MAT PO CAT

# Quantitative Aptitude

## Sample Paper 5

Question 1: The average age of all the girls in a class of 42 students is 13 years. The average age of all the boys as well as the average age of 23 of the boys of the same class is 16 years. Which of the following could be the average age of all the students in the class?

(a) 13.5

(b) 14

(c) 14.5

(d) 15

**Answer:** (c) 14.5

**Explanation:** Let us assume that the number of boys = 23

So, total age of boys `= 23 xx 16 = 368`

If number of boys is 23 then number of girls `= 42 – 23 = 19`

So, total age of girls `= 19 xx 13 = 247`

Total age of all students `= 368 + 247 = 615`

Average age of all students `= (615)/(42) = 14.5` (approx)

Question 2: The price of 35 pens, 28 erasers and 14 books is Rs. 336, whereas the price of 15 pens, 12 erasers and 10 books is Rs. 184. Find the total cost of 20 pens, 16 erasers and 1 book.

(a) 122

(b) 140

(c) 136

(d) 128

**Answer:** (a) 122

**Explanation:** `35P + 28E + 14B = 336` ……….(1)

`15P + 12E + 10B = 184` …………..(2)

Subtracting equation (2) from (1), we get;

`35P + 28E + 14B – 15P – 12E – 10B = 336 – 184`

Or, `20P + 16E + 4B = 152` …………(3)

Dividing above equation by 4, we get;

`5P + 4E + B = 38` ………..(4)

Subtracting equation (4) from (3), we get;

`20P + 16E + 4B – 5P – 4E – B = 152 – 38`

Or, `15P + 12E + 3B = 114` …….(5)

Subtracting equation (5) from (2), we get;

`15P + 12E + 10B – 15P – 12E – 3B = 184 – 114`

Or, `7B = 70`

Or, `B = 10`

Now, `15P + 12E + B = ?`

Value of this equation can be found by subtracting the value of 3B from equation (3)

`15P + 12E + 4B – 3E = 152 – 30 = 122`

Question 3: A boy is trying to cover a distance of 100 m up a ramp. He takes a jump forward and covers 2 m, but every time he jumps forward he also slips backwards by 1 m. In all, how many jumps would be required to cover the distance?

(a) 99

(b) 100

(c) 98

(d) 97

**Answer:** (a) 99

**Explanation:** After every jump, the boy covers 1 m, i.e. 2 m – 1m = 1m

After 98th jump, the boy will cover 98 m

In 99th jump, he will reach 100 m, i.e. 98 + 2

Question 4: Three runners X, Y and Z run at uniform speeds. X beats Y by 12 meter and beats Z by 24 meter. Y beats Z by 15 meter. Find the length of the race.

(a) 50

(b) 80

(c) 90

(d) 60

**Answer:** (d) 60 m

**Explanation:** Let us assume that distance = D

When X covers D

Y covers D – 12

And Z covers D – 24

So, when Y covers D then Z will cover `((D – 24) xx D)/(D – 12)`

As per question; when Y covers D then Z covers D – 15

So, `(D^2 - 24D)/(D – 12) = D – 15`

Or, `D^2 - 24D = D^2 - 27D + 180`

Or, `- 24D = 180 – 27D`

Or, `180 – 27D + 24D = 0`

Or, `180 – 3D = 0`

Or, `3D = 180`

Or, `D = 60` m

Question 5: There are two clocks, which are set to correct time on Sunday at 12:00 noon. The first clock gains 2.5 minutes every hour while the second clock loses 1.5 minutes every hour. When will they be 2 hours apart?

(a) Monday 9:00 pm

(b) Tuesday 12:00 midnight

(c) Monday 6:00 pm

(d) Tuesday 6:00 am

**Answer:** (c) Monday 6:00 pm

**Explanation:** Difference between two clocks after 1 hour = 2.5 + 1.5 = 4 min

To be 2 hours apart they need to spend following time

`(2 xx 60 text(min))/(4 text(min)) = 30` hours

So, it will be Monday 6:00 pm