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Is x < 0? (1) -2x > 0 (2) x^3 < 0

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed May 16, 2018 5:02 pm
alanforde800Maximus wrote:Is x < 0?

(1) -2x > 0
(2) x^3 < 0
Target question: Is x < 0?

Statement 1: -2x > 0
Divide both sides by -2 to get: x < 0 [since we're dividing both sides of an inequality by a NEGATIVE value, we REVERSE the inequality symbol]
So, the answer to the target question is YES, x < 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x^3 < 0
Since x^2 must be POSITIVE here, we can safely divide both sides of the inequality by x^2 to get: x < 0
So, the answer to the target question is YES, x < 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

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Brent
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by [email protected] » Thu May 17, 2018 6:13 pm
Hi alanforde800Maximus,

We're asked if X is less than 0. This is a YES/NO question and can be solved with Number Properties.

1) -2X > 0

The ONLY way for (-2)(X) to be positive is if X is a NEGATIVE number. Thus, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

2) X^3 < 0

When cubing a number, there are 3 possible outcomes:
IF
X = positive, then X^3 = positive
X = 0, then X^3 = 0
X = negative, then X^3 = negative

Fact 2 tells us that X^3 is negative, so X MUST be negative and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: D

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Rich
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