Number Theory Previous Year Questions (CAT)  Set 0020

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

Question 1
If x is a positive integer such that 2x +12 is perfectly divisible by x, then the number of possible values of x is
(a) 2
(b) 5
(c) 6
(d) 12Â (CAT 1991)

Question 2
If 8 + 12 = 2, 7 + 14 = 3 then 10 + 18 = ?
(a) 10
(b) 4
(c) 6
(d) 18 (CAT 1991)

Question 3
There were x pigeons and y mynahs in a cage. One fine morning p of them escaped to freedom. If the bird keeper, knowing only that p = 7, was able to figure out without looking into the cage that at least one pigeon had escaped, then which of the following does not represent a possible (x,y) pair?
(a) (10,8 )
(b) (7,2)
(c) (25,6)
(d) (12,4)Â (CAT 1990)

Question 4

Question 5

Question 6
The remainder when 2^{60 }is divided by 5 equals
(a) 0
(b) 1
(c) 2
(d) None of theseÂ (CAT 1990)

Question 7
If n is any positive integer, then n^{3}â n is divisible
(a) Always by 12
(b) Never by 12
(c) Always by 6
(d) Never by 6Â (CAT 1990)

Question 8
The value of (1d^{3})/(1d) is
(a) > 1 if d > 1
(b) > 3 if d > 1
(c) > 2 if 0 < d < 0.5
(d) < 2 if d < 2 (CAT 1990)

Question 9
I brought 30 books on Mathematics, Physics, and Chemistry, priced at Rs.17, Rs.19, and Rs.23 per book respectively, for distribution among poor students of Standard X of a school. The physics books were more in number than the Mathematics books but less than the Chemistry books, the difference being more than one. The total cost amounted to Rs.620. How many books on Mathematics, Physics, and Chemistry could have been bought respectively?
(a) 5, 8, 17
(b) 5, 12, 13
(c) 5, 10, 15
(d) 5, 6, 19Â Â Â (CAT 1990)

Question 10
The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50 and Rs.5.00 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did Rahul give?
(a) 8
(b) 9
(c) 10
(d) 11Â (CAT 1990)