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# Is A multiple of 6?

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Intern
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Is A multiple of 6? [#permalink]

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17 Sep 2012, 05:50
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Is A multiple of 6?

(1) A = B(B+4)(B-4)
(2) B-4 is a multiple of 3.
[Reveal] Spoiler: OA
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Re: Is A multiple of 6? [#permalink]

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17 Sep 2012, 06:01
1
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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]

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17 Sep 2012, 08:53
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Expert's post
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]

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23 Jan 2015, 05:19
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Re: Is A multiple of 6? [#permalink]

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23 Jan 2015, 12:52
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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IS A multiple of 6 ? [#permalink]

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07 Feb 2016, 09:18
Need help on this problem

IS A multiple of 6 ?

1) A = B(B+4)(B-4)
2) B-4 is a multiple of 3
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Is A multiple of 6? [#permalink]

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07 Feb 2016, 09:32
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Sunil01 wrote:
IS A multiple of 6 ?

1) A = B(B+4)(B-4)
2) B-4 is a multiple of 3

Target question: Is A multiple of 6 ?

Given: If the average (arithmetic mean) the 4 numbers is 30

Statement 1: A = B(B+4)(B-4)
Since we're not told whether or not A and B are integers, this one seems insufficient.
If B = 6 then we have A = (6)(something)(something) and this means A is definitely divisible by 6.
However, if B = 1.4993949349394994, I know right away that A is not even an integer, which means A is definitely NOT divisible by 6.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: B-4 is a multiple of 3
Since there's no related information about A, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Test some values of B that satisfy statement 2. Here are two:
Case a: B = 7, in which case A = 7(7+4)(7-4) = (7)(11)(3) = some ODD integer. Here, we can see that A is NOT divisible by 6
Case b: B = 10, in which case A = 10(10+4)(10-4) = (10)(14)(6). Here, we can see that A IS divisible by 6
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Last edited by GMATPrepNow on 28 May 2016, 14:26, edited 1 time in total.
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Re: Is A multiple of 6? [#permalink]

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07 Feb 2016, 09:39
Expert's post
Sunil01 wrote:
Need help on this problem

IS A multiple of 6 ?

1) A = B(B+4)(B-4)
2) B-4 is a multiple of 3

Merging topics. Please refer to the discussion above.
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Re: Is A multiple of 6?   [#permalink] 07 Feb 2016, 09:39
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