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

Redeem

HOW 2 SOLVE - ABSOLUTE VALUE, ON BOTH SIDES? - CONCEPT PLS

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 52
Joined: Sat Aug 13, 2011 8:34 am
Thanked: 2 times

HOW 2 SOLVE - ABSOLUTE VALUE, ON BOTH SIDES? - CONCEPT PLS

by kaps786 » Sat Aug 13, 2011 11:10 am
Hi ,

Totally lost on how to solve absolute value on both sides of equation.

Can some experts guide here and provide a step by step approach for such qn types, and the concept please.

Also whats the key point to bear in mind, while solving these questions?

Which would be a better approach, plugging numbers or solving, for such type of questions.

I have an MGMAT q'n as sample below and I have read som explanations which I could not follow completely.

Hope some experts can help.


Data Sufficiency -


Is |x| < 1 ?

(1) |x + 1| = 2|x - 1|

(2) |x - 3| > 0

OA below...



OA C


Thank you in advance,

Kaps
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 351
Joined: Mon Jul 04, 2011 10:25 pm
Thanked: 57 times
Followed by:4 members

by akhilsuhag » Sun Aug 14, 2011 6:09 am
Is |x| < 1 ?

I am just trying I hope I can get an expert to comment on this.

(1) |x + 1| = 2|x - 1|

(2) |x - 3| > 0
Statement 1:

It will give us 4 cases, We will look at each individually:

(a) x+1 = 2(x-1), this gives x=3.
(b) x+1 = 2 * -1(x-1) or x+1 = 2(-x +1); giving us x = 1/3
(c) x+1 = -(2(x-1))
(d) x+1 = -(2* -1(x-1))

What is happening here is that x+1 can take both a +ve and -ve value. So can the other term in the absolutes. Giving us a total of 4 cases. We you solve you will find that a = d and b = c.

So x can be 3 or 1/3. So, Insufficient.

Statement 2:

Gives us: x-3 > 0; x>3 (if x-3 is Positive)
-x+3>0; x<3 (if x-3 is negative)

Insufficient

T0gether; x= 1/3

So sufficient
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 312
Joined: Tue Aug 02, 2011 3:16 pm
Location: New York City
Thanked: 130 times
Followed by:33 members
GMAT Score:780

by gmatboost » Mon Aug 15, 2011 10:08 am
There are only two cases, you never need to do 4 cases:

1. (x+1) = 2(x-1)
2. -(x+1) = 2(x-1)

Solve each one, that's it.
Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.
Top
Post new topic Post Reply
• Page 1 of 1