PDF800 SET3 Question 5

[zozo123]

Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| &#8800; 0

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

The answer is C, please explain me how can I resolve it?

[givemeanid]

Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| &#8800; 0

The answer is C, please explain me how can I resolve it?

1. x+1 = 2(x-1)
x+1 = 2x-2
x=3
OR
x+1 = -2(x-1)
x+1 = -2x+2
3x = 1
x=1/3

NOT SUFFICIENT.


2. x-3 &#8800; 0
x &#8800; 3
x = 1/3, |x| < 1. True.
x = 5 |x| > 1. False.

NOT SUFFICIENT.


Together, only x=1/3 satisfies both. Hence, SUFFICIENT. Answer is C.