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7. 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.

solve and explain

n is a positive integer it can be even or odd. i.e it can be 1,2,3,4,5,6,7,8,...infinity. any number

now lets see what statement 1 has to say. statement 1 means the n is a multiple of 3 that is it can be 3,6,9,12,15,...,upto infinity i.e n=3a where a = 1,2,3,4,5,..infinity. when a is even then n is divisible by 6 and the remainder is 0 .but when a is odd n is divisible by 3 as it is multiple of 3 but not by 2 that is it is not divisible by 6 and we get a remainder equal to 1. so (1) is not sufficient.

similarly(2) is not sufficient. because in 2 we just know that n is a multiple of 2.

When we take (1)&(2) together. then statement 1 says that n is multiple of 3 and statement 3 says that n is multiple of 2 so can say that n is multiple of both 2 & 3 i.e 6. so n is completely divisible by 6. So the answere is (C).