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# Is x > 0 ?

tagged by: M7MBA

#### Is x > 0 ?

Is x > 0 ?

(1) x < x^2
(2) x < x^3

The OA is the option E.

Can some expert explain how do we eliminate choice "C" for this DS question? I will wait for your answer.

### GMAT/MBA Expert

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M7MBA wrote:
Is x > 0 ?

(1) x < x²
(2) x < x³
Target question: Is x > 0 ? (i.e., is x POSITIVE?)

Statement 1: x < x²
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = -0.5 (notice that (-0.5)² = 0.25, so this meets the condition that x < x²) . In this case, x is NEGATIVE
Case b: x = 2 (notice that 2² = 4, so this meets the condition that x < x²). In this case, x is POSITIVE
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

Statement 2: x < x³
There are several values of x that satisfy statement 2. Here are two:
Case a: x = -0.5 (notice that (-0.5)³ = -0.125, so this meets the condition that x < x³) . In this case, x is NEGATIVE
Case b: x = 2 (notice that 2³ = 8, so this meets the condition that x < x³). In this case, x is POSITIVE
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: x = -0.5. In this case, x is NEGATIVE
Case b: x = 2. In this case, x is POSITIVE
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent

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