anairamitch1804 wrote:

Is a < 0 ?

(1) a³ < a² + 2a

(2) a² > a³

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 > 0Case b: a = -10. In this case,

a < 0Since 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 > 0Case b: a = -10. In this case,

a < 0Since 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 > 0Case b: a = -10. In this case,

a < 0Since we cannot answer the

target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,

Brent

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