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Is it true that x > 0?

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Is it true that x > 0?

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Is it true that x > 0?

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

OA C

Source: GMAT Prep

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BTGmoderatorDC wrote:
Is it true that x > 0?

(1) x² = 2x
(2) x³ = 3x
Target question: Is it true that x > 0?

Statement 1: x² = 2x
Rewrite as: x² - 2x = 0
Factor: x(x - 2) = 0
So, EITHER x = 0 OR x = 2
Let's examine each possible case
Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0
Case b: If x = 2, then the answer to the target question is YES, it is true that x > 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x³ = 3x
Rewrite as: x³ - 3x = 0
Factor: x(x² - 3) = 0
Factor again: x(x - √3)(x + √3) = 0
So, x = 0, OR x = √3 OR x = -√3
Let's examine each possible case
Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0
Case b: If x = √3, then the answer to the target question is YES, it is true that x > 0
Case c: If x = -√3,, then the answer to the target question is NO, it is not true that x > 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = 0 OR x = 2
Statement 2 tells us that x = 0, OR x = √3 OR x = -√3
The only x-value that satisfies BOTH statements is x = 0
So, the answer to the target question is NO, it is not true that x > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

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BTGmoderatorDC wrote:
Is it true that x > 0?

(1) x^2 = 2x
(2) x^3 = 3x
Statement 1:
Case 1: x=0
In this case, the answer to the question stem is NO.
Case 2: x≠0, allowing us to divide both sides by x
x²/x = 2x/x
x = 2
In this case, the answer to the question stem is YES.
INSUFFICIENT.

Statement 2:
Case 1: x=0
In this case, the answer to the question stem is NO.
Case 2: x≠0, allowing us to divide both sides by x
x³/x = 3x/x
x² = 3
x = ±√3
If x=√3, the answer to the question stem is YES.
INSUFFICIENT.

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

The correct answer is C.

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