integer:

[7806]

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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

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.


A/C...?? i solved it as A.... but OA-C. pl confirm. thanks.

[Rahul@gurome]

(1) n(n + 1) is not divisible by 3 implies n and (n + 1) are not divisible by 3, which implies (n - 1) is always divisible by 3, since every 3rd number is divisible by 3.
So, (1) is SUFFICIENT.

(2) 3n+5 ≥ K+8 6r 3n ≥ K + 3, let us take K = 3M
Then 3n ≥ 3M + 3 or 3n ≥ 3(M + 1) or n ≥ (M + 1), but this is NOT SUFFICIENT to answer whether (n - 1) is divisible by 3.

The correct answer is [spoiler](A)[/spoiler].

Does that help?

[7806]

thanks rahul.

but you told ....n - 1 = 0, which is not divisible by 3

(1) n(n + 1) is not divisible by 3.
Let n = 1, then n^2 + n = 2, not divisible by 3. Here n - 1 = 0, which is not divisible by 3.
If n = 4, then n^2 + n = 20, not divisible by 3. But n - 1 = 3, which is divisible by 3.
No unique answer.
So, (1) is NOT SUFFICIENT.


isn't 0 is divisible by all numbers.??

Oa is C itself.

[Rahul@gurome]

You pointed that right. I have edited the post and did it straight away without taking any values. Statement (1) should be SUFFICIENT and that makes the OA as (A).