Modulus and inequality

Expert replies

Previous Topic Next Topic

rahulvsd: Master | Next Rank: 500 Posts; Posts: 184; Joined: Tue Sep 07, 2010 9:43 amFollowed by: 1 member; Thanked: 6 times

by rahulvsd » Wed Apr 18, 2012 8:02 am

If |x| is an integer, is |x| > 1 ?

A)(1 - 2x)(1 + x) < 0
B)(1 - x)(1 + 2x) < 0

[spoiler]OA: C[/spoiler]

Like this post

Source: Beat The GMAT — Data Sufficiency | Wed Apr 18, 2012 8:02 am

killer1387: Legendary Member; Posts: 581; Joined: Sun Apr 03, 2011 7:53 amFollowed by: 5 members; Thanked: 52 times

by killer1387 » Wed Apr 18, 2012 8:10 am

rahulvsd wrote:If |x| is an integer, is |x| > 1 ?

A)(1 - 2x)(1 + x) < 0
B)(1 - x)(1 + 2x) < 0

[spoiler]OA: C[/spoiler]

need to find if
x>1 and x<-1

A)x<-1 and x>1/2
Insufficient

B) x<-1/2 and x>1
Insufficient

both: Sufficient

C

Like this post

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Wed Apr 18, 2012 8:14 am

Statement 1: (1 - 2x)(1 + x) < 0
multiplying by -1 on both sides,
(2x - 1)(x + 1) > 0
By plotting critical points,
x < -1 , x > 1/2
So |x| can be < 1 or > 1.

Statement 2: (1 - x)(1 + 2x) < 0
multiplying by -1 on both sides,
(x - 1)(2x + 1) > 0
By plotting critical points,
x < -1/2, x > 1
So |x| can be < 1 or > 1.

Lets combine them.
The common solution is x > 1, x < -1.
and, |x| > 1.

The answer to the question is a conclusive YES.
(C) is the answer.

Note: Plot a number line to understand better. And, the Critical Points method is very useful in such questions.

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

Like this post

sam2304: Legendary Member; Posts: 1239; Joined: Tue Apr 26, 2011 6:25 amFollowed by: 26 members; Thanked: 233 times; GMAT Score:680

by sam2304 » Wed Apr 18, 2012 9:47 am

If |x| is an integer, is |x| > 1 ?

A)x < -1 and x > 1/2
x = -2, |x| = 2 YES
x = 1, |x| = 1 No
Insufficient

B) x < -1/2 and x > 1
x = -1, |x| = 1 NO
x = 2, |x| = 2 YES
Insufficient

combining both we need to take the common range which satisfies both the inequalities
So x > 1 and x < -1. Be it any value |x| is > 1. SUFF

IMO C

Getting defeated is just a temporary notion, giving it up is what makes it permanent.
https://gmatandbeyond.blogspot.in/

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review