DS Question - 22

n is a positive integer. What is the remainder when n is divided by 6?

(1) n is a multiple of 3.
(2) When n is divided by 2, the remainder is 1.

Answer: C

From statement (1) - n can be 3, 6, 9, 12...

Therefore:

(i) If n is odd, the reminder is 3 on dividing by 6.
(ii) If n is even, the reminder is 0 on dividing by 6.

Hence Insufficient.

From statement (2) - When n is divided by 2, the remainer is 1. Hence this is an odd integer as when an odd number is divided by 2, the remainder is 1.

n = 2*k + 1

(i) If n = 7 then n/6 = 6*1 + 1
(ii) If n = 9 then n/6 = 6*1 + 3

Hence insufficient.

taking statement (1) and (2) together - From Statement (1) we know that we need to know that whether n is odd or even in order to be able to conclude.Statement (2) gives us this information.

Hence Sufficient

Hence, C is the answer.