BTGModeratorVI wrote: ↑Fri Apr 03, 2020 9:34 am
Is a < 0 ?
(1) a³ < a² + 2a
(2) a² > a³
Answer:
E
Source: Manhattan prep
Target question: Is a < 0 ?
Statement 1: a³ < a² + 2a
Subtract a² and 2a from both sides to get: a³ - a² - 2a < 0
Factor: a(a² - a - 2) < 0
Factor more: a(a - 2)(a + 1) < 0
There are several values of a that satisfy this inequality. Here are two:
Case a: a = 0.5. In this case,
a > 0
Case b: a = -10. In this case,
a < 0
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a² > a³
There are several values of a that satisfy this inequality. Here are two:
Case a: a = 0.5. In this case,
a > 0
Case b: a = -10. In this case,
a < 0
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are several values of a that satisfy BOTH statements Here are two:
Case a: a = 0.5. In this case,
a > 0
Case b: a = -10. In this case,
a < 0
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
