Is 12 a factor of x(y2)? 1) X is a multiple of 24 2) Y is a multiple 6

Question

If x and y are integers, is 12 a factor of x(y^2)?

1) X is a multiple of 24
2) Y is a multiple of 6

Bunuel · Answer

It should be mentioned in the stem that x and y are positive integers. Otherwise the answer cannot be D.  Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only).

utkarshthapak · Answer

Thanks for the input  Bunuel . I am curious, what if x is negative? Say x= -24 and y is any integer negative or positive, Can 12 not be a factor of x(y^2) then? Sorry if my question is stupid.

Bunuel · Answer

12 is a factor of of -24. But again, every GMAT divisibility question will tell you in advance that any unknowns represent positive  integers  (ALL GMAT divisibility questions are limited to positive integers only). The word " integer " being most crucial part there. But apart from "integer" part, you won't be bothered with negative divisors/remainders or factors/remainders of negative integers too.

jy295 · Answer

I thought that the question was deliberately trying to trick the reader by omitting that x and y are integers, which would make A and B both insufficient on their own. However, when combined together, it is clear that both X and Y are integers and hence C should be the answer.

Can the original poster confirm what the real question should be?

Bunuel · Answer

Since the OA is given as D that was not the intent. Moreover if this were the intent the question would not be very GMAT-like as discussed above.

MathRevolution · Answer

==> In the original condition, there are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. However, for con 1), x has 12 as a factor from 24=2(12), hence yes, it is sufficient. For con 2), y^2 also has 36 as a factor, and from 36=3(12), y^2 has 12 as a factor as well, hence yes. The answer is D.

Answer: D

Answer: D

Bunuel · Answer

This solution is wrong. Please read the discussion above. What if y is, say  \sqrt {2}  for (1)? In this case x(y^2) won't be an integer and thus it will make no sense talking about its divisibility by 12. Similarly, what if x is, say  \sqrt{2}  for (2)? In this case x(y^2) won't be an integer and thus it will make no sense talking about its divisibility by 12. In its current form this is a poor quality, non-GMAT question.

MathRevolution · Answer

You are correct. Original intent is that x and y are integers.
The question is fixed now.

Thank you for your careful comment.

Bunuel · Answer

Thank you for fixing the question. Poor quality tag is removed.

Is 12 a factor of x(y2)? 1) X is a multiple of 24 2) Y is a multiple 6

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Is 12 a factor of x(y2)? 1) X is a multiple of 24 2) Y is a multiple 6

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