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.

_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto