harikris wrote:

Hi Guys,

Could you please a solution to this problem ?

If n is a positive integer is n-1 divisible by 3 ?

1) n^2+n is not divisible by 6.

2)3n=3k+3 where k is a positive multiple of 3.

Thanks,

harikris

If you look at any three consecutive integers, one of them will always be a multiple of 3, since multiples of 3 are exactly 3 apart.

From Statement 1, we know that (n)(n+1) is not divisible by 6. One of n or n+1 is even, since n and n+1 are consecutive integers, so (n)(n+1) must be divisible by 2. So if (n)(n+1) is not divisible by 6, it must not be divisible by 3, so neither n nor n+1 are divisible by 3. But n-1, n, and n+1 are three consecutive integers, and one of them must be divisible by 3. If n and n+1 are not, then n-1 must be, so Statement 1 is sufficient.

From Statement 2, if 3n = 3k + 3, then n = k + 1. So n-1 = k, and since k is a multiple of 3, so must be n-1, since they're the same number. So Statement 2 is also sufficient and the answer is D.

Either you've miscopied Statement 2 or the OA is not right.

_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com