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Is it true that x > 0?

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Source: — Data Sufficiency |
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by GMATGuruNY » Tue Feb 06, 2018 4:47 am
ardz24 wrote:Is it true that x > 0?

(1) x^2 = 2x
(2) x^3 = 3x
Statement 1:
x² - 2x = 0
x(x-2) = 0.
The resulting equation is satisfied by x=0 (in which case the answer to the question stem is NO) or by x=2 (in which case the answer to the question stem is YES).
INSUFFICIENT.

Statement 2:
x³ - 3x = 0
x(x² - 3) = 0.
The resulting equation is satisfied by x=0 (in which case the answer to the question stem is NO) or by ±√3 (in which case the answer to the question could be YES or NO).
INSUFFICIENT.

Statements combined:
Only x=0 satisfies both statements.
Thus, the answer to the question stem is NO.

The correct answer is C.
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by Jeff@TargetTestPrep » Mon Feb 12, 2018 4:27 pm
ardz24 wrote:Is it true that x > 0?

(1) x^2 = 2x
(2) x^3 = 3x
x^2 = 2x

We can solve the equation as follows:

x^2 - 2x = 0

x(x - 2) = 0

x = 0 or x = 2

We see that if x = 0, then x is not greater than 0. However, if x = 2, then x is greater than 0. Statement one alone is not sufficient.

Statement Two Alone:

x^3 = 3x

We can solve the equation as follows:

x^3 - 3x = 0

x(x^2 - 3) = 0

x = 0 or x^2 = 3
x = 0 or x = √3 or x = -√3

We see that if x = 0 or -√3, then x is not greater than 0. However, if x = √3, then x is greater than 0. Statement two alone is not sufficient.

Statements One and Two Together:

Using both statements, we see that x can only be 0. Thus, x is not greater than 0. Both statements together are sufficient.

Answer: C

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