Quote:
Is |x| < 1 ?
(1) |x + 1| = 2|x – 1|
(2) |x – 3| > 0
I'm happy to respond.
I dare say, this problem is a little bit harder than what the GMAT will ask of you.
Statement #1:
|x+1| = 2|x-1| If we are given |P| = |Q|, this means: P = Q OR P = -Q. Notice that the word "or" is not a piece of garnish there: rather, it is an essential piece of mathematical equipment.
|x + 1| = 2|x - 1|
Case I
(x + 1) = 2(x - 1)
x + 1 = 2x - 2
x = 3
Case II
(x + 1) = -2(x - 1)
x + 1 = -2x + 2
3x = 1
x = 1/3
This, from statement #1, we have x = 3 or x = 1/3. With this, we do not have sufficient information to answer the prompt question. This statement, by itself, is
insufficient.
Statement #2:
|x-3| > 0Forget about everything we did in statement #1. Here, x could equal 10, in which case |x| is not less than 1, or x could equal 0, in which cases |x| is less than 1. We can pick different values that satisfy |x-3| > 0, x = 10 and x = 0, that give two different answers to the prompt question. Therefore, we do not have sufficient information to answer the prompt question. This statement, by itself, is
insufficient.
Combined:
#1 gives us x = 3 or x = 1/3
The value x = 3 does not satisfy the second statement, so we reject that value.
The value x = 1/3 is only value that satisfies both statements, and with this, |x| < 1.
Combined, the statements are sufficient.
Answer =
(C)Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)