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Is x greater than 1? .......Inequality question

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by GMATGuruNY » Mon May 08, 2017 8:04 am
Mo2men wrote:Is x greater than 1?

(1) 1/x > −1

(2) 1/x^5 > 1/x^3
Statement 1:
It's possible that x=2 (in which case the answer to the question stem is YES) or that x=1 (in which case the answer to the question stem is NO).
INSUFFICIENT.

Statement 2:
The inequality in Statement 2 implies that x is nonzero, since division by 0 is not allowed.
Implication:
We can multiply the inequality by ANY EVEN POWER OF X, since (nonzero number)^(even power) = positive.
Multiplying each side by x�, we get:
x�/x� > x�/x³
x > x³.
When a value greater than 1 is cubed, the result is GREATER then the original value.
Thus, no value greater than 1 will satisfy x > x³, implying that x is NOT greater than 1.
SUFFICIENT.

The correct answer is B.
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by [email protected] » Mon May 08, 2017 9:56 am
Hi Mo2men,

This question can be solved by TESTing VALUES.

We're asked if X is greater than 1. This is a YES/NO question.

1) 1/X > -1

IF...
X = 1, then 1/1 > -1 and the answer to the question is NO
X = 2, then 1/2 > -1 and the answer to the question is YES
Fact 1 is INSUFFICIENT

2) 1/(X^5) > 1/(X^3)

With this Fact, we can use Number Property patterns to determine the values of X that are NOT possible...

IF...
X = 1, then 1/1 and 1/1 are equal - and that does NOT fit what we were told, so X CANNOT be 1

IF... X > 1, then X^5 will be bigger than X^3 (try any value of X greater than 1 and you'll see). Thus, when X > 1, 1/(X^5) will be SMALLER than 1/(X^3) - and that does NOT fit what we were told, so X CANNOT be greater than1.

Since X cannot be greater than/equal to 1, the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT

Final Answer: B

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