{7}{12} \div \frac{1}{40} of \frac{2}{5} - 3\frac{2}{3} \div \frac{11}{30} of \frac{2}{3}$$
$$\frac{3}{8} of \frac{4}{5} \div 1\frac{1}{5} + \frac{3}{7} of \frac{7}{12} \div \frac{1}{40} of \frac{2}{5} - 3\frac{2}{3} \div \frac{11}{30} of \frac{2}{3}$$
=$$\frac{3}{10} \div \frac{6}{5} + \frac{3}{12} \div \frac{1}{100} - 3\frac{2}{3} \div \frac{11}{45}$$
=$$\frac{1}{4} + 25 - 3\frac{2}{3} \div \frac{11}{45}$$
=$$\frac{1}{4} + 25 - \frac{11}{3} \div \frac{11}{45}$$
=$$\frac{1}{4} + 25 - 15$$
=10.25
What is the value of $$\left[45of\left(\frac{3}{7}\div\frac{15}{14}\right)-\left(6\frac{1}{2}\div3-4\right)+2\right]$$?
Expression : $$\left[45of\left(\frac{3}{7}\div\frac{15}{14}\right)-\left(6\frac{1}{2}\div3-4\right)+2\right]$$
= $$\left[45\times(\frac{3}{7}\times\frac{14}{15})-(\frac{13}{2}\div3-4)+2\right]$$
= $$18-\frac{13}{6}+4+2$$
= $$24-\frac{13}{6}=\frac{131}{6}$$
=> Ans - (A)
The value of $$7\frac{1}{2} \times \left(3\frac{1}{5} \div 4\frac{1}{2} of 5\frac{1}{3}\right) + \left[11 - \left(\frac{5}{8} + 3 - 1\frac{1}{4}\right)\right] \div 5\frac{3}{4} - 5 \div 5 \times 5 of 5 \div 25$$ is:
Apply bodmas rule to this problem to simplify
BODMAS RULE. BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. In certain regions, PEDMAS (Parentheses, Exponents, Division, Multiplication, Addition and Subtraction) is the synonym of BODMAS. It explains the order of operations to solve an expression
First solve the bracket then orders then division then multiplication then addition then subtraction
The value of $$\sqrt{3\frac{1}{16}} + \frac{1}{2} - \frac{3}{4} = $$
$$ = \sqrt{3\frac{1}{16}} + \frac{1}{2} - \frac{3}{4}$$
$$=\sqrt{\frac{49}{16}}+\frac{1}{2}-\frac{3}{4}$$
$$=\frac{7}{4}+\frac{1}{2}-\frac{3}{4}$$
$$=\frac{7}{4}-\frac{3}{4}+\frac{1}{2}$$
$$=\frac{4}{4}+\frac{1}{2}$$
$$= 1+\frac{1}{2}$$
$$= 1\frac{1}{2}$$
What approximate value should comein place of the question mark (?) in the following equation?
($$\frac{1}{9}\div\frac{1}{9}$$ of $$\frac{1}{3}$$) of $$\frac{1}{6}=?$$
($$\dfrac{1}{9}\div\dfrac{1}{9}$$ of $$\dfrac{1}{3}$$) of $$\dfrac{1}{6} = (\dfrac{1}{9} \div \dfrac{1}{27}$$) of $$\dfrac{1}{6}$$
$$= \dfrac{1}{9} \times 27$$ of $$\dfrac{1}{6}$$
$$= 3 \times \dfrac{1}{6} = \dfrac{1}{2}$$
What is the value of $$2 - 2 \div 2 \times 2 + 2 (2 of 2 - 2 - 2 \div 2)$$?
= $$2 - 2 \div 2 \times 2 + 2 (2 of 2 - 2 - 2 \div 2)$$
= $$2-\frac{2}{2}\times2+2(2\times2-2-\frac{2}{2})$$
= $$2-1\times2+2(4-2-1)$$
= $$2-2+2(4-3)$$
= $$2\times\ 1$$
= 2
What is the value of $$(9\div30)^2\times2.4+0.3\ of\ 12\times(1-0.3)^2+9\times(0.3)^2$$?
= $$\left(\frac{3}{10}\right)^2\times2.4+0.3\ of\ 12\times(0.7)^2+9\times0.09$$
= $$0.09\times2.4+3.6\times0.49+0.81$$
= $$0.216+1.764+0.81$$
= $$0.216+1.764+0.81$$
= 2.79
What should come in place of the question mark (?) in the following question?
$$1 - [5 - \left\{2 + (-5 + 6 - 2)2\right\}] = ?$$
Expression : $$1 - [5 - \left\{2 + (-5 + 6 - 2)2\right\}] = ?$$
= $$1 - [5 - \left\{2 + (-1\times2)\right\}]$$
= $$1 - [5 -(2-2)]$$
= $$1-(5-0)$$
= $$1-5=-4$$
=> Ans - (D)
If A = $$40 \div 8 + 5 \times 2 - 4 + 4 + 5 of 3$$ and $$B = 24 \div 4(4 + 2) + 19 of 2$$, then what is the value of $$A - B$$?
Firstly solve bracket then apply bodmass
A = $$40 \div 8 + 5 \times 2 - 4 + 4 + 5 of 3$$
A= $$5+ 5 \times 2 - 4 + 4 + 15$$
A= $$5+ 10 - 4 + 4 + 15$$
A= 30
$$B = 24 \div 4(4 + 2) + 19 of 2$$
$$B = 24 \div 4(6) + 19 of 2$$
$$B = 1 + 38$$
= 39
$$A - B$$ = 30 - 39 = -9
What is the largest four-digit number, whichis divisible by 32, 40, 36 and 48?
The LCM of 32,40,36,40 is 1440
Only 8640 is divisible by 1440
What is the value of $$\left(\frac{4 \div 2 + 2 - \frac{1}{2} \times \frac{1}{4}}{8 - 3 \div \frac{1}{4} + 6}\right)$$?
Solving the numerator,
$$\dfrac{4}{2}+2-\dfrac{1}{2}\times\dfrac{1}{4}$$
= $$2+2-\dfrac{1}{8}$$
= $$4-\dfrac{1}{8} = \dfrac{32-1}{8}$$
= $$\dfrac{31}{8}$$
Solving the denominator,
$$8-3\times4+6 = 8-12+6 = 2$$
Therefore, $$\left(\dfrac{4 \div 2 + 2 - \dfrac{1}{2} \times \dfrac{1}{4}}{8 - 3 \div \dfrac{1}{4} + 6}\right) = \dfrac{(\dfrac{31}{8})}{2} = \dfrac{31}{16}$$
What should come in place of question mark (?) in the following questions?
$$1.5\times78\div0.5=?$$
$$1.5\times78\div0.5= \dfrac{1.5\times78}{0.5}$$
$$=\dfrac{15\times78}{5} = 78\times3 = 234$$
75% of 260 + 30% of 320 = ?
$$\frac{75}{100}\times\ 260+\frac{30}{100}\times\ 320$$
$$3\times\ 65+3\times32$$
$$195+96\ =291$$
Find the value of:
$$(11 + 4) - 9 \times 1 \div 3$$ of $$4$$
$$(11 + 4) - 9 \times 1 \div 3$$ of $$4 = 15-9\times\dfrac{1}{3\times4} = 15-\dfrac{3}{4} = \dfrac{57}{4}$$
The value of $$24 \div 4 \times (3 + 3) \div 2$$ is:
$$24 \div 4 \times (3 + 3) \div 2 = \dfrac{24}{4} \times \dfrac{6}{2} = 18$$
The value of $$(3576 + 4286 + 6593) \div (201 + 105 + 107)$$is:
(3576+4286+6593)/(201+105+107)
=14455/413
=35
The value of $$\left(8 \div \frac{2}{3} of \frac{4}{5 }\right) \div \left(8 \times \frac{2}{3} \div \frac{4}{5}\right) of \left(8 \div \frac{2}{3} \times \frac{4}{5}\right)$$ is:
= $$\left(8 \div \frac{2}{3} of \frac{4}{5 }\right) \div \left(8 \times \frac{2}{3} \div \frac{4}{5}\right) of \left(8 \div \frac{2}{3} \times \frac{4}{5}\right)$$
= $$\left(8\div\frac{8}{15}\right)\div\left(8\times\frac{2}{3}\times\frac{5}{4}\right)of\left(8\times\frac{3}{2}\times\frac{4}{5}\right)$$
= $$\left(8\times\frac{15}{8}\right)\div\left(4\times\frac{1}{3}\times\frac{5}{1}\right)of\left(8\times\frac{3}{1}\times\frac{2}{5}\right)$$
= $$15\div\left(\frac{20}{3}\right)of\left(\frac{48}{5}\right)$$
= $$15\div\left(\frac{4}{1}\right)of\left(\frac{16}{1}\right)$$
= $$15\div\frac{64}{1}$$
= $$\frac{15}{64}$$
The value of $$2 \times 2 + 4 \times 4 + 2 of 3 \times 6 - 7 \times (5 + 4 \div 2)$$ is:
= $$2\times2+4\times4+2\ of\ 3\times6-7\times(5+4\div2)$$
= $$4+16+6\times6-7\times(5+2)$$
= $$20+36-7\times7$$
= $$56-49$$
= 7
What is the value of: $$(1 \times 2 + 3 \times 4 + 5 \times 6 + 7 \times 8 - 9 \times 10) \div 2 of 5$$ ?
= $$(1\times2+3\times4+5\times6+7\times8-9\times10)\div2\ of\ 5$$
= $$(2+12+30+56-90)\div10$$
= $$(10)\div10$$
= 1
What is the value of $$\left(11 \div 4 - \frac{2}{3} of \frac{9}{8} + 11\right)$$?
$$\left(11 \div 4 - \frac{2}{3} of \frac{9}{8} + 11\right) = \dfrac{11}{4} - \dfrac{3}{4} + 11 = \dfrac{8}{4} + 11 = 2+11 = 13$$
What should come in place of the question mark (?) in the following question?
$$6\div6\times9+6-9\times6-6+6\times9=?$$
$$6\div6\times9+6-9\times6-6+6\times9=?$$
Using BODMAS rule,
$$=1\times9+6-9\times6-6+6\times9$$
$$=9+6-54-6+54= 9$$
Option D is correct.
Find the cube root of (-13824)
OR
Find the value of $$ \sqrt[3]{-13824} $$
$$ \sqrt[3]{-13824} $$
= $$ \sqrt[3]{(- 24)^3} $$
= -24
So, the answer would be option d) - 24.
If $$A = 3\frac{1}{4} \times 4 \frac{1}{4} \div 34 - \frac{47}{32} + \frac{47}{16}$$ and $$B = 2\frac{1}{2} \times 5 \frac{1}{2} \div 55 - \frac{11}{10}$$, then what is the value of $$A - B?$$
$$A = 3\frac{1}{4} \times 4 \frac{1}{4} \div 34 - \frac{47}{32} + \frac{47}{16}$$
$$A = 3\frac{1}{4} \times \frac{1}{8} - \frac{47}{32} + \frac{47}{16}$$
$$A = 3\frac{1}{4} \times \frac{1}{8} +\frac{47}{32} $$
$$A = \frac{13}{32} +\frac{47}{32} $$
$$A = \frac{15}{8} $$
$$B = 2\frac{1}{2} \times 5 \frac{1}{2} \div 55 - \frac{11}{10}$$
$$B = 2\frac{1}{2} \times \frac{1}{10} - \frac{11}{10}$$
$$B = \frac{1}{4} - \frac{11}{10}$$
$$B = \frac{-17}{20}$$
A-B=(15/8)+(17/20)
=109/40
If sign ‘$$\times$$’ is interchanged with ‘$$\div$$’ and number ‘3’ is interchanged with ‘2’, then which of the following equations would be correct?
Natu and Buchku each have certain number of oranges. Natu says to Buchku,"If you give me 10 of your oranges, I will have twice the number of oranges left with you". Buchku replies,"If you give me 10 of your oranges, I will have the same number of oranges as left with you". What is the number of oranges with Natu and Buchku, respectively?
What is the value of $$\frac{1}{3 \times 7} + \frac{1}{7 \times 11} + \frac{1}{11 \times 15} +.....+\frac{1}{899 \times 903}?$$
We have :
$$\frac{1}{3\times\ 7}+\frac{1}{7\times\ 11}+.....+\frac{1}{899\times\ 903}$$
Now we always use partial fraction in such sums
Therefore we get
$$\frac{1}{4}\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+........-\frac{1}{903}\right)$$
solving we get $$\frac{1}{4}\left(\frac{1}{3}-\frac{1}{903}\right)=\frac{1}{4}\left(\frac{300}{903}\right)=\frac{75}{903}=\frac{25}{301}$$
The value of
$$3\frac{1}{5} \div 4\frac{1}{2} of 5\frac{1}{3} - 2\frac{1}{3} of \left\{\frac{3}{7} - \left(1\frac{4}{15} - \frac{13}{30}\right) \times 1\frac{1}{5}\right\}$$ is:
Given Equation :
$$3\frac{1}{5} \div 4\frac{1}{2} of 5\frac{1}{3} - 2\frac{1}{3} of \left\{\frac{3}{7} - \left(1\frac{4}{15} - \frac{13}{30}\right) \times 1\frac{1}{5}\right\}$$
Lets Solve this as per the rule of BODMAS :
$$\therefore\ \frac{16}{5}\div\frac{9}{2}of\ \frac{16}{3}-\frac{7}{3}of\left\{\frac{3}{7}-\left(\frac{19}{15}-\frac{13}{30}\right)\times\ \frac{6}{5}\right\}$$
$$\therefore\ \frac{16}{5}\div24-\frac{7}{3}of\left\{\frac{3}{7}-\frac{\left(38-13\right)}{30}\times\ \frac{6}{5}\right\}$$
$$\therefore\ \frac{16}{5}\times\ \frac{1}{24}-\frac{7}{3}of\left\{\frac{3}{7}-\frac{25}{30}\times\ \frac{6}{5}\right\}$$
$$\therefore\ \frac{2}{15}-\frac{7}{3}of\left\{\frac{3}{7}-1\ \right\}$$
$$\therefore\ \frac{2}{15}-\frac{7}{3}of\left\{-\frac{4}{7}\right\}$$
$$\therefore\ \frac{2}{15}+\frac{4}{3}$$
$$\therefore\ \frac{22}{15}$$
$$\therefore\ 1\frac{7}{15}$$
Hence, Option D is correct.
The value of
$$72 \div 6 of 12 + 4 \times (5 - 3) of 2 \div 4 - 2 $$ is:
$$\frac{72}{6\times\ 12}+\ \ \frac{\ 4\times\ \left(5-3\right)\times2}{4}-2$$
$$1+\ 4-2$$
$$3$$
Thrice of a number is 24 more than one-third of it. The number is:
Let's assume the number is 'y'.
Thrice of a number is 24 more than one-third of it.
$$3y=\frac{y}{3}+24$$
$$3y-\frac{y}{3}=24$$
$$\frac{9y}{3}-\frac{y}{3}=24$$
$$\frac{8y}{3}=24$$
$$\frac{y}{3}=3$$
the number = y = 9
What is the value of x so that the seven digit number 91876x2 is divisible by 72?
As per the question,
Number 91876x2 is divisible by 72,
It means that it is individually divisible by 9 and 8 because $$72=8\times 9$$
Divisible by 8-
Any number is divisible by 8, if the last 3 digit of that particular number is divisible by 8.
So here, 6x2 will be divisible by 8 if, x=3 and 7.
Divisible by 9-
Any number is divisible by 9, if the sum of the digit of the number is divisible by 9.
So, here $$\Rightarrow 9+1+8+6+x+2=33+x$$
By taking x=3, the number will be divisible by 9.
Hence, x=3 will be the correct answer.
What value should come in place of the question mark (?) in the following questions?
$$31 \div 3 \times 15 = ?$$
By applying BODMAS we have
$$(31/3)\times 15$$
=$$31\times 5$$
=155
If a 10-digit number 1330x5582 is divisible by 88, then the value of (x + y) is:
The value of $$\left(2\frac{1}{6} + 1\frac{13}{18} - \frac{1}{6}\right) \times 16 \div 4$$ is:
= $$\left(2\frac{1}{6} + 1\frac{13}{18} - \frac{1}{6}\right) \times 16 \div 4$$
= $$\left(\frac{13}{6}+\frac{31}{18}-\frac{1}{6}\right)\times\frac{16}{4}$$
= $$\left(\frac{12}{6}+\frac{31}{18}\right)\times4$$
= $$\left(\frac{36}{18}+\frac{31}{18}\right)\times4$$
= $$\frac{67}{18}\times4$$
= $$\frac{67}{9}\times2$$
= $$\frac{134}{9}$$
What is the value of: 2 of 3$$ \div $$3 $$\times$$2+{4$$\times3$$-(5$$\times$$2+3)}?
= 2 of 3$$ \div $$3 $$\times$$2+{4$$\times3$$-(5$$\times$$2+3)}
= $$2\times\frac{3}{3}\times2+12-(10+3)$$
= $$4+12-13$$
= 4-1
= 3
What is the value of $$28 \div (11 - 4) + 384 \div (15 + 16 \div 4 + 4)$$?
Expression : $$28 \div (11 - 4) + 384 \div (15 + 16 \div 4 + 4)$$
= $$(28 \div7) + 384 \div (15 + 4 + 4)$$
= $$4+\frac{384}{23}$$
= $$\frac{92+384}{23}=\frac{476}{23}$$
=> Ans - (B)
What is the value of x so that the seven digit number 8439x53 is divisible by 99?
8439x53 will be divisible by 99 if it is divisible by both 9 and 11.
Rule for 9:A number is divisible by 9 if the sum of the digits is divisible by 9
Rule for 11:Subtract and then add the digits in an alternating pattern from left to right. If the answer is 0 or 11, then the result is divisible by 11
If x= 4 , then sum would be 36, satisfying the rule for 9.
Now , check for 11 : 8 - 4 + 3 - 9 + 4 - 5 + 3 = 0
So , the answer would be option b)4.
The value of $$16 \div 4 of 4 \times [3 \div 4 of \left\{4 \times 3 \div (3 + 3)\right\}] \div (2 \div 4 of 8)$$ is:
The value of $$\frac{5+2 of 3 \div3 of 2\times3}{9+72\div3-2\times(3-2)-3}$$ is $$\frac{a}{b}$$, where a and b are prime numbers. The value of $$(b - a)$$ is:
$$\frac{a}{b}=\frac{5+2\ of\ 3\div3\ of\ 2\times3}{9+72\div3-2\times(3-2)-3}$$
$$\frac{a}{b}=\frac{5+6\div6\times3}{9+24-2\times1-3}$$
$$\frac{a}{b}=\frac{5+1\times3}{33-2-3}$$
$$\frac{a}{b}=\frac{5+3}{33-5}$$
$$\frac{a}{b}=\frac{8}{28}$$
$$\frac{a}{b}=\frac{2}{7}$$
value of $$(b - a)$$ = (7-2)
= 5
The value of the following expression:
150% of 15 + 75% of 75 is
150% of 15 = $$\dfrac{225}{10} = 22.5$$
75% of 75 = $$\dfrac{75^2}{100} = 56.25$$
Therefore, 150% of 15 + 75% of 75 = 22.5+56.25 = 78.75
What is the least value of x such that 517x324 is divisible by 12?
Given that,
Number $$517x324$$ is divisible by $$12$$
So, the multiple of $$12=3\times 4$$
The mentioned number will be divisible by 12 if it is individually divisible by $$3$$ and $$4$$
Divisibility by $$4$$- Any number will be divisible by $$4$$ if last two digit of that number will be divisible by $$4$$.
so, in this case last two digits are $$24$$, which is divisible by $$4$$.
Hence, for any value of $$x$$ the mentioned number will be divisible by $$4$$
Divisibility by $$3$$- Any number will be divisible by $$3$$, if the sum of the digit of that number will be divisible by $$3$$.
But as per question we have to find the minimum value of $$x$$, so that i can be divisible.
Hence, $$5+1+7+x+3+2+4=22+x$$
the nearest value of$$22+x$$ which is divisible by $$3=24$$ ,
So $$22+x=24$$
$$x=2$$
What is the value of $$\left[10\frac{1}{3} \div \frac{5}{3} (10 + 14 \div 3 - 1)\right]$$?
$$\left[10\frac{1}{3} \div \frac{5}{3} (10 + 14 \div 3 - 1)\right] = \dfrac{31}{3} \div \dfrac{5}{3}(10+\dfrac{14}{3}-1)$$
$$= \dfrac{31}{3} \div \dfrac{5}{3}\times (\dfrac{30+14-3}{3})$$
$$= \dfrac{31}{3} \div \dfrac{5}{3} \times \dfrac{41}{3}$$
$$= \dfrac{31}{3} \div \dfrac{205}{9}$$
$$= \dfrac{31}{3} \times \dfrac{9}{205} = \dfrac{93}{205}$$
What is the value of $$\left[75 \div 25 of \left(\frac{4}{3}-\frac{1}{2}+\frac{1}{6}\right)\right]$$?
Expression : $$\left[75 \div 25 of \left(\frac{4}{3}-\frac{1}{2}+\frac{1}{6}\right)\right]$$
= $$\left[75 \div 25 \times \left(\frac{8-3+1}{6}\right)\right]$$
= $$75\div(25\times1)$$
= $$\frac{75}{25}=3$$
=> Ans - (B)
The value of $$165 - [135 - \left\{84 \div 4 of 3 - (16 - 18 \div 3)\right\}]$$ is:
= $$165 - [135 - \left\{84 \div 4 of 3 - (16 - 18 \div 3)\right\}]$$
= $$165-[135-\left\{84\div12-(16-6)\right\}]$$
= $$165-[135-\left\{7-(16-6)\right\}]$$
= $$165-[135-\left\{7-10\right\}]$$
= $$165-[135-\left\{-3\right\}]$$
= $$165-[135+3]$$
= 165-138
= 27
The value of $$x$$
$$45 \times x = 25\% of 900$$ is:
$$45\times x=25\times\frac{900}{100}$$
45x=225
x=225/45
x=5
What is the value of 12.5% of 30% of 1440?
value of 12.5% of 30% of 1440 = $$\frac{12.5}{100}\times\frac{30}{100}\times1440$$
= $$\frac{1}{8}\times3\times144$$
= $$1\times3\times18$$
= 54
What is the value of:
$$8 \times 3 \div 6 + 7 - 4 \times 2 \div 4 + 8 - 10 = ?$$
$$8 \times 3 \div 6 + 7 - 4 \times 2 \div 4 + 8 - 10 = 8 \times \dfrac{3}{6} + 7 - (4 \times \dfrac{2}{4}) + 8 - 10 = 4+7-2+8-10 = 7$$
What should come in place of the question mark (?) in the following question?
$$2 - [6 - \left\{3 + (-4 + 5 + 1) \times 8\right\} +12] =?$$
Expression : $$2 - [6 - \left\{3 + (-4 + 5 + 1) \times 8\right\} +12]$$
= $$2 - [6 - \left\{3 + (2\times 8)\right\} +12]$$
= $$2-[6-19+12]$$
= $$2+1=3$$
=> Ans - (C)
Find the least square number which is divisible by 4, 8, 2, 6 and 12?
The least number which is divisible by 4, 8, 2, 6 and 12
= L.C.M. (2,4,6,8,12) = 24
Now, prime factorization of $$24=2^3\times3$$
Now to make it a perfect square, we need to multiply it by $$2\times3=6$$
=> The least square number which is divisible by 4, 8, 2, 6 and 12 = $$24\times6=144$$
=> Ans - (D)
If a 9-digit number 32x4115y2 is divisible by 88, then the value of (4x - y) for the smallest possible value of y, is:
Given that,
32x4115y2 is a nine-digit number that is divisible by $$88=11\times 8$$.
The above number will be divisible by 88 if it is individually divisible by 11 and 8.
Divisibility by 8: Any number is always divisible by 8 if the last three-digit number off that particular number is divisible by 8.
so the last three-digit number of the given number is 5y2, so the minimum possible value of y for which it is divisible by 8 =1,5.
Divisibility by 11: Any number is divisible by 11 if the difference between the sum of odd place digit and even place digit is divisible by 11.
Hence, $$2+5+1+x+3-y-1-4-2=4+x-y$$
There is two possible conditions for $$y = 1 and 5$$
i) $$ 4+x-1=3+x $$it will be divisible $$ 11 $$ if $$x=8$$,
ii) $$ 4+x-5=x-1 $$ it will be divisible $$11 $$ if $$x=1$$,
Now,
If substituting the first values
i) x=8 and y=1 (Here smallest possible value of y)
$$(4x - y) =4\times 8-1=31$$ ( Option A is matching with the answer)
If substituting the second values,
ii) x=1 and y=5 (Largest possible value of Y)
$$(4x-y)=4\times1-5=-1$$ (Not given in the option, so neglecting this.)
If $$a^3 = 117 + b^3$$ and $$a = 3 + b$$, then the value of $$a + b$$ is:
The value of the following expression.
$$(47 \times 588) \div (28 \times 120) = ?$$
By Applying BODMAS we have 47*21/120
=47*7/40
=329/40
=8.225
The value of x in the given equation $$23^2 + \sqrt{x} = 625$$
529+$$\ \ \sqrt{\ }$$x=625
625-529=$$\ \ \sqrt{\ }$$x
96=$$\sqrt{\ }$$x
x=96$$\times\ $$96
x=9216
What is the value of $$ 3\frac{3}{4} - \frac{61}{122} + \frac{9}{2} \div \frac{1}{2} of \frac{4}{3} \left(1 + \frac{1}{3}\right) + \frac{1}{2} \times \frac{4}{3}$$?
= $$ 3\frac{3}{4} - \frac{61}{122} + \frac{9}{2} \div \frac{1}{2} of \frac{4}{3} \left(1 + \frac{1}{3}\right) + \frac{1}{2} \times \frac{4}{3}$$
= $$\frac{15}{4}-\frac{1}{2}+\frac{9}{2}\div\frac{2}{3}\times\left(\frac{4}{3}\right)+\frac{2}{3}$$
= $$\frac{15}{4}-\frac{1}{2}+\frac{9}{2}\times\frac{3}{2}\times\frac{4}{3}+\frac{2}{3}$$
= $$\frac{15}{4}-\frac{1}{2}+9+\frac{2}{3}$$
= $$\frac{45}{12}-\frac{6}{12}+\frac{108}{12}+\frac{8}{12}$$
= $$\frac{39}{12}+\frac{108}{12}+\frac{8}{12}$$
= $$\frac{155}{12}$$
What is the value of : $$\frac{0.56 \times 0.36 + 0.42 \times 0.32}{0.8 \times 0.21}$$?
= $$\frac{0.56 \times 0.36 + 0.42 \times 0.32}{0.8 \times 0.21}$$
= $$\frac{0.2016+0.1344}{0.168}$$
= $$\frac{0.336}{0.168}$$
= 2
What is the value of x so that the seven digit number 55350x2 is divisible by 72?
Break 72 into prime factors
72 = $$ 2^3 \times 3^2$$
Rule for 2 : last digit should be even.
Rule for 3 : Sum should be divisible by 3.
For 55350x2 to be divisible by 72 , x = 7.
So , the answer should be option c)7.
Compute $$(15 + 3 \times 1.1) \div 0.0003$$
$$(15+3.3)\div0.0003$$
$$18.3\div0.0003$$
61000
If $$(28 \div 4 \times 7) + (44 \div 4 \times 7) - (12 \times x) = 18$$, then the value of $$x$$ is:
$$(28 \div 4 \times 7) + (44 \div 4 \times 7) - (12 \times x) = 18$$
$$\left(\frac{28}{4}\times7\right)+\left(\frac{44}{4}\times7\right)-12x=18$$
$$\left(7\times7\right)+\left(11\times7\right)-12x=18$$
$$49+77-12x=18$$
126-12x=18
12x = 126-18
12x = 108
x = 9
If an 11-digit number 5y5884805x6, is divisible by 72, then the value of $$\sqrt{xy}$$ is:
5y5884805x6 will be divisible by 72
to divide that no it should be divided by 9 and 8 both
If the six digit number 15x1y2 is divisible by 44, then (x + y) is equal to:
15x1y2 will be divisible by 44
to divide that no it should be divided by 4 and 11 both
Simplify: $$8.65-[4+0.5\ of\ (8.8-2.3\times3.5)]$$
=$$8.65-[4+0.5\ of\ (8.8-2.3\times3.5)]$$
=$$8.65-[4+0.5\ of\ (8.8-8.05)]$$
=$$8.65-[4+0.5\ of\ (0.75)]$$
=$$8.65-[35/8]$$
=8.65-4.375
=4.275
The value of 5$$\frac{1}{3}$$ $$\times$$ 2$$\frac{1}{7}$$ $$\times$$ 9$$\frac{2}{5}$$ $$\times$$ 4$$\frac{3}{8}$$ $$\times$$ 2$$\frac{6}{47}$$ is?
$$\frac{16}{3}\times\frac{15}{7}\times\frac{47}{5}\times\frac{35}{8}\times\frac{100}{47}$$
=1000
The value of $$8 of 3 \div 6 + (10 + 2) \times 3 - 96 \div 3$$ is:
= $$8\ of\ 3\div6+(10+2)\times3-96\div3$$
= $$24\div6+12\times3-32$$
= $$4+36-32$$
= 4+4
= 8
The value of $$[9.5 \div (0.6 \times 0.75 + 0.8 \div 16) + 0.75] \div (0.03 \div 0.6 of 0.01)$$ lies between:
=$$[9.5 \div (0.6 \times 0.75 + 0.8 \div 16) + 0.75] \div (0.03 \div 0.6 of 0.01)$$
=$$[9.5 \div (0.6 \times 0.75 + 0.05) + 0.75] \div (5)$$
=$$[9.5 \div (0.45 + 0.05) + 0.75] \div (5)$$
=$$[19+0.75] \div (5)$$
=(19.75/5)
=3.95
The value of $$\left(5\frac{1}{4}\div\frac{3}{7} of \frac{1}{2}\right)\times \left(5\frac{1}{4}\times\frac{3}{7} \div\frac{1}{2}\right)\div \left(5\frac{1}{4}\div\frac{3}{7}\times \frac{1}{2}\right)$$ is
$$=\left(\frac{21}{4}\div\frac{3}{14}\right)\times\left(\frac{21}{4}\times\frac{3}{7}\times2\right)\div\left(\frac{21}{4}\times\ \frac{7}{3}\times\frac{1}{2}\right)$$
$$=\left(\frac{21}{4}\times\frac{14}{3}\right)\times\left(\frac{9}{2}\right)\div\left(\frac{49}{8}\right)$$
$$=\left(\frac{7}{2}\times\frac{7}{1}\right)\times\left(\frac{9}{2}\right)\div\left(\frac{49}{8}\right)$$
$$=\left(\frac{49}{2}\right)\times\left(\left(\frac{9}{2}\right)\times\ \left(\frac{8}{49}\right)\right)$$
$$=9\times\ 2$$
= 18
What is the value of $$6\frac{1}{2} + 80 \div 40 - \frac{30}{7} of \left(5 - \frac{1}{3}\right)$$?
$$6\frac{1}{2} + 80 \div 40 - \frac{30}{7} of \left(5 - \frac{1}{3}\right) = \dfrac{13}{2} + \dfrac{80}{40} - \dfrac{30}{7} \times \dfrac{14}{3}$$
$$= \dfrac{13}{2} + 2 - 20 = \dfrac{13}{2} - 18$$
$$= \dfrac{13-36}{2} = \dfrac{-23}{2}$$
What is the value of $$\left(\frac{5}{2} of 5 \div 4 - 2 of \frac{1}{7} \div \frac{1}{7}\right)$$?
$$\left(\frac{5}{2} of 5 \div 4 - 2 of \frac{1}{7} \div \frac{1}{7}\right) = \dfrac{5}{2} \times \dfrac{5}{4} - 2\times \dfrac{1}{7} \times 7 = \dfrac{25}{8} - 2 = \dfrac{25-16}{8} = \dfrac{9}{8}$$
A square play ground measures 1127.6164 sq.m. If a man walks 2$$\frac{9}{20}$$ m a minutes then time taken by him to complete one round around it is approximately
If '$$\div$$' means '$$+$$', '$$-$$' means '$$\times$$', '$$\times$$' means '$$-$$', and '$$+$$' means '$$\div$$', then:
$$664+4\div34\times28=?$$
What is the sum of all natural numbers between 100 and 400 which are divisible by 13?
13*8=104
13*30=390
So sum =104+117+.....390
a=104
l=390
number of terms=((390-104)/13)+1
=22+1
=23
Sum=n(a+l)/2
=23(390+104)/2
=247*23
=5681
What is the unit digit of $$1^5 + 2^5 + 3^5 + … + 20^5?$$
Which two signs should be interchanged to make the following equation correct?
$$18+12\times8-6\div3=9$$
Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is
L.C.M. of 12,16,18,21 is 1008
then multiply by 2 =1008×2=2016
sum of the number of 16 is 1+6=7
The value of $$0.5\overline{6} - 0.7\overline{23} + 0.3\overline{9} \times 0.\overline{7}$$ is:
$$0.5\overline{6} - 0.7\overline{23} + 0.3\overline{9} \times 0.\overline{7}$$
= $$0.5\overline{6} - 0.7\overline{23} + \frac{39}{90} \times \frac{7}{9}$$
= $$0.5\overline{6} - 0.7\overline{23} + \frac{28}{90}$$
= $$0.5\overline{6} - 0.7\overline{23} + 0.3\overline{1}$$
= $$0.8\overline{7} - 0.7\overline{23}$$
= $$0.1\overline{54}$$
The value of $$\left(2\frac{6}{7}of4\frac{1}{5}\div\frac{2}{3}\right)\times1\frac{1}{9}\div\left(\frac{3}{4}\times2\frac{2}{3}of\frac{1}{2}\div\frac{1}{4}\right)$$ is:
$$\left(2\frac{6}{7}of4\frac{1}{5}\div\frac{2}{3}\right)\times1\frac{1}{9}\div\left(\frac{3}{4}\times2\frac{2}{3}of\frac{1}{2}\div\frac{1}{4}\right)$$
= $$\left(\frac{20}{7}of\frac{21}{5}\div\frac{2}{3}\right)\times\frac{10}{9}\div\left(\frac{3}{4}\times\frac{8}{3}of\frac{1}{2}\div\frac{1}{4}\right)$$
= $$\left(12\div\frac{2}{3}\right)\times\frac{10}{9}\div\left(\frac{3}{4}\times\frac{4}{3}\div\frac{1}{4}\right)$$
= $$18\times\frac{10}{9}\div\left(\frac{3}{4}\times\frac{16}{3}\right)$$
= $$18\times\frac{10}{9}\div4$$
= $$18\times\frac{10}{9}\times \frac{1}{4}$$ = 5
If '+' means '$$\div$$', '-' means '$$\times$$', '$$\times$$' means '+', and '$$\div$$' means '-', then:
$$64 - 81 + 9 \times 4 = ?$$
If $$N = 9^9$$, then N is divisible by how many positive perfect cubes?
$$N = 9^9$$ is divisible by $$1^3,\ 3^3,\ 9^3,\ 27^3,\ 81^3,243^{3\ }and\ 729^3\ .$$
So, B is correct choice.
The value of $$9 \times 6 \div 24 + 8 \div 2 of 5 - 30 \div 4 of 4 + 27 \times 5 \div 9$$ is:
$$9 \times 6 \div 24 + 8 \div 2 of 5 - 30 \div 4 of 4 + 27 \times 5 \div 9$$
= $$\frac{9}{4}+ 8 \div 10 - 30 \div 16 + 15$$
= $$\frac{9}{4}+ \frac{4}{5} - \frac{15}{8} + 15$$
= $$\frac{90 + 32 - 75 + 600}{40} = \frac{647}{40}$$
The unit digit in the product $$(2467)^{153} \times (841)^{72}$$is
The value of $$4-\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}}$$
Which value among $$3^{200},\ 2^{300}\ and\ 7^{100}$$ is the largest?
Terms = $$3^{200},\ 2^{300}\ and\ 7^{100}$$
Dividing all the exponents by 100, we get :
$$\equiv3^2,2^3,7^1$$
= $$9,8,7$$
Thus, the largest number = $$9\equiv3^{200}$$
=> Ans - (A)
What would come in place of ($) mark in the following equation ?
* 2 $ 20 ÷ 156 = 145
*2$20= $$156\times\ 145$$
we get *2$20=22,620
so$=6
If 13 L 4 A 7 = 41 and 14 A 3 L 12 = 54, then 12 L 3 A 9 = ?
Expression : 13 L 4 A 7 = 41
The pattern followed is : $$A\rightarrow\times$$ and $$L\rightarrow+$$
=> $$13+(4\times7)=41$$
and Similarly, $$14\times3+12=54$$
$$\therefore$$ 12 L 3 A 9
= $$12+3\times9=12+27=39$$
=> Ans - (B)
If 85 x 5 - 3 = 20 and 18 x 2 - 1 = 10, then 100 x 20 - 5 = ?
The pattern followed is $$\times$$ is replaced by $$\div$$ and $$-$$ is replaced by $$+$$
Eg :- 85 x 5 - 3 = $$\frac{85}{5}+3=17+3=20$$
and 18 x 2 - 1 = $$\frac{18}{2}+1=9+1=10$$
Similarly, 100 x 20 - 5 = $$\frac{100}{20}+5=5+5=10$$
=> Ans - (C)
By interchanging which two signs the equation will be correct?
16 + 31 - 3 x 93 ÷ 11 = 966
Expression : 16 + 31 - 3 x 93 ÷ 11 = 966
By exchanging :
(A) + and -
L.H.S. = $$16-31+3\times93\div11$$
= $$-15+25.36=10.36\neq$$ R.H.S.
(B) - and ÷
L.H.S. = $$16+31\div3\times93-11$$
= $$16+(31\times31)-11$$
= $$5+961=966=$$ R.H.S.
=> Ans - (B)
By interchanging which two signs the equation will be correct?
25 + 18 ÷ 2 - 4 = 20
Expression : 25 + 18 ÷ 2 - 4 = 20
(A) : + and ÷
$$\equiv25\div18+2-4=20$$
L.H.S. = $$1.39-2=-0.61\neq20$$
(B) : + and -
$$\equiv25-18\div2+4=20$$
L.H.S. = $$25-9+4=20$$
=> Ans - (B)
By interchanging which two signs the equation will be correct?
19 + 36 x 12 ÷ 4 - 26 = 5
Expression : 19 + 36 x 12 ÷ 4 - 26 = 5
(A) : + and -
$$\equiv19-36\times12\div4+26=5$$
L.H.S. = $$19-(36\times3)+26=19-108+26=-63\neq$$ R.H.S.
(B) : x and ÷
$$\equiv19+36\div12\times4-26=5$$
L.H.S. = $$19+(3\times4)-26=19+12-26=5=$$ R.H.S.
=> Ans - (B)
If ‘P’ means ‘+’, ‘Q’ means ‘-’, ‘R’ means ‘÷’ and ‘S’ means ‘x’, then which of the following equation is correct?
Given : ‘P’ means ‘+’, ‘Q’ means ‘-’, ‘R’ means ‘÷’ and ‘S’ means ‘x’
(A) : 14 R 7 S 6 P 4 Q 3 = 11
L.H.S. = $$14\div7\times6+4-3$$
= $$12+1=13\neq$$ R.H.S.
(B) : 3 S 6 P 2 Q 3 R 6 = 35/2
L.H.S. = $$3\times6+2-3\div6$$
= $$18+2-0.5=19.5=\frac{39}{2}\neq$$ R.H.S.
(C) : 11 R 12 S 48 P 10 Q 6 = 48
L.H.S. = $$11\div12\times48+10-6$$
= $$44+4=48=$$ R.H.S.
=> Ans - (C)
In a certain code language, '$$+$$' represents '$$-$$', '$$-$$' represents '$$\times$$', '$$\times$$' represents '$$\div$$' and '$$\div$$' represents '$$+$$'. Find out the answer to the following question.
$$ 196 \div 4 - 125 \times 50 + 10 = ? $$
According to the problem, by applying given conditions
$$196+4\times125\div50-10=196+4\times2.5-10$$
$$=196+10-10$$
$$=196$$
Hence, the correct answer is Option B
In a certain code language, '$$+$$' represents '$$-$$', '$$-$$' represents '$$\times$$', '$$\times$$' represents '$$\div$$' and '$$\div$$' represents '$$+$$'. Find out the answer to the following question.
$$96 \times 4 \div 125 + 25 - 5 = ?$$
According to the problem, by applying given conditions
$$96\div4+125-25\times5=24+125-25\times5$$
$$=24+125-125$$
$$=24$$
Hence, the correct answer is Option B
In a certain code language, '$$+$$' represents '$$-$$', '$$-$$' represents '$$\times$$', '$$\times$$' represents '$$\div$$' and '$$\div$$' represents '$$+$$'. Find out the answer to the following question.
$$90 \times 10 \div 25 - 5 + 50 = ?$$
According to the problem by applying the given conditions,
$$90\div10+25\times5-50=9+25\times5-50$$
$$=9+125-50$$
$$=84$$
Hence, the correct answer is Option B
In a certain code language, '+' represents '-', '-' represents $$ '\times', '\times' $$ represents $$'\div'$$ and $$'\div'$$ represents '+'. Find out the answer to the following question.
$$ 950 \times 50 + 8 - 5 \div 20 = ? $$
In a certain code language, '$$+$$' represents '$$-$$', '$$-$$' represents '$$\times$$', '$$\times$$' represents '$$\div$$' and '$$\div$$' represents '$$+$$'. Find out the answer to the following question.
$$100 \times 5 + 15 - 12 \div 6 = ?$$
According to the problem,
$$100\div5-15\times12+6=20-15\times12+6$$
$$=20-180+6$$
$$=-154$$
Hence, the correct answer is Option D
In a certain code language, '+' represents '-', '-' represents '$$\times$$', '$$\times$$' represents '$$\div$$' and '$$\div$$' represents '+'. Find out the answer to the following question.
$$ 160 \times 40 \div 20 + 10 - 2 = ? $$
By applying the given conditions,
$$160\div40+20-10\times2=4+20-10\times2$$
$$=4+20-20$$
$$=4$$
Hence, the correct answer is Option D
In a certain code language, '+' represents '-', '-' represents 'x', 'x' represents '÷' and '÷' represents '+'. Find out the answer to the following question.
$$16 - 25 \times 40 \div 60 + 15 = ?$$
In a certain code language, '+' represents '-', '-' represents 'x', 'x' represents '÷' and '÷' represents '+'. Find out the answer to the following question.
$$240 \div 60 - 15 \times 25 + 5 = ?$$
By applying the given conditions,
$$240+60\times15\div25-5=240+60\times\frac{3}{5}-5$$
$$=240+36-5$$
$$=271$$
Hence, the correct answer is Option A
In a certain code language, '+' represents '-', '-' represents 'x', 'x' represents '÷' and '÷' represents '+'. Find out the answer to the following question.
$$128 - 125 \times 100 + 144 \div 12 = ?$$
By applying the given conditions,
$$128\times125\div100-144+12=128\times\frac{5}{4}-144+12$$
$$=160-144+12$$
$$=28$$
Hence, the correct answer is Option C
In a certain code language, '+' represents '-', '-' represents 'x', 'x' represents '÷' and '÷' represents '+'. Find out the answer to the following question.
$$200 \div 50 \times 25 - 20 + 10 = ?$$
By applying the given conditions,
$$200+50\div25\times20-10=200+2\times20-10$$
$$=200+40-10$$
$$=230$$
Hence, the correct answer is Option D
In a certain code language, '+' represents '-', '-' represents 'x', 'x' represents '÷' and '÷' represents '+'. Find out the answer to the following question.
$$120 \times 8 - 25 \div 36 + 6 = ?$$
By applying the given conditions,
$$120\div8\times25+36-6=15\times25+36-6$$
$$=375+36-6$$
$$=405$$
Hence, the correct answer is Option B
In a certain code language, '+' represents '-', '-' represents 'x', 'x' represents '÷' and '÷' represents '+'. Find out the answer to the following question.
$$225 \times 25 - 5 \div 100 + 20 = ?$$
In a class, there are 40 students. Some of them passed the examination and others failed. Raman’s rank among the student who have passed is 13 th from top and 17 th from bottom. How many students have failed?
Total number of students = 40
Among the student who have passed, Raman's rank from top = 13th
Raman's rank from bottom = 17th
=> Total students who passed = $$(13+17)-1=30-1=29$$
$$\therefore$$ Number of students who have failed = $$40-29=11$$
=> Ans - (A)
If $$A = 20 \times 50$$ and $$B = 20 \times 3$$ then what is the value of $$A \times B$$ ?
A =$$20\times\ 50\ =\ 1000$$
B=$$20\times\ 3=60$$
AB = 60,000
If $$A = 23 \times 3$$ and $$B = 25 \times 3$$, then what is the value of $$A \times B$$ ?
A =69
B=75
$$A\times\ B\ =69\times\ 75$$
If $$\ x^{2}+9y^{2}\ $$= 6xy, then x: y is
$$x^{2}+9y^{2}$$=6xy
$$\Rightarrow x^{2}-6xy+9y^{2}$$=0
$$\Rightarrow (x-3y)^{2}$$=0
$$\Rightarrow$$ x-3y=0
$$\Rightarrow$$ x=3y
$$\Rightarrow \frac{x}{y}$$=$$\frac{3}{1}$$
$$\therefore$$ x:y=3:1
- If x < y, w > x and w < z, which of the following must be true?
I. y < w
II. z < x
z > w > x < y
Neither I nor II true.
$$\therefore$$ The correct answer is option A.
If a < b, d > c and a < d, which of the following is true?
I. b < c
II. c > a
a < b, d > c and a < d
By combination,
a < d > c
There is no relation b to c and c to a.
Hence, neither I nor II statement true.
If e < f, i > e and f < g, which of the following must be true?
I. f < i
II. g > e
e < f, i > e and f < g
By the combination,
i > e < f < g
I. There is no relation between i and f.
II. g > e is true.
So, only statement II is true.
$$\therefore$$ The correct answer is option B.
If j < k, l > k , k < i , which of the following must be true?
I. j < l
II. i > j
j < k, l > k , k < i
By the combination,
l > k > j or i > k > j
I. j < l is true.
II. i > j is true.
$$\therefore$$ Both I and II statements are true.
If m > l, m < n and n < o, which of the following must be true?
I. l < o
II. n > l
If o < l, x < o, a < l and p < o, which of the following must be true?
I. a > p
II. l > p
III. x < l
If v < y, x < y, w < z and z > y, which of the following is true?
I. z > v
II. w > v
III. x < z
v < y, x < y, w < z and z > y,
By the combination,
w < z > y > v, z > y > x
So, I and III are true.
$$\therefore$$ The correct answer is option D.
The weights of five boxes are 10, 20, 50, 70, and 90 kilograms. Which of the following cannot be the total weight (in kilograms) of any combination of these boxes?
The different possible weights using the combination of given weights is
90+70+20 = 180
90+70+50+10 = 220
90+70+50+10+20 = 240
Weight of 200 kilograms cannot be formed with combination of given weights.
The weights of five boxes are 10, 30, 40, 70 & 70 kilograms. Which of the following cannot be the total weight (in kilograms) of any combination of these boxes?
For 190 kilograms = 70 + 70 + 40 + 10
For 180 kilograms = 70 + 70 + 40
For 210 kilograms = 70 + 70 + 40 + 30
We can not measure 200 by adding above weights.
The weights of five boxes are 10, 30, 50, 70 & 80 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes?
Combination of 160 kilograms = 70, 50, 30, 10
Combination of 180 kilograms = 80, 70, 30
Combination of 150 kilograms = 70, 50, 30
But there is no combination for 220 kilograms.
$$\therefore$$ The correct answer is option B.
The weights of five boxes are 20, 30, 40, 70 & 90 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes?
The weights of five boxes are 20, 40, 40, 70 & 90 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes?
The combination of 190 = 20, 40, 40, 90
The combination of 180 = 20, 70, 90
The combination of 170 = 20, 40, 40, 70
There is no combination for 210.
$$\therefore$$ The correct answer is option C.
The weights of five boxes are 30, 40, 40, 70 & 90 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes?
Addition of 180 kilograms = 30 + 40 + 40 + 70
Addition of 190 kilograms = 30 + 70 + 90
Addition of 200 kilograms = 30 + 40 + 40 + 90
But we cannot get 210 by adding given weights.
$$\therefore$$ The correct answer is option is A.
The weights of five boxes are 30, 40, 50, 70 & 90 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes?
Combination for 210 = 30, 40, 50, 90
Combination for 200 = 90, 70, 40
Combination for 190 = 90, 70, 30
There is no combination for 220 kilograms.
If '+' is $$'\times'$$, '-‘ is '+', $$'\times'$$ is $$'\div'$$ and $$'\div'$$ is '-‘, then answer the following question based on this information.
$$ 13.5 \times 1.5 - 0.008 + 125 = ? $$
In a certain code language, '+' represents '$$\times$$', '-' represents '+', '$$\times$$' represents '$$\div$$' and '$$\div$$' represents '-'. Find out the answer to the following question.
$$0.0625 + 800 - 234 \times 6 = ?$$
In a certain code language, '+' represents '$$\times$$', '-' represents '+', '$$\times$$' represents '÷' and '÷' represents '-'. Find out the answer to the following question.
$$0.002 + 8000 - 126 \times 3$$ = ?
$$0.002 + 8000 - 126 \times 3$$ = ?
In code language,
$$0.002 $$\times$$ 8000 + 126 ÷ 3$$ = ?
16 + 42 = ?
? = 58
$$\therefore$$ The correct answer is option A.
In a certain code language, '+' represents $$'\times'$$, '-' represents '+', $$'\times'$$ represents $$'\div'$$ and $$'\div'$$ represents '-'. Find out the answer to the following question.
$$ 0.25 + 240: 300 \times 5 = $$ ?
0.25 + 240 -300 x 5
In code language,
0.25×240+300 ÷ 5
= 60 + 60 = 120
$$\therefore$$ The correct answer is option B.
In a certain code language, '+' represents '$$\times$$', '-' represents '+', '$$\times$$' represents '$$\div$$' and '$$\div$$' represents '-'. Find out the answer to the following question.
$$0.025 + 200 - 345 \times 15 = ?$$
$$0.025 + 200 - 345 \times 15 = ?$$
Apply the code language,
$$0.025 \times 200 + 345 \div 15 = ?$$
$$5+ 23 = ?$$
? = 28
$$\therefore$$ The correct answer is option C.
In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '÷' and '÷' represents '-'. Find out the answer to the following question
0.1 + 500 - 240 x 6 = ?
0.1 + 500 - 240 x 6 = ?
In code language,
0.1 x 500 + 240 ÷ 6 = ?
50 + 40 = ?
? = 90
In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '÷' and '÷' represents '-'. Find out the answer to the following question.
$$0.125+32-54\times3=?$$
$$0.125+32-54\times3=?$$
On applying code language,
$$0.125 \times 32 + 54 \div 3 = ?$$
$$0.125 \times 32 + 18 = ?$$
4 + 18 = ?
? = 22
If p < r, r < s and t > p, which of the following must be true?
I. p < s
II. s > t
p is less than r and r is less than s. Hence p is less than s and also p is less than t. But nothing can't be said regarding s and t. Hence only 1 is true
The weights of five boxes are 10, 30, 40, 70 & 90 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes?
In a certain code language, '+' represents $$'\times'$$, '-' represents '+', $$'\times'$$ represents $$'\div'$$ and $$'\div'$$ represents '-'. Find out the answer to the following question.
$$ 0.02 + 400 - 123 \times 3 = ? $$
Some equations are solved on the basis of a certain system. On the same basis, find out the correct answer from amongst the four alternatives to the unsolved equation
1 × 2 × 3 = 231
3 × 4 × 5 = 453
5 × 6 × 7 = ?
The pattern followed is that the position of numbers are interchanged starting from the second number, then third and finally the first is written.
Eg : 1 × 2 × 3 = 231
and 3 × 4 × 5 = 453
Similarly, 5 × 6 × 7 = 675
=> Ans - (B)
If 24x2=84, and 32x3=69, then 13x3=?
The numbers are multiplied and the digits in the result are interchanged.
Eg : $$24\times2=48\equiv84$$
and $$32\times3=96\equiv69$$
Similarly, $$13\times3=39\equiv93$$
=> Ans - (B)
An equation of the form ax + by + c = 0. Where, a ≠ 0, b ≠ 0 and c = 0 represents a straight line which passes through
As c=0, and substituting the point (0,0) in the equation, we get ax+by+c = 0 at the point (0,0).
Hence, the line passes through origin.
The fifth term of the sequence for which $$t_{1}=1$$, $$t_{2}=2$$ and $$t_{n+2}$$ = $$t_{n}+t_{n+1}$$, is
$$t_{1}=1$$, $$t_{2}=2$$
$$t_{n+2}$$ = $$t_{n}+t_{n+1}$$
put n=3, then $$t_{5}$$ = $$t_{3}+t_{4}$$
$$t_{3}$$ = $$t_{1}+t_{2}$$ = 1+2 = 3
$$t_{4}$$ = $$t_{2}+t_{3}$$ = 2+3 = 5
$$t_{5}$$ = $$t_{3}+t_{4}$$ = 3+5 = 8
so the answer is option D.
If X = 0.3 $$\times$$ 0.3, the value of X is
Expression : $$X=0.3\times0.3$$
=> $$X=0.09$$
=> Ans - (C)
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