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The solution is not correct- The answer should be c

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by GMATGuruNY » Mon Jul 29, 2013 8:28 am
is x between 0 and 1?
1) x² is less than x
2) x³ is positive
Statement 1: x² < x
Consider the following options for x:
-2, -1, -1/2, 0, 1/2, 1, 2.
Only the value in red satisfies the constraint that x²<x:
(1/2)² < 1/2
1/4 < 1/2.
The implication is that x must be a POSITIVE FRACTION BETWEEN 0 AND 1.
SUFFICIENT.

Statement 2: x³ > 0
Consider the following options for x:
-2, -1, -1/2, 0, 1/2, 1, 2.
Any of the values in red will satisfy the constraint that x³>0.
If x = 1/2, then x is between 0 and 1.
If x = 1, then x is NOT between 0 and 1.
INSUFFICIENT.

The correct answer is A.
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by [email protected] » Mon Jul 29, 2013 6:15 pm
GMATGuruNY wrote:
is x between 0 and 1?
1) x² is less than x
2) x³ is positive
Statement 1: x² < x
Consider the following options for x:
-2, -1, -1/2, 0, 1/2, 1, 2.
Only the value in red satisfies the constraint that x²<x:
(1/2)² < 1/2
1/4 < 1/2.
The implication is that x must be a POSITIVE FRACTION BETWEEN 0 AND 1.
SUFFICIENT.

Statement 2: x³ > 0
Consider the following options for x:
-2, -1, -1/2, 0, 1/2, 1, 2.
Any of the values in red will satisfy the constraint that x³>0.
If x = 1/2, then x is between 0 and 1.
If x = 1, then x is NOT between 0 and 1.
INSUFFICIENT.

The correct answer is A.
But Mitch they are asking if x is between 0 and 1, nowhere is it mentioned that x is between 0 and -1
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by Matt@VeritasPrep » Tue Jul 30, 2013 8:35 am
Here's some algebraic justification:

On the GMAT, x² ≥ 0, no matter what.

If x > x², then we really have the equation x > x² ≥ 0

0 isn't a valid solution to x > x², so x is positive, and our equation is x > x² > 0.

Dividing the entire equation by x, we get 1 > x > 0 -- since x is positive, division by x doesn't change the signs -- and the first statement is sufficient.
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