Register    Login    Search    Rss Feeds

Forums Home » Ask An Instructor » GMAT Math » Manhattan GMAT Math Strategy Guides


 Page 1 of 1 [ 4 posts ] 



  Print view Print view Previous topic Previous topic | Next topic Next topic
 

MGMAT: Question bank: Is |x| < 1 ?

Author Message
Khalid
 Post subject: MGMAT: Question bank: Is |x| < 1 ?
 Post Posted: Sat Jan 31, 2009 8:39 pm 
Is |x| < 1 ?

(1) |x + 1| = 2|x – 1|

(2) |x – 3| > 0

What is the best way to solve for statement 1. I have seen the explanation and wondering if there are any easier quick ways! Do I really have to consider 4 scenarios when there is abs. sign on both sides of a equation:

Left and Right >0
Left <0 and Right >0
Left > 0 and Right <0
Left <0 and Right <0

Thanks!
Top 
StaceyKoprince
 Post subject: Re: MGMAT: Question bank: Is |x| < 1 ?
 Post Posted: Thu Feb 12, 2009 11:25 pm 
Offline
ManhattanGMAT Staff


Posts: 6077
Location: San Francisco
If you want to be thorough? Then yes. :) But I think the real test wouldn't give you something this computation intensive unless you were really scoring at the very very top of the range.

Most of the time (and that's usually good enough on this test), you can get away with just two scenarios: both the same and one negated.
both the same: x+1 = 2(x-1) this solves to x=3
one negated: x+1 = -2(x-1) this solves to 3x = 1, or x = 1/3

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
Top 
kanaks123
 Post subject: Re: MGMAT: Question bank: Is |x| < 1 ?
 Post Posted: Sun Feb 15, 2009 12:47 pm 
Offline
Course Students


Posts: 3
Here is my rule of thumb.

When there is equality between left hand side and right hand side, you always end up with two scenarios.

|x+1| = 2 |x-1|

(1) x+1 < 0 x-1 < 0 => -(x+1) = - 2(x-1)
(2) x+1 < 0 x-1 > 0 => -(x+1) = 2(x-1)
(3) x+1 > 0 x-1 < 0 => (x+1) = - 2(x-1)
(4) x+1 > 0 x-1 > 0 => (x+1) = 2(x-1)

As you can see (1) -(x+1) = -2(x-1) is always equal to (x+1) = 2(x+1), which is (4)
Similarly (2) is same as (3)

**Please note this works only for equality. For inequality you must consider all four cases.
Top 
esledge
 Post subject: Re: MGMAT: Question bank: Is |x| < 1 ?
 Post Posted: Sun Feb 22, 2009 3:55 pm 
Offline
ManhattanGMAT Staff


Posts: 901
Location: St. Louis, MO
Good point, kanaks123. The inequality exception is important.

It's also worth noting that we aren't really ignoring any real solutions. Technically, some of the 4 solutions are invalid for their scenario. These "dummy" solutions are just a by-product of equations with absolute value on both sides.

(1) x+1 < 0, x-1 < 0 => -(x+1) = - 2(x-1) --> x = 3 (INVALID: x = 3 makes x+1>0, i.e. scenario 4)
(2) x+1 < 0, x-1 > 0 => -(x+1) = 2(x-1) --> x = 1/3 (INVALID: x = 1/3 makes x-1<0, i.e. scenario 3)
(3) x+1 > 0, x-1 < 0 => (x+1) = - 2(x-1) --> x = 1/3
(4) x+1 > 0, x-1 > 0 => (x+1) = 2(x-1) --> x = 3

_________________
Emily Sledge
Instructor
ManhattanGMAT
Top 
Display posts from previous:  Sort by  
 
 Page 1 of 1 [ 4 posts ] 





Who is online

Users browsing this forum: No registered users and 0 guests

 
 

 
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to: