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OG If x is negative, is x < -3?

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG If x is negative, is x < -3?

Post Tue Aug 22, 2017 7:44 pm
If x is negative, is x < -3?

(1) x^2 > 9
(2) x^3 < -9

A

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Post Fri Aug 25, 2017 9:54 am
AbeNeedsAnswers wrote:
If x is negative, is x < -3?

(1) x^2 > 9
(2) x^3 < -9

A
We are given that x is negative and we must determine whether x < -3.

Statement One Alone:

x^2 > 9

Taking the square root of both sides of the inequality in statement one, we have:

√x^2 > √9

|x| > 3

x > 3 OR -x > 3

x > 3 OR x < -3

Since we are given that x is negative, we see that x must be less than -3. Statement one alone is sufficient to answer the question.

Statement Two Alone:

x^3 < -9

Using the information in statement two, we see that x can be less than -3 or not less than -3.

For example, if x = -4, (-4)^3 = -64, (which fulfills the statement) and -4 is less than -3.

However, if x = -3, (-3)^3 = -27, (which fulfills the statement) but -3 is not less than -3.

Statement two alone is not sufficient to answer the question.

Answer: A

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GMAT/MBA Expert

Post Wed Aug 23, 2017 9:41 am
Hi AbeNeedsAnswers,

We're told that X is NEGATIVE. We' asked if X < -3. This is a YES/NO question. We can answer it with a mix of basic math and TESTing VALUES

1) X^2 > 9

With this inequality, there would typically be two 'groups' of answers: those that are GREATER than 3 and those that are LESS than -3. Here though, the prompt tells us that X is NEGATIVE, so there is only one group of answers: those LESS than -3. Thus, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) X^3 < -9

IF....
X = -3, then the answer to the question is NO.
X = -4, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

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

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Contact Rich at Rich.C@empowergmat.com

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