Which of the following inequalities represents the entire solution set for x if |x| > x?

This topic has expert replies
Moderator
Posts: 6112
Joined: 07 Sep 2017
Followed by:20 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Which of the following inequalities represents the entire solution set for x if |x| > x?

A. x ≥ 0
B. x > 0
C. x ≤ 0
D. x < 0
E. x < −1


OA D

Source: Veritas Prep

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 15867
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770
BTGmoderatorDC wrote:
Fri Oct 08, 2021 6:26 pm
Which of the following inequalities represents the entire solution set for x if |x| > x?

A. x ≥ 0
B. x > 0
C. x ≤ 0
D. x < 0
E. x < −1


OA D

Source: Veritas Prep
One approach is to test numbers...

For example, does x = 1 satisfy the given inequality?
When we test, we get |1| > 1, which is not true.
Since x = 1 is NOT a solution, we can eliminate answer choices A and B, because they say that x = 1 IS a solution.

Now let's test another number.
Does x = 0 satisfy the given inequality?
When we test, we get |0| > 0, which is not true.
Since x = 1 is NOT a solution, we can eliminate answer choice C, because it says that x = 0 IS a solution.

We are down to D or E.
Does x = -1 satisfy the given inequality?
When we test, we get |-1| > -1, which is true.
Since x = -1 IS a solution, we can eliminate answer choice E, because is says that x = 0 is NOT a solution.

By the process of elimination, the correct answer is D.
Brent Hanneson - Creator of GMATPrepNow.com
Image