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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon Jun 18, 2012 9:10 am
cypherskull wrote:Is xy > 0?

(1) x - y > -2
(2) x - 2y < -6
Statement 1: x > (y - 2)
x and y can have any sign.
For example,
  • x = 2, y = 2 --> x > (y - 2) --> xy > 0
    x = 2, y = 0 --> x > (y - 2) --> xy = 0
Not sufficient

Statement 2: x < (2y - 6)
x and y can have any sign.
For example,
  • x = 2, y = 8 --> x < (2y - 6) --> xy > 0
    x = 0, y = 4 --> x < (2y - 6) --> xy = 0
Not sufficient

1 & 2 Together: (y - 2) < x < (2y - 6)
Hence, (y - 2) < (2y - 6) ---> y > 4

Therefore, x > (y - 2) = (4 - 2) = 2 > 0

Therefore, xy > 0

Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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