CAT 3: Absolute Range

[GMAT85]

Is |x| < 1 ?

(1) |x + 1| = 2|x - 1|
(2) |x - 3| > 0

I solved this problem a little differently. Can this problem be solved the following way?
Rephrase the question as "Is x <1?" or "Is x > -1?" or "Is -1 < x < 1?"

Statement 2. Not Sufficient! x>3 or x<3; therefore x is anything but 3.

Statement 1. Not Sufficient! When x>0 , (x + 1) = 2(x -1). This gives x=3.
When x<0 , -(x + 1) = -2(x -1). This gives x=1/3.
3rd scenario: -(x + 1) = 2(x -1). This gives x=1/3.
So, x=1/3 or 3. Insufficient to solve the problem.

Combining statement (1) and (2). x cannot equal 3 according to statement (1). x equal 1/3 or 3. Therefore, x=1/3. This is sufficient to answer the question.

Answer: C

I am not so good at absolute value questions. So please suggest the correct way of doing this problem.

[Maverick]

Is |x| < 1 ?

(1) |x + 1| = 2|x - 1|
(2) |x - 3| > 0

(1) Taking + sign, x+1=2x-2 => -x = -3 => x=3
Taking -sign, x+1=-2x+2 => 3x=1 => x=1/3
Insufficient.

(2) |x - 3| > 0
So, x<>3. Insuff.

Combining: x=1/3. Suff.

[RonPurewal]

ha, this problem has been posted on about 4 different threads in the space of a week. i understand it's hard to search for problems whose statements consist largely of mathematical symbols, but you should at least try.

http://www.manhattangmat.com/forums/abs ... t3648.html