Data Sufficiency

Gmat_mission wrote: ↑

Sun Sep 19, 2021 12:37 pm

Is it true that \(x > 0?\)

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

Answer: C

Source: GMAT Prep

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