MAT PO CAT

Quantitative Aptitude

Sample Paper 7

Question 1: Fresh raisins contain 90% water by weight, while dry raisins contain 20% water by weight. Jack buys 64 kg of fresh raisins for $ 160. If he wants to earn 20% profit then what should be the price of one kg dry raisins?

  1. 24
  2. 30
  3. 36
  4. 40

Answer: (b)

Explanation: CP of 64 kg fresh raisins = $ 160

So, CP of 1 kg fresh raisins `(160)/(64)=$ 2.50`

In 100 unit of fresh raisins, there are 10 units raisin and 90 units water

When 100 unit of fresh raisins are dried it contains 10 units raisin

Here, 10 is 80%

So,20% = `(10)/(80)xx20=2.5` units

So, 100 kg fresh raisin will become `10+2.5=12.5` kg dry raisin

Profit on CP of 1 kg fresh raisin `=2.50xx20%=0.50`

So, SP of 1 kg fresh raisin `=2.50+0.50=3`

So, SP of 100 kg fresh raisin `=100xx3=300`

This is same as SP of 12.5 kg dry raisins

So, SP of 1 kg dry raisins `=(300)/(12.5)= $ 24`


Question 2: A and B do a particular work in `(24)/5` days. B and C do the same work in `(48)/7` days. A and C do the same work in `(16)/3` days. In how many days A, B and C will complete the work alone?

  1. 8, 12, 16
  2. 9, 12, 18
  3. 9. 15. 18
  4. 12, 16, 18

Answer: (a)

Explanation: Let us first find 1 day’s work for different pairs as follows:

`A+B=5/(24)`

`B+C=7/(48)`

`A+C=3/(16)`

Adding above three equations, we get:

`A+B+B+C+A+C=5/(24)+7/(48)+3/(16)`

Or, `2(A+B+C)=(10+7+9)/(48)``=(26)/(48)`

Or, `A+B+C=(26)/(48xx2)``=(13)/(48)`

Work done by A can be calculated as follows:

`A=A+B+C-(B+C)`

Or, `A=(13)/(48)-7/(48)`

Or, `A=6/(48)=1/8`

So, A will finish the work in 8 days

Similarly,

`B=A+B+C-(A+C)``=(13)/(48)-3/(16)`

Or, `B=(13-9)/(48)``=4/(48)=1/(12)`

So, B will finish the work in 12 days

Similarly,

`C=A+B+C-(A+B)=(13)/(48)-5/(24)=3/(48)``=1/(16)`

So, C will finish the work in 16 days


Question 3: Each interior angle of a regular polygon measures 157.5° This polygon has how many sides?

  1. 18
  2. 12
  3. 16
  4. 15

Answer: (c)

Explanation: Measure of each exterior angle of polygon `=180-157.5=22.5°`

So, number of sides `=(360)/(22.5)=16`


Question 4: Find the largest number which divides 238, 358 and 418 leaving the same remainder in each case.

  1. 45
  2. 60
  3. 90
  4. 120

Answer: (c)

Explanation: Let us solve it by using options

Let us start with the largest value, i.e. 120

238+2=240 is divisible by 120

358+2=360 is divisible by 120

But 418+2=420 is not divisible by 120

Let us take the second largest value, i.e. 90

This number can only divide 360

Let us take the next largest value, i.e. 60

It is clear that 60 divides 240, 360 and 420


Question 5: Height of a building is projected as 10 m more if angle of elevation increases from 45° to 60°. What is the height if angle of elevation is 60°

  1. `(10)/(sqrt3+1)`
  2. `10(sqrt3-1)`
  3. `10(sqrt3+1)`
  4. `(10)/(sqrt3-1)`

Answer: (d)

Explanation: If p is the altitude and b is the base of triangle in case of ∠ 45°

`text(tan)45°=p/b=11`

Or, `p=b`

In case of ∠60°

`text(tan)60°=(p+10)/(b)`

Or, `sqrt3=(p+10)/p`

Or, `p\sqrt3=p+10`

Or, `p\sqrt3-p=10`

Or, `10=p(sqrt3-1)`

Or, `p=(10)/(sqrt3-1)`