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If x ≠ y and x and y are non-zero integers...

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Nov 01, 2017 10:01 pm
AAPL wrote:If x ≠ y and x and y are non-zero integers, is (x+y)/(x−y) > 0?

(1) x > y
(2) |x| > |y|

The OA is B.

I don't understand this DS question. Please, can any expert help with it? Thanks.
(1) x > y

Case 1: x = 3 and y = 2, then (x+y)/(x−y) = (3 + 2)/(3 − 2) = 5 > 0. The answer is Yes.
Case 2: x = 3 and y = -2, then (x+y)/(x−y) = (3 - 2)/(3 + 2) = 1 > 0. The answer is Yes.
Case 3: x = 2 and y = -3, then (x+y)/(x−y) = (2 - 3)/(2 + 3) = -1/5 < 0. The answer is No. Insufficient.

(2) |x| > |y|

Only Case 1 and Case 2 are applicable here, thus, the answer is Yes. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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