Is x negative?
(1) At least one of x and x^2 is greater than x^3.
(2) At least one of x^2 and x^3 is greater than x.
OAC
Please explain.
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Is x negative
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In each of the inequalities below, test the following list of values:Is x negative?
(1) At least one of x and x^2 is greater than x^3.
(2) At least one of x^2 and x^3 is greater than x.
-2, -1, -1/2, 0, 1/2, 1, 2.
Statement 1: x > x³ or x² > x³ (or both)
Testing the list of values above, we get:
x > x³ is satisfied by -2 and 1/2.
x² > x³ is satisfied by -2, -1, -1/2, and 1/2.
Since can be negative or positive, INSUFFICIENT.
Statement 2: x² > x or x³ > x (or both)
Testing the list of values above, we get:
x² > x is satisfied by -2, -1, -1/2, and 2.
x³ > x is satisfied by -1/2 and 2.
Since x can be negative or positive, INSUFFICIENT.
Statements combined:
The values in red satisfy both statements.
All of the values in red are negative.
Implication:
To satisfy both statements, x must be negative.
SUFFICIENT.
The correct answer is C.
Last edited by GMATGuruNY on Sun Aug 20, 2017 6:37 pm, edited 1 time in total.
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Hi rsarashi,
This question is built around a couple of Number Property rules. If you recognize those patterns, then you can answer this question without too much trouble (you can also TEST VALUES to get to the solution).
We're asked if X is negative. This is a YES/NO question.
1) At least one of X and X^2 is greater than X^3.
With this Fact, X could be ANY negative value OR any positive fraction. For example...
IF....
X = -1, then
X^2 = +1
X^3 = -1
And X^2 is greater than X^3. The answer to the question is YES.
IF....
X = +1/2, then
X^2 = +1/4
X^3 = +1/8
And both X and X^2 are greater than X^3. The answer to the question is NO.
Fact 1 is INSUFFICIENT
2) At least one of X^2 and X^3 is greater than X.
With this Fact, X could be ANY negative value OR any positive value GREATER than 1. For example...
IF....
X = -1, then
X^2 = +1
X^3 = -1
And X^2 is greater than X. The answer to the question is YES.
IF....
X = +2, then
X^2 = +4
X^3 = +8
And both X^2 and X^3 are greater than X. The answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, there is only one group of numbers that 'fit' both Facts: negative values. Thus, X MUST be negative and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
This question is built around a couple of Number Property rules. If you recognize those patterns, then you can answer this question without too much trouble (you can also TEST VALUES to get to the solution).
We're asked if X is negative. This is a YES/NO question.
1) At least one of X and X^2 is greater than X^3.
With this Fact, X could be ANY negative value OR any positive fraction. For example...
IF....
X = -1, then
X^2 = +1
X^3 = -1
And X^2 is greater than X^3. The answer to the question is YES.
IF....
X = +1/2, then
X^2 = +1/4
X^3 = +1/8
And both X and X^2 are greater than X^3. The answer to the question is NO.
Fact 1 is INSUFFICIENT
2) At least one of X^2 and X^3 is greater than X.
With this Fact, X could be ANY negative value OR any positive value GREATER than 1. For example...
IF....
X = -1, then
X^2 = +1
X^3 = -1
And X^2 is greater than X. The answer to the question is YES.
IF....
X = +2, then
X^2 = +4
X^3 = +8
And both X^2 and X^3 are greater than X. The answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, there is only one group of numbers that 'fit' both Facts: negative values. Thus, X MUST be negative and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
