jennysussna wrote:
Is x > 0?
(1) (x² - 1)(x³) > 0
(2) x² < 1
Target question: Is x > 0? Statement 1: (x² - 1)(x³) > 0 Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 2. In this case, the answer to the target question is
YES, x is greater than 0Case b: x= -2. In this case, the answer to the target question is
NO, x is not greater than 0Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x² < 1Let's TEST some values.
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 0.5. In this case, the answer to the target question is
YES, x is greater than 0Case b: x= -0.5. In this case, the answer to the target question is
NO, x is not greater than 0Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 2 tells us that x² < 1
Subtract 1 from both sides to get: x² - 1 < 0
In other words,
x² - 1 is negativeStatement 1 tells us that (x² - 1)(x³) > 0
Divide both sides of the inequality by
(x² - 1) to get: x³ < 0
[ since we divided both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol]If x³ < 0, then we can be certain that
x is negativeThe answer to the target question is
NO, x is not greater than 0Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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