viktorija wrote:
Is it true that x > 0?
(1) x^2 = 2x
(2) x^3 = 3x
The GMAC explanation for the statement (2) states, that for the x^3=3x, values for x are 0 and 3. It sounds incorrect to me.
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 = 2Let'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 > 0Case b: If x = 2, then the answer to the target question is
YES, it is true that x > 0Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x³ = 3xRewrite 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 = -√3Let'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 > 0Case b: If x = √3, then the answer to the target question is
YES, it is true that x > 0Case c: If x = -√3,, then the answer to the target question is
NO, it is not true that x > 0Since 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 = 2Statement 2 tells us that
x = 0, OR x = √3 OR x = -√3The only x-value that satisfies BOTH statements is
x = 0So, the answer to the target question is
NO, it is not true that x > 0Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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