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Is x^2 > 1/x ?

This topic has 3 expert replies and 0 member replies

Is x^2 > 1/x ?

Post Thu Sep 14, 2017 1:48 pm
Is x^2 > 1/x ?

(1) x^2 > x

(2) 1 > 1/x

The OA is D.

Really each statement alone is sufficient? Why?

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Post Fri Sep 15, 2017 10:49 am
Vincen wrote:
Is x² > 1/x ?

(1) x² > x
(2) 1 > 1/x
Target question: Is x² > 1/x ?

Statement 1: x² > x
First off, this inequality tells us that x ≠ 0
Second, we can conclude that x² is POSITIVE.
So, we can safely divide both sides of the inequality by x² to get: 1 > 1/x
If 1 > 1/x, then there are two possible cases:
Case a: x > 1. If x is a positive number greater than 1, then 1/x will definitely be less than 1.
Case b: x is negative. If x is negative, then 1/x will definitely be less than 1.

IMPORTANT: So how do these two cases affect the answer to the target question? Let's find out.
Case a: If x > 1, then x² is greater than 1, AND 1/x is less than 1. This means x² > 1/x
Case b: If x is negative, then x² is positive, AND 1/x is negative. This means x² > 1/x
Perfect - in both cases, we get the SAME answer to the target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 1 > 1/x
Notice that this inequality is the SAME as the inequality derived from statement 1 (we got 1 > 1/x)
Since we already saw that statement 1 is sufficient, it must be the case that statement 2 is also SUFFICIENT

Answer: D

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
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Top Reply
Post Fri Sep 15, 2017 9:43 am
Hi Vincen,

We're asked if X^2 is greater than 1/X. This is a YES/NO question. You can solve it by TESTing VALUES or using Number Properties.

1) X^2 > X

With the information in Fact 1, there are 2 'groups' of numbers that fit this inequality:
-ANY negative number
-Positive numbers that are GREATER than 1

IF... X = a negative, then X^2 is greater than 1/X and the answer to the question is YES.
IF... X = a negative, then X^2 is greater than 1/X and the answer to the question is YES.
Thus, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) 1 > 1/X

With the information in Fact 1, there are 2 'groups' of numbers that fit this inequality:
-ANY negative number
-Positive numbers that are GREATER than 1

These are the SAME 2 groups of numbers that fit Fact 1 - so we already know the answer to the question:
IF... X = a negative, then X^2 is greater than 1/X and the answer to the question is YES.
IF... X = a negative, then X^2 is greater than 1/X and the answer to the question is YES.
Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: D

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

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Contact Rich at Rich.C@empowergmat.com

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Post Fri Sep 15, 2017 10:49 am
Vincen wrote:
Is x² > 1/x ?

(1) x² > x
(2) 1 > 1/x
Target question: Is x² > 1/x ?

Statement 1: x² > x
First off, this inequality tells us that x ≠ 0
Second, we can conclude that x² is POSITIVE.
So, we can safely divide both sides of the inequality by x² to get: 1 > 1/x
If 1 > 1/x, then there are two possible cases:
Case a: x > 1. If x is a positive number greater than 1, then 1/x will definitely be less than 1.
Case b: x is negative. If x is negative, then 1/x will definitely be less than 1.

IMPORTANT: So how do these two cases affect the answer to the target question? Let's find out.
Case a: If x > 1, then x² is greater than 1, AND 1/x is less than 1. This means x² > 1/x
Case b: If x is negative, then x² is positive, AND 1/x is negative. This means x² > 1/x
Perfect - in both cases, we get the SAME answer to the target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 1 > 1/x
Notice that this inequality is the SAME as the inequality derived from statement 1 (we got 1 > 1/x)
Since we already saw that statement 1 is sufficient, it must be the case that statement 2 is also SUFFICIENT

Answer: D

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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Thanked by: Vincen
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