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 18th 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
Q 18 Image of Parallelogram
(A)
(B)
(C) 12cm2
(D) 16cm2
Ans: D
Solution:
Q 18 1 Image of Parallelogram
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 1st year
Interest at end of 2nd year
Total amount
Amount repaid
Interest on amount remaining
Total money repaid
Interest
Total money repaid
Interest
Hence option A