Number Theory Previous Year Questions (CAT)  Set 0022

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

Question 1
How many even integers n, where 100 ≤ n ≤200, are divisible neither by seven nor by nine?
(1) 40
(2) 37
(3) 39
(4) 38 (CAT 2003 Leaked)

Answer: Option 3

Question 2
How many three digit positive integers, with digits x, y and z in the hundred's, ten's and unit's place respectively, exist such that x < y, z < y and x ≠ 0?
(1) 245
(2) 285
(3) 240
(4) 320 (CAT 2003 Leaked)

Answer: Option 3

Question 3
If the product of n positive real numbers is unity, then their sum is necessarily
(1) a multiple of n
(2) equal to n + 1/n
(3) never less than n
(4) a positive integer (CAT 2003 Leaked)

Answer: Option 3

Question 4

Answer: Option 4

Question 5

Answer: Option 3

Question 6
The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product
(n − 1)(n − 2)...3.2.1 is not divisible by n is
(1) 5
(2) 7
(3) 13
(4) 14 (CAT 2003 Leaked)

Answer: Option 2

Question 7
Let T be the set of integers {3, 11, 19, 27, ..., 451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is
(1) 32
(2) 28
(3) 29
(4) 30 (CAT 2003 Leaked)

Answer: Option 4

Question 8
A certain perfume is available at a dutyfree shop at the Bangkok international airport. It is priced in the Thai currency Baht but other currencies are also acceptable. In particular, the shop accepts Euro and US Dollar at the following rates of exchange:
US Dollar 1 = 41 Bahts and Euro 1 = 46 Bahts
The perfume is priced at 520 Bahts per bottle. After one bottle is purchased, subsequent bottles are available at a discount of 30%. Three friends S, R and M together purchase three bottles of the perfume, agreeing to share the cost equally. R pays 2 Euros. M pays 4 Euros and 27 Thai Bahts and S pays the remaining amount in US Dollars.
How much does R owe to S in Thai Baht?
(1) 428
(2) 416
(3) 334
(4) 324
How much does M owe to S in US Dollars?
(1) 3
(2) 4
(3) 5
(4) 6 (CAT 2003 Leaked)

Answer: Option 4 Option 3

Question 9

Answer: Option 2

Question 10
A, B, C are three numbers. Let
@ (A, B ) = average of A and B,
/ (A, B ) = product of A and B, and
X (A, B ) = the result of dividing A by B
The sum of A and B is given by
(1) /(@( A, B ), 2)
(2) X(@(A, B ), 2)
(3) @(/(A, B ), 2)
(4) @(X(A, B ), 2) (CAT 2000)