Number System Questions for SSC CHSL and MTS 2022 – Download PDF

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Question 1: What is the value of
$\frac{3}{4}  of  \left(\frac{1}{3} \div \frac{1}{2}\right) + \left(2 – \frac{2}{5}\right) \times \frac{3}{2} + \frac{2}{3}$?

a) $\frac{107}{30}$

b) $\frac{103}{25}$

c) $\frac{109}{17}$

d) $\frac{101}{6}$

Question 2: What is the value of $\frac{2 \div 3 \times (1 + 3) + 5 – 6}{2  of  3 \div 5 \times 4 + 3 – 2}$?

a) $\frac{36}{89}$

b) $\frac{31}{73}$

c) $\frac{25}{87}$

d) $\frac{27}{92}$

Question 3: What is the mode of given data?
4, 3, 7, 13, 16, 23, 3, 4, 7, 4, 3, 3, 9, 6, 9, 6

a) 9

b) 4

c) 3

d) 6

Question 4: What is the mode of the given data?
4, 3, 4, 3, 2, 2, 2, 5, 5, 3, 4, 6, 4, 3, 3

a) 3

b) 2

c) 5

d) 4

Question 5: What is the value of
$36 \div 8 \times 4 + 2 \div 4 – 1 + 5  of  3 \div (4 \times 2 – 3) – 3$?

a) $\frac{31}{2}$

b) $18$

c) $\frac{35}{2}$

d) $16$

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Question 6: What is the value of $\frac{39 \div 26 + 22 \div 11 \times 2 + 4 \times 3}{2  of  5 – 3(7 + 10 \div 2 – 3 \times 3)}$?

a) $\frac{39}{2}$

b) $\frac{49}{2}$

c) $\frac{61}{2}$

d) $\frac{35}{2}$

Question 7: What is the value of $(24 + 16 \times 5 – 8  of  4) \div 84 \times 48 \div 24 \times 6 + 4 + 3 ?$

a) $\frac{139}{3}$

b) $\frac{121}{7}$

c) $\frac{56}{3}$

d) $\frac{156}{5}$

Question 8: If $X : Y : Z = 1 : 2 : 3$ and, $X^2 + Y^2 + Z^2 = 224$, then what is the value of $X + Y + Z$?

a) 24

b) 48

c) 36

d) 32

Question 9: What is the value of $(3 \times 4  of  12 \div 2) \div 9 \times 4 + 4 \div 8 + 3 \times 2 ?$

a) $\frac{37}{2}$

b) $\frac{77}{2}$

c) $\frac{89}{3}$

d) $\frac{94}{3}$

Question 10: If $A = 8 \div 4 \times (3 – 1) + 6 \times 3 \div 2  of  3  and  B = 4 \div 8 \times 2 + 7 \times 3$, then what is the value of $A + B$?

a) 33

b) 29

c) 31

d) 35

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Question 11: What is the least number of four digits which is exactly divisible by 2, 4, 6 and 8?

a) 1016

b) 1024

c) 1008

d) 1096

Question 12: What is the value of $\frac{3}{4} \div \left(\frac{1}{2} + \frac{1}{16}\right) + \frac{2}{3} of \frac{4}{9} \div \left(\frac{1}{3} – \frac{11}{81}\right) + \frac{1}{4} \times \frac{2}{3}$?

a) 3

b) 1

c) 2

d) 4

Question 13: What is the difference of mean and median of the given data : 4, 13, 8, 15, 9, 21, 18, 23, 35, 1?

a) 0.7

b) 1.7

c) 1.2

d) 2.1

Question 14: 60% of a number is 168, then what is the number?

a) 280

b) 320

c) 240

d) 200

Question 15: What is the value of: $5  of  5  of  5 \div 5 + 5 – 6 \div 3 \times 4 + 2 + (3 \div 6 \times 2)?$

a) 21

b) 25

c) 28

d) 19

Question 16: The mode of 2, 2, 3, 3, 5, 5, 5, 7, 8, 8, 9, 10 is:

a) 5

b) 2

c) 3

d) 6

Question 17: The mode of the following data is 36. What is the value of x ?

a) 11

b) 15

c) 13

d) 12

Question 18: When 6892, 7105 and 7531 are divided by the greatest number x, then the remainder in each case is y. What is the value of (x – y)?

a) 123

b) 137

c) 147

d) 113

Question 19: The sum of the perfect square between 120 and 300 is:

a) 1400

b) 1024

c) 1296

d) 1204

Question 20: The difference between the greatest and the least four digit numbers that begins with 3 and ends with 5 is:

a) 990

b) 900

c) 909

d) 999

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Answers & Solutions:

1) Answer (A)

$\frac{3}{4}  of  \left(\frac{1}{3} \div \frac{1}{2}\right) + \left(2 – \frac{2}{5}\right) \times \frac{3}{2} + \frac{2}{3}$

$\frac{3}{4}\times(\frac{1}{3}\times\frac{2}{1}) + (\frac{10 – 2}{5})\times\frac{3}{2} + \frac{2}{3}$

$\frac{3}{4}\times\frac{2}{3} + \frac{8}{5}\times\frac{3}{2} + \frac{2}{3}$

$\frac{6}{12} + \frac{24}{10} + \frac{2}{3}$

$\frac{30 + 144 + 40}{60}$

$\frac{214}{60}$ = $\frac{107}{30}$

Therefore option A is the answer.

2) Answer (C)

$\frac{2 \div 3 \times (1 + 3) + 5 – 6}{2  of  3 \div 5 \times 4 + 3 – 2}$

$\frac{\frac{2}{3}\times4 + 5 – 6}{2\times\frac{3}{5}\times 4 + 3 – 2}$

$\frac{\frac{8}{3} + 5 – 6}{\frac{24}{5} + 3 – 2}$

$\frac{\frac{8 + 15 – 18}{3}}{\frac{24 + 15 – 10}{5}}$

$\frac{8 + 15 – 18}{3}\times\frac{5}{24 + 15 – 10}$

$\frac{5}{3}\times\frac{5}{29}$

$\frac{25}{87}$

3) Answer (C)

Number 3 is repeated more number of times when compared to other numbers.Therefore 3 is the answer.

4) Answer (A)

The mode of a data set is the number that occurs most frequent in the set

To find the mode :

Step 1: arrange numbers in ascending order

2, 2 , 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6

Step 2 : count how many times each number occurs

2 three times

3 five times

4 four times

5 two times

6 one time

Step 3 : The number that occurs the most is the mode

3 is the mode

5) Answer (C)

$36 \div 8 \times 4 + 2 \div 4 – 1 + 5 of 3 \div (4 \times 2 – 3) – 3 $

$ = 36 \div 8 \times 4 + 2 \div 4 – 1 + 5 of 3 \div 5 – 3 $

$ =36 \div 8 \times 4 + 2 \div 4 – 1 + 15 \div 5 – 3 $

$ =\frac{9}{2} \times 4 + \frac{1}{2} – 1 + 3 – 3 $

$ =18 + \frac{1}{2} – 1 + 3 – 3 $

$ =18 + \frac{1}{2} + 3 – 4 $

$ = \frac{35}{2} $

6) Answer (D)

$\frac{39 \div 26 + 22 \div 11 \times 2 + 4 \times 3}{2  of  5 – 3(7 + 10 \div 2 – 3 \times 3)}$

$\frac{\frac{39}{26} + \frac{22}{11} \times 2 + 4 \times 3}{2 \times 5 – 3(7 + \frac{10}{2} – 3\times 3)}$

$\frac{\frac{3}{2} + 4 + 12}{10 – 3(7 + 5 -9)}$

$\frac{\frac{3 + 8 + 24}{2}}{10 – 3(3)}$

$\frac{\frac{35}{2}}{10 – 9}$

$\frac{35}{2}$

7) Answer (B)

$(24 + 16 \times 5 – 8  of  4) \div 84 \times 48 \div 24 \times 6 + 4 + 3 $

$\frac{(24 + 16\times5 – 8\times4)}{84}\times\frac{48}{24}\times6 + 4 + 3 $

$\frac{24 + 80 + 32}{7} + 4 + 3$

$\frac{72 + 28 + 21}{7}$

$\frac{121}{7}$

8) Answer (A)

$X : Y : Z = 1 : 2 : 3$

let X = a, Y= 2a , Z= 3a

now $X^2 + Y^2 + Z^2 = 224$ = $\left(a\right)^{2} +\left(2a\right)^{2} +\left(3a\right)^{2} = 224$

$a^2 + 4a^2 + 9a^2 = 224$

$ 14a^2 = 224$ , $ a^2 = \frac{224}{14}$ , $ a^2 = 16$

a=4

$X + Y + Z$ = $a+2a+3a= 6a $ = $6\times 4$ = 24

9) Answer (B)

using the BODMAS rule { priority brackets > of > division > multiplication > addition > subtraction}

solving the bracket first (1st priority brackets)

$(3 \times 4  of  12 \div 2)$ , now since ‘of’ is the priority hence it should be solved first

simplifying  it we get

$(3 \times 4\times12 \div 2)$ (here 4 of 12 is $4\times12$ ) =$(3 \times 4\times 6)$

substituting in original  question we get

$(3 \times 4\times 6) \div 9 \times 4 + 4 \div 8 + 3 \times 2 $

simpliying it further we get

$\frac{(3 \times 4\times 6)}{9} \times 4 +\frac{4}{8}+ 3 \times 2 $

= 32+$\frac{1}{2}$+ 6 = $\frac{77}{2}$

10) Answer (B)

Applying the BODMAS { priority brackets > of > division > multiplication > addition > subtraction }

To solve A , first solve the subtraction in the brackets i.e (3-1) = 2

simplifying A, we get

$A = 8 \div 4 \times 2 + 6 \times 3 \div 2  of  3 $ = $\frac{8}{4}\times 2 + \frac{6 \times 3}{6}$ ( here 2 of 3 is $2\times 3$ = 6)

A= 7

similarly applying BODMAS we solve for B

$B = 4 \div 8 \times 2 + 7 \times 3$ = $B = \frac{4}{8} \times 2 + 7 \times 3$ = 22

B = 22

A+B = 7+22 = 29

11) Answer (C)

For a number to be divisible 2,4,6,8 should be multiple of 2 and 3,as numbers 2,4,8 have common factor 2 and number 6 is a multiple of 2 and 3.

So, from the options given we get 1008 as a multiple of 2 and 3 both.

Hence option C is a correct choice

12) Answer (A)

$\frac{3}{4} \div \left(\frac{1}{2} + \frac{1}{16}\right) + \frac{2}{3} of \frac{4}{9} \div \left(\frac{1}{3} – \frac{11}{81}\right) + \frac{1}{4} \times \frac{2}{3}$

$ \Rightarrow$ $\frac{3}{4} \div \frac{9}{16} + \frac{8}{27} \div \frac{16}{81} + \frac{1}{6}$

$ \Rightarrow$ $\frac{3}{4}\times\frac{16}{9}+\frac{8}{27}\times\frac{81}{16}+\frac{1}{6}$

$ \Rightarrow$ $\frac{4}{3}+\frac{3}{2}+\frac{1}{6}$

$ \Rightarrow$ 3.

13) Answer (A)

Mean:

No. of samples (n) = 10

Mean = $\frac{\sum x}{n} = \frac{4+13+8+15+9+21+18+23+35+1}{10}= \frac{147}{10} = 14.7$

Median:

Arranging the data in ascending order, we get:

1, 4, 8, 9, 13, 15, 18, 21, 23, 35

n = 10 (even)

Therefore, median is the average of 5th and 6th term.

Median = $  \frac{13+15}{2}  = 14$

Mean – Median = 14.7 – 14 = 0.7

Therefore, Option A is correct.

14) Answer (A)

60% of the number is 168.

Let’s assume the number is ‘y’.

60% of y = 168

0.6y = 168

y = 280

15) Answer (B)

$5\times5\times\frac{5}{5}+5-\frac{6}{3}\times4+2+\frac{3}{6}\times2$

$25+5-8+2+1$

25

16) Answer (A)

Mode : The value that appears most often in a set of given data values.

Given Data : 2, 2, 3, 3, 5, 5, 5, 7, 8, 8, 9, 10

• Most number repeated in above data is 5.

So, Mode of the given data is 5.

Hence, Option A is correct.

17) Answer (D)

As per given data,

Class interval of 30-40 has highest frequency, thatswhy it is modal class

As we know,

M = $l+\left\{\frac{\left(f_1-f_0\right)}{2f_1-f_0-f_2}\right\}\times\ h$

where, h= size of the class interval,

l = lower limit of the modal class,

$f_{1=}$ frequency of the modal class,

$f_{_0=}$ frequency of the class preceding the modal class

$f_{_2=}$ frequency of the class succeeding the modal class

putting the values from the given data :

$36=30+\frac{\left(16-10\right)}{2\times\ 16-10-x}\times\ 10$

$36-30=\frac{6}{22-x}\times\ \ 10$

$22-x=10$

$x=12$

Hence, Option D is correct.

18) Answer (B)

We have to find HCF of given numbers : 6892, 7105, 7531

7105 – 6892 = 213

7531 – 7105 = 426

426 – 213 = 213

So, Either the difference or the factor of difference is the HCF of those given number.

Here , 213 is the HCF.

When 6892, 7105, 7531 is divided by 213 we get 76 as an remainder

So, x = 213 and y = 76

According to Question :

x – y = 213 – 76 = 137

Hence, Option B is correct.  

19) Answer (A)

Sum of the squares of n consecutive numbers =

The sum of the perfect square between 120 and 300 = $11^2+12^2+13^2+14^2+15^2+16^2+17^2$

$=\frac{17\left(17+1\right)\left(2\left(17+1\right)\right)}{6}-\frac{10\left(10+1\right)\left(2\left(10\right)+1\right)}{6}$

$=\frac{17\left(18\right)\left(35\right)}{6}-\frac{10\left(11\right)\left(21\right)}{6}$

$=51\times35-11\times35$

$=35\left(51-11\right)$

$=35\left(40\right)$

$=1400$

Hence, the correct answer is Option A

20) Answer (A)

The greatest four digit number that begins with 3 and ends with 5 = 3995

The least four digit number that begins with 3 and ends with 5 = 3005

$\therefore\ $The difference between the greatest and the least four digit numbers that begins with 3 and ends with 5 = 3995 – 3005 = 990

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