Is Zero divisible 3????

[Saurabh Malpani]

Is N*(N+1) divisible by 6

a) N is an even integer
2) N is divisible by 3


Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

My COncern:.

I don’t think the answer is correct WHY Didn’t we consider ZERO here isn’t zero divisible by 3??

Can't N=0?

Please respond this is a very Important Question

[Guest]

I don't know what answer is given to you. But I would go for (B)
Here's why:

* N is divisible by 3. Therefore for a non-zero N, (N + 1) is even and hence N*(N + 1) is divisible by (3*2) i.e. 6. If N = 0, N*(N + 1) = 0 and hence is still divisible by 6 (if 0 is divisible by 3, it is also divisible by 6). Sufficient
* N is even. Here (N+1) is odd, but not necessarily divisible by 3. e.g. if N = 4, N + 1 = 5 and N*(N + 1) is not divisible by 6. However, if N = 2, N + 1 = 3 and N*(N + 1) is divisible by 6. So, not sufficient

[Saurabh Malpani]

I don't know what answer is given to you. But I would go for (B)
Here's why:

* N is divisible by 3. Therefore for a non-zero N, (N + 1) is even and hence N*(N + 1) is divisible by (3*2) i.e. 6. If N = 0, N*(N + 1) = 0 and hence is still divisible by 6 (if 0 is divisible by 3, it is also divisible by 6). Sufficient
* N is even. Here (N+1) is odd, but not necessarily divisible by 3. e.g. if N = 4, N + 1 = 5 and N*(N + 1) is not divisible by 6. However, if N = 2, N + 1 = 3 and N*(N + 1) is divisible by 6. So, not sufficient

Oh ho!!! I see where I was wrong, thank you very much!!! What a silly mistake...

Thanks a ton!!

Saurabh Malpani

[j_sibal]

What about in the following case: is N(N+1)(N-1) divisible by 6?

1) N is a positive integer

2) N is divisible by 3

In this case can one consider 0 to be divisible by 6? (plugging in 1 in the first statement)

[RonPurewal]

What about in the following case: is N(N+1)(N-1) divisible by 6?

1) N is a positive integer

2) N is divisible by 3

In this case can one consider 0 to be divisible by 6? (plugging in 1 in the first statement)

heh, nice four-year bump.

yes, 0 is divisible by 6. in fact, 0 is divisible by EVERY positive integer.