Number Theory Previous Year Questions (CAT)  Set 0015

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

Question 1
If m and n are integers divisible by 5, which of the following is not necessarily true?
a. m – n is divisible by 5
b. m^{2}– n^{2} is divisible by 25
c. m + n is divisible by 10
d. None of these (CAT 1997)

Question 2

Question 3
P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is 3 less than two times R, find the value of R.
a. 5
b. 7
c. 9
d. 11 (CAT 1997)

Question 4
ABC is a threedigit number in which A > 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?
a. 9
b. 7
c. 4
d. 2 (CAT 1997)

Question 5

Question 6
If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be
a. 7 and 8
b. 8 and 0
c. 5 and 8
d. None of theseÂ Â (CAT 1996)

Question 7
If n is any odd number greater than 1, then n(n^{2}– 1) is
a. divisible by 96 always
b. divisible by 48 always
c. divisible by 24 always
d. None of these (CAT 1996)

Question 8
Once I had been to the post office to buy fiverupee, tworupee and onerupee stamps. I paid the clerk Rs. 20, and since he had no change, he gave me three more onerupee stamps. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought?
a. 10
b. 9
c. 12
d. 8 (CAT 1996)

Question 9
A salesman enters the quantity sold and the price into the computer. Both the numbers are twodigit numbers. But, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1,148, but the inventory reduced by 54.
What is the actual price per piece?
a. Rs. 82
b. Rs. 41
c. Rs. 6
d. Rs. 28 (CAT 1996)

Question 10