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

Please explain!!!
Thanks

|x|<1 means x lies in between -1 and 1 on number line.
Let x>1
then
x+1=2x-2
then x=3.... Answer is NO

Let x<1
then
x+1 = 2-2x
x=1/3......YES

INSUFFICIENT.

|x - 3| ≠ 0
x is not equal to 3.
This will not tell us anything.
INSUFFICIENT.

Combining.
We have x i snot equal to 3, x=3,x=1/3
Hence.. x=1/3
YES

pick C

In absolute value questions, testing cases in the different points of interest can be a good way to tackle a problem.

1. |x + 1| = 2*|x - 1|

If x > 1, values inside absolute sign will be positive.

=> x + 1 = 2*(x - 1)
=> x + 1 = 2x - 2
=> x = 3

If -1 < x < 1, lhs sign is positive, rhs sign is negative

=> x + 1 = 2*(1 - x)
=> x + 1 = 2 - 2x
=> 3x = 1
=> x = 1/3

If x < -1, both lhs and rhs would be negative qtys.

=> -(x + 1) = 2(1 - x)
=> -x - 1 = 2 - 2x
=> x = 3

EDIT: Made a math error here before, corrected it. Gmatmachoman is correct, this is the same as case 1 since we are multiplying both sides by -1.

Thus |x| may be 3 or 1/3 ....INSUFFICIENT

2. |x - 3| ≠ 0

=> x ≠ 3

But x could be any value other than 3, i.e. less than 1 or greater than 1.... INSUFFICIENT

Both 1 and 2:

If x cannot be 3, then x MUST be 1/3

Thus |x| < 1
SUFFICIENT

Pick C.

Some time back...

https://www.beatthegmat.com/is-x-1-1-x-1 ... tml#267058

My mentor also knocked me for this!!

gmatmachoman wrote:Some time back...

https://www.beatthegmat.com/is-x-1-1-x-1 ... tml#267058

My mentor also knocked me for this!!

Thanks everyone for taking time to reply and for the link to previous discussions on this question.