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

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 am; Thanked: 1 times; Followed by:5 members

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

by AbeNeedsAnswers » 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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Source: Beat The GMAT — Data Sufficiency | Tue Aug 22, 2017 7:44 pm

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by [email protected] » 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

Contact Rich at [email protected]

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by Scott@TargetTestPrep » 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:

âˆšx^2 > âˆš9

|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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