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Is xy > 16?

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Mar 09, 2018 5:42 am
ardz24 wrote:Is xy > 16?

(1) 1 < |x| < 4
(2) y > 16
Both statements are satisfied by the following cases:
Case 1: x=2 and y=20, with the result that xy > 16.
Case 2: x=-2 and y=20, with the result that xy < 16.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Mar 09, 2018 7:20 am
ardz24 wrote:Is xy > 16?

(1) 1 < |x| < 4
(2) y > 16
Target question: Is xy > 16?

Statement 1: 1 < |x| < 4
Since there's no information about y, we cannot determine whether xy is greater than 16
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y > 16
Since there's no information about x, we cannot determine whether xy is greater than 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 2 and y = 20, in which case xy = 40. In this case, the answer to the target question is YES, xy IS greater than 16
Case b: x = -2 and y = 20, in which case xy = -40. In this case, the answer to the target question is NO, xy is NOT greater than 16
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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