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If 1 < y < 2, and 0 < x < 1, is x > 1/2?

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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Feb 13, 2014 9:23 pm
gmattesttaker2 wrote:Hello,

Can you please help with this:

If 1 < y < 2, and 0 < x < 1, is x > 1/2?

1) xy = 1

2) (x - 2/3)(x + 1) = 0

OA: D

Thanks a lot,
Sri
Statement 1: xy = 1
Thus, y = 1/x.
The question stem indicates that y < 2.
Substituting y = 1/x into y < 2, we get:
1/x < 2.

Since x>0, we can safely multiply each side by x:
1/x * x < 2x
1 < 2x
1/2 < x.
SUFFICIENT.

Statement 2: (x - 2/3)(x + 1) = 0
The solutions of the equation above are x = 2/3 or x = -1.
Since the question stem requires that x be between 0 and 1, it is not possible that x = -1.
Thus, x = 2/3, with the result that x > 1/2.
SUFFICIENT.

The correct answer is D.
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