Is b < 0 ?

(1) b^3 < b

(2) b^2 > b

The OA is C .

I don't have this DS question clear. Experts, may you clarify this to me?

Thanks.

## Is b < 0 ?

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### GMAT/MBA Expert

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Vincen wrote:Is b < 0 ?

(1) bÂ³ < b

(2) bÂ² > b

**Target question:**

**Is b < 0 ?**

**Statement 1: bÂ³ < b**

There are several values of b that satisfy statement 1. Here are two:

Case a: b = -2 (which means bÂ³ = -8, and -8 < -2). In this case, the answer to the target question is YES, b IS less than 0

Case b: b = 1/2 (which means bÂ³ = 1/8, and 1/8 < 1/2). In this case, the answer to the target question is NO, b is NOT less than 0

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

**Statement 2: bÂ² > b**

There are several values of b that satisfy statement 2. Here are two:

Case a: b = -1 (which means bÂ² = 1, and 1 > -1). In this case, the answer to the target question is YES, b IS less than 0

Case b: b = 2 (which means bÂ² = 4, and 4 > 2). In this case, the answer to the target question is NO, b is NOT less than 0

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

**Statements 1 and 2 combined**

Statement 1 tells us that bÂ³ < b

Statement 2 tells us that bÂ² > b

Combine the inequalities to get: bÂ³ < b < bÂ²

This tells us that bÂ³ < bÂ²

Subtract bÂ² from both sides to get: bÂ³ - bÂ² < 0

Factor to get: b(bÂ² - b) < 0

If b(bÂ² - b) < 0, then there are TWO POSSIBLE CASES:

Case a: b < 0 and (bÂ² - b) > 0

OR

Case b: b > 0 and (bÂ² - b) < 0

If we take statement 2 (bÂ² > b) and subtract b from both sides, we get: bÂ² - b > 0

This RULES OUT case b (above), which means case a must be true.

If case a is true, then it must be the case that b < 0

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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We're asked if B is less than 0. This is a YES/NO question. You can solve it by TESTing VALUES and/or by using Number Property Rules.

1) B^3 < B

There are two types of numbers that fit the inequality we're given in Fact 1:

-Negative numbers that are LESS than -1 (using any of these values would get us a YES answer).

-Positive fractions (using any of these values would get us a NO answer).

Fact 1 is INSUFFICIENT

2) B^2 > B

There are two types of numbers that fit the inequality we're given in Fact 2:

-Positive numbers that are GREATER than 1 (using any of these values would get us a NO answer).

-ANY Negative numbers (using any of these values would get us a YES answer).

Fact 2 is INSUFFICIENT

Combined, we have to look for 'overlap' between the two Facts (what groups of numbers fit BOTH Facts?). There's only one group that fits both:

-Negative numbers that are LESS than -1.

Since we're limited to just these values, the answer to the question is ALWAYS YES).

Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,

Rich