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is -4/X^3 negative ?

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Source: — Data Sufficiency |
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by theCodeToGMAT » Wed Oct 30, 2013 10:25 pm
To find: -4/X^3 negative

Statement 1:
X is positive
So, -/+ ==> -ve
SUFFICIENT

Statement 2:
x^3 - x^2 => POSITIVE
x^2(x-1) is POSITIVE
here, x^2 will always be positive.. So, x-1 must be positive.. that means x is positive and greater than 1
SUFFICIENT

Answer [spoiler]{D}[/spoiler]??
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by mevicks » Wed Oct 30, 2013 11:16 pm
canbtg wrote:if x is not equal to 0, is -4/x³ negative ?

1)x is positive
2)x³ - x² is positive
Given: x ≠ 0

Q: Is -4 / x³ negative ?
Simplify:
-4 / x³ < 0 ?
Multiply both sides by -1
4/x³ > 0 ?
4/x³ positive ?
Since cube of a number preserves the sign, the fraction would be positive ONLY WHEN x > 0 (x is +ive)
Thus the question becomes :
Is x positive ?

St1:
Directly gives the answer
SUFFICIENT

St2:
x³ - x² is positive
x³ - x² > 0
x³ > x²
Now cube of a number can be only greater than its square if x > 1
In other words x is positive.
SUFFICIENT

x = 1; x³ = x²
x = 0; x³ = x² (prob states this as an invalid option)
x = -1; x³ < x²

[spoiler]Answer : D[/spoiler]
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by GMATGuruNY » Thu Oct 31, 2013 2:55 am
canbtg wrote:if x is not equal to 0, is -4/X^3 negative ?

1)x is positive
2)X^3-x^2 is positive

OAD
A very useful strategy:
When x≠0, we can safely divide each side of an inequality by x², which must be equal to a POSITIVE value.

Is (-4)/x³ < 0?
Since negative/positive = negative, (-4)/x³ < 0 only if x³ > 0.
Dividing each side of x³ > 0 by x², we get:
x³/x² > 0/x²
x > 0.

Question rephrased: Is x > 0?

Statement 1: x > 0
SUFFICIENT.

Statement 2: x³ - x² > 0
x³ > x²
x³/x² > x²/x²
x > 1.
SUFFICIENT.

The correct answer is D.
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