HOW 2 SOLVE - ABSOLUTE VALUE, ON BOTH SIDES? - CONCEPT PLS - The Beat The GMAT Forum

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

Expert replies

kaps786: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Aug 13, 2011 8:34 am; Thanked: 2 times

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

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 13, 2011 11:10 am

akhilsuhag: Master | Next Rank: 500 Posts; Posts: 351; Joined: Mon Jul 04, 2011 10:25 pmFollowed by: 4 members; Thanked: 57 times

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

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; 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.
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