Striver wrote:Is |X| <1 ?
1) |X+1| = 2|X-1|
2) |X-3| is not equal to 0.
Statement 1: |x+1| = 2|x-1|
Case 1:
x+1 = 2x-2
3 = x
Case 2:
x+1 = -(2x-2)
3x = 1
x = 1/3.
Confirm that both solutions are valid:
|3+1| = 2|3-1|
4=4.
|1/3 + 1| = 2|1/3 - 1|
4/3 = 4/3.
Since x=3 and x=1/3 are both valid solutions, we cannot determine whether |x|<1.
INSUFFICIENT.
Statement 2: |x-3| is not equal to 0
It's possible that x=0 or that x=10.
INSUFFICIENT.
Statements 1 and 2 combined:
Since x=3 does not satisfy statement 2, x=1/3.
Thus, |x|<1.
SUFFICIENT.
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
