Is A multiple of 6?

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.

GMAT assassins aren't born, they're made,
Rich

Target question: Is A multiple of 6 ?

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

Answer = E

Cheers,
Brent

For A to be a multiple of 6, A must be divisible by both 2 and 3.

I believe the concept of having the product as it is in statement 1 is the following:

If B is an integer, the 3 factors would be three terms separated by a common difference of +4.

Accordingly , since we have three evenly spaced integers, there will always be exactly ONE multiple of 3 no matter the integer value of B.

(The ONE EXCEPTION being if the common difference is +3 and each integer is NOT a multiple of 3)

So if we know that B is an integer, the question becomes

“is A even?”

Statement 1: is A a multiple of 6?

Even if we knew whether or not B were an integer (and we don’t have any information either way):

Case 1:
If B = ODD ——- we would have a product of three odd integers (one of them a multiple of 3).

In such a case, A would not be divisible by 2 , even thought it would be divisible by 3.

Not a multiple of 6.

Case 2: if B = EVEN —— then we would have three even factors, one of which must be a multiple of 3.

Yes: is a multiple of 6.

S1 not sufficient.

S2: no information is given regarding A.

S1 & S2 Together:

S2: (B - 4) = 3q ——- where q = any integer

Thus, we know that B must be an integer.

However, we already know from statement 1 that if B is an integer, the product of 3 evenly spaced integers will always include exactly one multiple of 3.

We still don’t know whether A is EVEN.

Case 1 and case 2 still hold.

*E*

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