Number Theory Previous Year Questions (CAT)  Set 0014

Previous years`s CAT questions: Number Theory
Post your solutions as reply to respective questions below.

Question 1
Number of students who have opted for subjects A, B and C are 60, 84 and 108 respectively. The examination is to be conducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions?
a. 28
b. 60
c. 12
d. 21 (CAT 1998 )

Question 2
How many fivedigit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?
a. 0
b. 1
c. 4
d. 3 (CAT 1998 )

Question 3
You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg. And each emerald weighs 0.4 kg. Your bag can carry at the most 12 kg. What should you collect to get the maximum wealth?
a. 20 rubies and 15 emeralds
b. 40 rubies
c. 28 rubies and 9 emeralds
d. None of these Â Â (CAT 1998 )

Question 4
A is the set of positive integers such that when divided by 2, 3, 4, 5, 6 leaves the remainders 1, 2, 3, 4, 5 respectively. How many integers between 0 and 100 belong to set A?
a. 0
b. 1
c. 2
d. None of these (CAT 1998 )

Question 5
What is the digit in the unit’s place of 2^{51} ?
a. 2
b. 8
c. 1
d. 4 (CAT 1998 )

Question 6
My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates he wishes. But then he must have biscuits twice the number of chocolates and should have apples more than biscuits and chocolates together. Each chocolate cost Re 1. The cost of apple is twice the chocolate and four biscuits are worth one apple. Then which of the following can be the amount that I spent on that evening on my son if number of chocolates, biscuits and apples brought were all integers?
a. Rs. 34
b. Rs. 33
c. Rs. 8
d. None of these (CAT 1998 )

Question 7
A number is formed by writing first 54 natural numbers in front of each other as 12345678910111213... Find the remainder when this number is divided by 8.
a. 1
b. 7
c. 2
d. 0 (CAT 1998 )

Question 8

Question 9
A student instead of finding the value of 7/8 of a number, found the value of 7/18 of the number. If his answer differed from the actual one by 770, find the number.
a. 1584
b. 2520
c. 1728
d. 1656 (CAT 1997)

Question 10
P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q ?
a. 20
b. 65
c. 16
d. 35 (CAT 1997)