Is |x|< 1?

[Nijeesh]

Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 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.

[neoreaves]

Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0

What we need to know is that -1 <x < 1. Thus we need to know if x is a fraction or not.

1) There are two cases here after removing the modulus. One is where both sides have same sign--> positive or negative. Second case will be where the signs are opposite :
i) x + 1 = 2(x-1)
x = 3
ii) -x -1 = 2x - 2
x = 1/3

Thus insufficient

2) We only know that x is not equal to 3. Insufficient

C) x = 1/3 so suffiicent

[sanju09]

Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 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.

(1) |x + 1| = 2|x - 1|

Squaring both sides:

x^2 + 2 x + 1 = 4 (x^2 - 2 x + 1)

3 x^2 - 10 x + 3 = 0

Solving, x is either 3 or 1/3. Insufficient

(2) |x - 3| ≠ 0

This implies that x ≠ 3, just insufficient to decide "Is |x|< 1?".

Taken together, x = 1/3, or [spoiler]YES |x|< 1?

C[/spoiler]