# CAT Model Paper 5 Questions and Answers with Explanation Part 4

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Q: 16. The average amount of money with a group of 20 students in . Two students with an average amount of leave the group. What can be maximum amount with any one of the 18 students if the minimum amount with everyone is ′

(A)

(B)

(C)

(D)

Ans: D

Solution:

Total amount with 20 students

Amount with 2 students who left

Remaining amount with 18 students

students have 20 each and the 18^{th} one would have .

Hence option D

Q: 17. Find the sum of all the four digit numbers that can be formed by using the digits 2, and , each digit being used at most once.

(A)

(B)

(C)

(D) None of these

Ans: A

Solution:

sum

Units place can be taken by times

Units place can be taken by times

Units place can be taken by times

Units place can be taken by times

Units place can be taken by times

Sum of the digits in the units place

Similarly, in tens, hundreds and thousands place, we get sum as

Sum of all 4 digits numbers formed

Hence option A

Q: 18. In a parallelogram ABCD, P and are the mid-points of AD and CD respectively. If the area of is , find the area of

(A)

(B)

(C) 12cm2

(D) 16cm2

Ans: D

Solution:

Let the height of the parallelogram be ‘h’ and the base of the parallelogram be ‘b’

From the above figure it is clear that the altitude of DPQ is the altitude of APB is h; the altitude of is h.

Area of the parallelogram

Area of

Area of

Area of

Hence, Area of

= Area of the parallelogram

Hence

Area of

Hence option D

Q: 19. What is the remainder when is divided by ?

(A)

(B)

(C) 2

(D) 6

Ans: A

Solution:

when divided by , always leaves a remainder of

when divided by , always leaves a remainder of

So the remainder when is divided by 12 is

Q: 20. Raju borrowed an amount from Raj at an interest rate of p. a. for a period of one year. Unfortunately he could not return the entire principal in one year. Hence Raj charged an interest rate of for the second year on the outstanding amount. But at the end of second year Raju returned only half of the amount that was payable at that time. Raj charged him p. a, on the third year on the outstanding amount. What is the total interest paid by Raju if he had borrowed an amount of?

(A)

(B)

(C)

(D) None of these

Ans: A

Solution:

Interest at end of 1^{st} year

Interest at end of 2^{nd} year

Total amount

Amount repaid

Interest on amount remaining

Total money repaid

Interest

Total money repaid

Interest

Hence option A