absolute value sufficiency

bullshark wrote:Is |x| < 1?

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

(2) |x - 3| is not equal to zero

If 1) is solved we get two values for x: 3 and 1/3.

The trick here is to answer the question Yes or NO Consistenly every time. IF not, then insufficient. If x=3, the answer is No and if x =1/3 the answer is Yes. So Not sufficient. We need a consistent "Yes" or a consistent "No" for sufficiency on Yes/No question type.

For 2) it follows that X is either greater than 3 or less than 3 for the absolute value not to be zero. If x is greater than 3, the Answer is "No". If X is less than 3 the answer is both No, for 2 and Yes for 1/2. Again not sufficient.

Combining doesnt help either.

So choose E.

bullshark wrote:Is |x| < 1?

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

(2) |x - 3| is not equal to zero

Asking whether -1<x<1.

1. x+1 = 2x-2 => x =3
x+1 = -2x+2 => x =1/3
For x<-1, x =1/3 which is not acceptable.
For -1<x<1: x = 1/3 which acceptable
For x>1, x = 3 which is acceptable.

2. x != 3

combine: x=1/3

so C

IMO C

According to statement 1, x can either be 3 or 1/3;
so it is not sufficient.

Statement 2 only says that |x-3| not equal to 0, it doesn't give any information on x except that it cannot be 3.
Not sufficient therefore.

Taking both together we see that x can only be 1/3.

This is information enough, so both statements together are sufficient.

I'm not clear on how to approach the first statement. If you multiply out a negative with the absolute value shouldn't you do the same on both sides and not just one??