BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is |x|< 1?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Fri Feb 19, 2010 6:31 am
Thanked: 2 times

Is |x|< 1?

by Nijeesh » Sun Mar 21, 2010 8:37 am
Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 208
Joined: Sun Sep 28, 2008 12:30 pm
Thanked: 22 times

by neoreaves » Sun Mar 21, 2010 11:32 am
Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0
What we need to know is that -1 <x < 1. Thus we need to know if x is a fraction or not.

1) There are two cases here after removing the modulus. One is where both sides have same sign--> positive or negative. Second case will be where the signs are opposite :
i) x + 1 = 2(x-1)
x = 3
ii) -x -1 = 2x - 2
x = 1/3

Thus insufficient

2) We only know that x is not equal to 3. Insufficient

C) x = 1/3 so suffiicent
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Mon Mar 22, 2010 4:00 am
Nijeesh wrote:Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
(1) |x + 1| = 2|x - 1|

Squaring both sides:

x^2 + 2 x + 1 = 4 (x^2 - 2 x + 1)

3 x^2 - 10 x + 3 = 0

Solving, x is either 3 or 1/3. Insufficient

(2) |x - 3| ≠ 0

This implies that x ≠ 3, just insufficient to decide "Is |x|< 1?".

Taken together, x = 1/3, or [spoiler]YES |x|< 1?

C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Post new topic Post Reply
• Page 1 of 1