Is a < 0 ?

[BTGModeratorVI]

Is a < 0 ?
(1) a³ < a² + 2a
(2) a² > a³

Answer: E
Source: Manhattan prep

[Brent@GMATPrepNow]

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