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

Redeem

Is x > 0?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Senior | Next Rank: 100 Posts
Posts: 87
Joined: Sun Jul 24, 2011 10:36 am

by [email protected] » Fri Sep 16, 2011 3:25 pm
ans is ddd

from 1: |x + 3| = 4x - 3
if x > 0, than x+3 = 4x -3 by solving this we get 6= 3x. thus x =2
if x< 0, than x +3 = -4x + 3, by solving this we get x =0 . but if we put x=0 in the question than we see that |x + 3| is not equal to 4x - 3. thus x is not equal to 0
(YOU CAN SEE THAT IF WE PUT X=2 IN THE INEQUALITY WE GET |x + 3| = 4x - 3
HENCE X = 2 THUS X >1
IN THE QUESTIONS RELATED TO MODE ALWAYS CROSS VERIFY THE INEQUALITY BY PUTTING VALUE IN THE QUESTION.

FROM 2: |x + 1| = 2x - 1
IF X>0 THAN, X+1 = 2X-1 . bY SOLVING THIS WE GET X= 2
IF X<0 THAN X+1 =2X-1. BY SOLVING THIS WE GET X = 0
PUT BOTH VALUES IN THE ORIGINAL INEQUALITIES. YOU WILL FIND THAT ONLY X=2 HOLD TRUE. THUS X= 2

HENCE ANSWER SHOULD BE D
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Sun Jul 04, 2010 12:48 pm
Thanked: 6 times
Followed by:3 members

by gmatdriller » Wed Sep 21, 2011 10:59 am
my concern is, considering the test condition, must we always substitute
to confirm which of the solution is correct? I feel there are other ways
to arrive at the answer without carrying out his check.

For example, we know that the expression in an absolute sign is always >= 0
so, from (1) we can say 4x - 3 >= 0
and x >= 4/3. Also, x > 0. Sufficient

By the same token, x >= 1/2 and thus > 0
Also sufficient.

Can anyone point an error in my explanations please.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Wed Sep 21, 2011 1:25 pm
gmatdriller wrote:

For example, we know that the expression in an absolute sign is always >= 0
so, from (1) we can say 4x - 3 >= 0
and x >= 4/3. Also, x > 0. Sufficient

By the same token, x >= 1/2 and thus > 0
Also sufficient.
That's the fast way to do the problem, and it's perfectly correct.
[email protected] wrote:ans is ddd

from 1: |x + 3| = 4x - 3
if x > 0, than x+3 = 4x -3 by solving this we get 6= 3x. thus x =2
if x< 0, than x +3 = -4x + 3, by solving this we get x =0 . but if we put x=0 in the question than we see that |x + 3| is not equal to 4x - 3. thus x is not equal to 0
Your analysis of these cases isn't quite right. |x+3| is equal to x+3 when *what's inside the absolute value* is positive. So |x+3| = x+3 when x > -3, not when x > 0. You then find, solving, the perfectly good solution x = 2. In the second case, |x+3| = -x-3 when what's inside the absolute value is negative. That is, |x+3| = -x-3 when x < -3 (and not when x < 0; |x+3| is still equal to x+3 if you plug in x = -1, say). So in the second case, when x < -3, we'd find, solving, that x = 0, but this solution doesn't agree with our assumption that x < -3, so cannot be a valid solution. You don't need to plug the value back into the equation.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Sun Jul 04, 2010 12:48 pm
Thanked: 6 times
Followed by:3 members

by gmatdriller » Wed Sep 21, 2011 9:11 pm
I appreciate your explanations, Ian.
First assumption when absolute expression > 0
Is that x>-3; we got x =2....satisfied and x>0. Sufficient

Second assumption absolute expression < 0
Is that x < -3; but we got x= 0..Not a solution.
Not sufficient.

Thanks all for your inputs.
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Sun Dec 02, 2007 1:06 pm

by jaguar123 » Thu Sep 22, 2011 6:20 am
I get x = 2,0 in the both the choices. Can any help - why to choose A in a easy way.
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Sun Jul 04, 2010 12:48 pm
Thanked: 6 times
Followed by:3 members

by gmatdriller » Sun Sep 25, 2011 12:03 am
jaguar123 wrote:I get x = 2,0 in the both the choices. Can any help -
why to choose A in a easy way.
Have you gone through the previous posts?
If yes and you still having problems, let me know for further explanations.
Top
Post new topic Post Reply
• Page 1 of 1