Number Theory Previous Year Questions (CAT)  Set 0016

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

Question 1
Out of twothirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than three fourths of the total number of matches, if it is true that no match can end in a tie?
a. 4
b. 6
c. 5
d. 3 (CAT 1996)

Question 2
A series S1 of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series S2, the nth term defined as the difference between the (n+1) term and the nth term of series S1, is an arithmetic progression with a common difference of 30.
First term of S1 is
a. 80
b. 90
c. 100
d. 120 (CAT 1996)

Question 3
5^{6}â 1 is divisible by
a.13
b. 31
c. 5
d. None of theseÂ Â (CAT 1995)

Question 4
A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is
a. 36
b. 40
c. 15
d. 20 (CAT 1995)

Question 5
For the product n(n + 1) (2n + 1), n element of N, which one of the following is not necessarily true?
a. It is even
b. Divisible by 3
c. Divisible by the sum of the square of first n natural numbers
d. Never divisible by 237 (CAT 1995)

Question 6

Question 7
The remainder obtained when a prime number greater than 6 is divided by 6 is
a. 1 or 3
b. 1 or 5
c. 3 or 5
d. 4 or 5 (CAT 1995)

Question 8
2/5 of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then the total number of voters is
a. 100
b. 110
c. 90
d. 95 (CAT 1995)

Question 9
Three consecutive positive even numbers are such that thrice the first number exceeds double the third by 2, then the third number is
a. 10
b. 14
c. 16
d. 12 (CAT 1995)

Question 10
Two positive integers differ by 4 and sum of their reciprocals is 10/21. Then one of the numbers is
a. 3
b. 1
c. 5
d. 21 (CAT 1995)