Divisibility question

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neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Tue May 18, 2010 4:39 am

Given that n is an integer, is n - 1 divisible by 3?
(1) n^2 + n is not divisible by 3
(2) 3n +5 >= k+8 , where k is a positive multiple of 3

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Source: Beat The GMAT — Data Sufficiency | Tue May 18, 2010 4:39 am

November Rain: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Tue Oct 13, 2009 1:25 am; Thanked: 14 times; GMAT Score:720

by November Rain » Tue May 18, 2010 5:26 am

Hi,
I think its A

Statement 1 says that (n^2 + N) = N(N+1) is not divisible by 3. However, the rule says that the product of N consecutive integers is divisble by N, or, in this case, the product of 3 consecutive integers is divisble by 3.

Since N(N+1) is not divisible by 3, N-1 must be divisble by 3.

Statement 2 says that 3n >= K + 3 or N >= K/3 + 1, or N-1>= K/3. This means that N-1 could be a multiple of 3, but it also may not.

Whats the OA?

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raviki8208: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Mon May 10, 2010 1:23 am

by raviki8208 » Tue May 18, 2010 6:16 am

neoreaves wrote:Given that n is an integer, is n - 1 divisible by 3?
(1) n^2 + n is not divisible by 3
(2) 3n +5 >= k+8 , where k is a positive multiple of 3

using 1 alone, n^2 + n is not divisible
=> (n + 1) * n is not divisible
=> n and N+1 are not multiples of 3 so, n-1 is multiple.
Sufficient

using 2 alone, 3n+5 >= k+8
can not judge n so my answer is A.
what is OA?

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