If x is negative, is x < -3?
(1) x^2 > 9
(2) x^3 < -9
A
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OG If x is negative, is x < -3?
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AbeNeedsAnswers
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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
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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Scott@TargetTestPrep
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We are given that x is negative and we must determine whether x < -3.AbeNeedsAnswers wrote:If x is negative, is x < -3?
(1) x^2 > 9
(2) x^3 < -9
A
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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