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Is A multiple of 6?

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Is A multiple of 6? [#permalink]  17 Sep 2012, 04:50
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68% (02:23) correct 32% (01:22) wrong based on 138 sessions
Is A multiple of 6?

(1) A = B(B+4)(B-4)
(2) B-4 is a multiple of 3.
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Re: Is A multiple of 6? [#permalink]  17 Sep 2012, 05:01
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Is A =6K ?

Statement 1 - A = (B-4)(B)(B+4)
B= 4, A =0 ----> No, A is not a multiple of 6
B= 6, A =(2)(6)(10) -----> Yes, A is a multiple of 6

Statement 2 - B is a multiple of 3 - B has no relationship with A.

Combined Statement 1 + Statement 2
B=6, As seen above "A" is a multiple of 6
B=9, A =(5)(9)(13) ----> No, A is not a multiple of 6

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Re: Is A multiple of 6? [#permalink]  17 Sep 2012, 07:53
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Is A multiple of 6?

(1) A = B(B+4)(B-4). If $$B=odd$$, then $$A=B(B+4)(B-4)=odd*odd*odd=odd$$ and the answer is NO but if $$B=6$$, then the answer is obviously YES. Not sufficient.

(2) B-4 is a multiple of 3. B is 4 more than a multiple of 3. Not sufficient, since no info about A.

(1)+(2) From (2) we have that B is 4 more than a multiple of 3 and from (1) that $$A=B(B+4)(B-4)$$. If $$B=odd$$ (for example if $$B=7$$), then the answer is NO but if $$B=4$$, then $$A=B(B+4)(B-4)=0$$ and the answer is YES (since zero is a multiple of all integers except zero itself). Not sufficient.

Hope it helps.
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Re: Is A multiple of 6? [#permalink]  23 Jan 2015, 04:19
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Re: Is A multiple of 6? [#permalink]  23 Jan 2015, 11:52
Expert's post
Hi All,

The approach that Pansi used (TESTing VALUES) is perfect for this question and the ultimate answer IS correct.

HOWEVER, I do want to point out one error in that particular explanation....

We're asked if A is a multiple of 6. This is YES/NO question.

Fact 1: A = B(B+4)(B-4)

IF....
B = 4
A = (4)(8)(0) = 0
0 IS a multiple of EVERYTHING, so the answer to the question is YES (not NO, as written).

IF....
B = 5
A = (5)(9)(1) = 45
45 is NOT a multiple of 6, so the answer to the question is NO.

So Fact 1 IS INSUFFICIENT, but not for the reason that Pansi originally stated.

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Re: Is A multiple of 6?   [#permalink] 23 Jan 2015, 11:52
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