Number Theory Previous Year Questions (CAT)  Set 0019

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

Question 1
Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal then said to Mushtaq. “If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the same number of cards, I will have thrice as many cards as you will have “. Of the given choices, which could represent the number of cards with Iqbal?
(a) 9
(b) 31
(c) 12
(d) 35 (CAT 1991)

Question 2

Question 3
The sum of two integers is 10 and the sum of their reciprocals is 5/12. Then the larger of these integers is
(a) 2
(b) 4
(c) 6
(d) 8Â (CAT 1991)

Question 4
x, y and z are three positive integers such that x > y > z. Which of the following is closest to the product xyz?
(a) (x1)yz
(b) x(y1)z
(c) xy(z1)
(d) x(y+1)z (CAT 1991)

Question 5
What is the greatest power of 5 which can divide 80! Exactly.
(a) 16
(b) 20
(c) 19
(d) None of these (CAT 1991)

Question 6
A third standard teacher gave a simple multiplication exercise to the kids. But one kid reversed the digits of both the numbers and carried out the multiplication and found that the product was exactly the same as the one expected by the teacher. Only one of the following pairs of numbers will fit in the description of the exercise. Which one is that?
(a) 14, 22
(b) 13, 62
(c) 19, 33
(d) 42, 28Â (CAT 1991)

Question 7
Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals
(a) 9
(b) 7
(c) 5
(d) 3Â (CAT 1991)

Question 8
Find the minimum integral value of n such that the division 55n/124 leaves no remainder.
(a) 124
(b) 123
(c) 31
(d) 62Â (CAT 1991)

Question 9
Gopal went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes, then the number of oranges he can buy is
(a) 25
(b) 20
(c) 18
(d) 6 (CAT 1991)

Question 10
In Sivakasi, each boy’s quota of match sticks to fill into boxes is not more than 200 per session. If he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him. Which of the following is the possible number of sticks assigned to each boy?
(a) 200
(b) 150
(c) 125
(d) 175 (CAT 1991)