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

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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: — Data Sufficiency |
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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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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

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