Is |x|

Question

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.

E. Statements (1) and (2) TOGETHER are NOT sufficient.


Any takers ????

mahesh004 · Answer

C it is....

The first if solved gives us x = 3, -1/3, 1/3 etc. so not sufficient. 
We need to show if -1 > x > 1.

Second tells us that ....
|x - 3| =! 0 

So combining two provides us the answer.

lan583 · Answer

mahes.. can you explain how you arrived with 3, 1/3, and -1/3... thanks

j8chan · Answer

i think you have to solve these to get 3, 1/3 and -1/3

|x + 1| = 2|x - 1| gives x=3

-|x + 1| = 2|x - 1| gives x=-1/3

and |x + 1| = -2|x - 1| gives x=1/3

v1rok · Answer

Should be (D)

ST1. Roots are 3 and -1. In both cases they are >=1 in abs value /SUFF/
ST2. The root is x=3, again SUFF

So, (D)

mahesh004 · Answer

v1rok --- I dont agree with your explaination...

|x - 3| =! 0

x - 3 != 0 so x != 3 this doesn't tell us if -1 < x < 1...

so answer is C

ps_dahiya · Answer

I agree that answer is C. But in statement 1, x = -1/3 is not correct. As per statement 1 x can be only 3 or 1/3.

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

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