Instructions

For the following questions answer them individually

Question 21

Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?

Video Solution

Solution

Let the total number of mints in the bowl be n
Sita took n/3 - 4. Remaining = 2n/3 + 4
Fatim took 1/4(2n/3 + 4) - 3. Remaining = 3/4(2n/3 + 4) + 3
Eswari took 1/2(3/4(2n/3+4)+3) - 2
Remaining = 1/2(3/4(2n/3+4)+3) + 2 = 17
=> 3/4(2n/3+4)+3 = 30 => (2n/3+4) = 36 => n = 48
So, the answer is option d)

Question 22

If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been a

Video Solution

Solution

30 years. The number of leap years is 8 (1972,1976,1980,1984,1988,1992,1996,2000).

So, the total number of days = 22*365 + 8*366 = 10958

10958 mod 7 = 3

Since 9/12/2001 is a Sunday, 9/12/1971 should be a Thursday.

Question 23

In a number system the product of 44$$_{10}$$ and 11$$_{10}$$ is 3414. The number 3111 of this system, when converted to the decimal number system, becomes

Video Solution

Solution

The product of 44 and 11 in decimal is 484.
If base is x , then 3*x^3+4*x^2+x+4 = 484 .
Hence, the given base system is of number 5.
Now, we have to convert 3111 (in base 5) to decimal number system.

3111 in base 5 equals $$1*5^0 + 1*5^1 + 1*5^2 + 3*5^3 = 1+5+25+375=406$$

Question 24

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour?

Video Solution

Solution

$$12/(R - S) = T$$
$$12/(R + S) = T - 6$$
$$12/(2R - S) = t$$
$$12/(2R + S) = t - 1$$
=> $$12/(R - S) - 12/(R + S) = 6$$ and $$12/(2R - S) - 12/(2R + S) = 1$$
=> $$12R + 12S - 12R + 12S = 6R^2 - 6S^2$$ and $$24R + 12S - 24R + 12S = 4R^2 - S^2$$
=> $$24S = 6R^2 - 6S^2 and 24S = 4R^2 - S^2$$
=> $$6R^2 - 6S^2 = 4R^2 - S^2$$
=> $$2R^2 = 5S^2$$
=> $$24S = 10S^2 - S^2 = 9S^2$$
=> $$S = 24/9 = 8/3$$

Question 25

Every 10 years the Indian Government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri.

Chota Hazri has 4,522 fewer males than Mota Hazri.

Mota Hazri has 4,020 more females than males.

Chota Hazri has twice as many females as males.

Chota Hazri has 2,910 fewer females than Mota Hazri.

What is the total number of males in Chota Hazri?

Video Solution

Solution

Let the number of males in Mota Hazri = x
No. of males in Chota Hazri = x - 4522
Let the number of females in Mota Hazri = y
No. of females in Chota Hazri = y - 2910
(y - 2910) = 2(x - 4522) => y = 2x - 9044 + 2910 = 2x - 6134
Also y = x + 4020
So, x + 4020 = 2x - 6134 => x = 10154
So, number of males in Chota Hazri = 10154 - 4522 = 5632

Question 26

Three classes X, Y and Z take an algebra test.

The average score in class X is 83.

The average score in class Y is 76.

The average score in class Z is 85.

The average score of all students in classes X and Y together is 79.

The average score of all students in classes Y and Z together is 81.

What is the average for all the three classes?

Video Solution

Solution

Let x , y and z be no. of students in class X, Y ,Z respectively.

From 1st condition we have

83*x+76*y = 79*x+79*y which give 4x = 3y.

Next we have 76*y + 85*z = 81(y+z) which give 4z = 5y .

Now overall average of all the classes can be given as $$\frac{83x+76y+85z}{x+y+z}$$

Substitute the relations in above equation we get,

$$\frac{83x+76y+85z}{x+y+z}$$ = (83*3/4 + 76 + 85*5/4)/(3/4 + 1 + 5/4) = 978/12 = 81.5

Question 27

Two sides of a plot measure 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. What is the area of the plot?

Video Solution

Solution

Length of the diagonal of the right triangle is 40.

The height of the isosceles triangle formed, with 40 as its base is 15.
So, area = (1/2 * 32 * 24) + (1/2 * 40 * 15) = 384 + 300 = 684 $$m^2$$

Question 28

All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

Video Solution

Solution

If the number of pages is 44, the sum will be 44*45/2 = 22*45 = 990
So, the number 10 was added twice

Question 29

Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

Video Solution

Solution

Let the number of steps on the escalator be x.

So, by the time Shyama covered 25 steps, the escalator moved 'x-25' steps.

Hence, the ratio of speeds of Shyama and escalator = 25:(x-25)

Similarly, the ratio of speeds of Vyom and escalator = 20:(x-20)

But the ratio is 3:2

Ratio of speeds of Shyama and Vyom = 25(x-20)/20*(x-25) = 3/2

=> 10(x-20) = 12(x-25)

=> 2x = 100 => x = 50

Question 30

At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

Video Solution

Solution

Let the price of 1 burger be x and the price of 1 shake be y and the prize of 1 french fries be z
3x + 7y + z = 120
4x + 10y + z = 164.5
=> x + 3y = 44.5
=> x = 44.5 - 3y
=> 3(44.5 - 3y) + 7y + z = 120 => z = 120 - 133.5 + 2y
So, x+y+z = 44.5 - 3y + y -13.5 + 2y = 31
So, the cost of a meal consisting of 1 burger, 1 shake and 1 french fries = Rs 31

CAT Content

CAT 2001 Question Paper

If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been a

In a number system the product of 44$$_{10}$$ and 11$$_{10}$$ is 3414. The number 3111 of this system, when converted to the decimal number system, becomes

Two sides of a plot measure 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. What is the area of the plot?

All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

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CAT Content

CAT 2001 Question Paper

If 09/12/2001(DD/MM/YYYY) happens to be Sunday, then 09/12/1971 would have been a

In a number system the product of 44$$_{10}$$ and 11$$_{10}$$ is 3414. The number 3111 of this system, when converted to the decimal number system, becomes

Two sides of a plot measure 32 m and 24 m and the angle between them is a perfect right angle. The other two sides measure 25 m each and the other three angles are not right angles. What is the area of the plot?

All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

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