Is x > y?

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Is x > y?

by VJesus12 » Thu Nov 23, 2017 6:54 am
Is x > y?

(1) x - 5 > y - 5
(2) x^2> xy

The OA is A .

Experts, why statement (2) is not sufficient? I would like your explanation here.
Source: — Data Sufficiency |

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Is x>y?

by GMATGuruNY » Thu Nov 23, 2017 7:46 am
VJesus12 wrote:Is x > y?

(1) x - 5 > y - 5
(2) x^2> xy
Statement 1:
Adding 5 to both sides, we get:
x > y.
Thus, the answer to the question stem is YES.

Statement 2:
Case 1: x=1 and y=0, with the result that x² = 1² = 1 and xy = (1)(0) = 0
In this case, x > y, with the result that the answer to the question stem is YES.
Case 2: x=-1 and y=0, with the result that x² = (-1)² = 1 and xy = (-1)(0) = 0
In this case, x < y, with the result that the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

The correct answer is A.
Last edited by GMATGuruNY on Sat Nov 25, 2017 4:18 pm, edited 1 time in total.
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by ceilidh.erickson » Sat Nov 25, 2017 4:15 pm
Remember also that we cannot simply divide both sides by x. If x were negative, the inequality sign would flip. If x were 0 and y were negative, we wouldn't be allowed to divide by x at all.

You can either test cases as Mitch did, or you can give yourself a positive, a negative, and a 0 case.
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