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Is the value of x less than 0?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Nov 05, 2017 8:54 pm
LUANDATO wrote:Is the value of x less than 0?

(1) The product of x and y is negative.
(2) The difference between x and its reciprocal is positive.

The OA is E.

I don't understand this DS question. Please can any expert explain it for me? Thanks.
(1) The product of x and y is negative.

If x is negative and y is positive, the answer is Yes; however, if y is negative and x is positive, the answer is No. Insufficient.

(2) The difference between x and its reciprocal is positive.

x - 1/x > 0

=> x > 1/x

Case 1: Say x = -1/2, then 1/x = -2 and -1/2 > -2. The answer is yes, x is negative,
Case 2: Say x = 2, then 1/x = 1/2 and 2 > 1/2. The answer is no, x is NOT negative. Insufficient.

(1) and (2) combined:

Even after combing the two statements, we cannot conclude that x is negative or no.

The correct answer: E

Hope this helps!

-Jay
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