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If x is an integer, is x/y an integer?

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by Vincen » Sun Oct 08, 2017 10:53 am
If x is an integer, is x/y an integer?

(1) 2x/y is an integer
(2) y is an odd integer.

The OA is C.

I don't know how to use both statements together. Can any expert give me some help here?
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Oct 08, 2017 11:16 pm
Vincen wrote:If x is an integer, is x/y an integer?

(1) 2x/y is an integer
(2) y is an odd integer.

The OA is C.

I don't know how to use both statements together. Can any expert give me some help here?
(1) 2x/y is an integer

If, for example, x/y = 1, then 2x/y = 2, the answer is Yes. However, x/y = 1/2, then 2x/y = 1, the answer is No. No unqie answer. Insufficient.

(2) y is an odd integer.

Clearly insufficient.

(1) and (2)

Since 2x/y is an integer and y cannot be 2 (since y is an odd integer), x must be a multiple of y. Thus, x/y is an integer. Sufficient.

The correct answer: C

Hope this helps!

-Jay

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