gmatusa2010 wrote:Is |X|= A-B?

1) X=A-B
2) X=B-A

Still trying to understand the logic if absolute value DS.

|X| is always a positive number. If X is positive, |X| = X, but if X is negative, |X| = -X. And Yes, |0| = 0.

Statement 1:
X = A - B
If A - B is a positive number then its modulus, i.e. |X| = |A - B| = A - B, but if A - B is a negative number then |X| = |A - B| = B - A.
INSUFFICIENT, because we do not not if A - B is positive or not.

Statement 2:
X = B - A.
|X| = |B - A| = B - A if B - A is positive and |X| = |B - A| = A - B if B - A is negative.
INSUFFICIENT. We do not know is B - A is positive or negative.

Combining,
X = A - B as well as B - A, which is the negative of A - B.
When can that happen?
when A = B, or X = 0.

Is |X| = A - B?
X = 0, so is |X|.
A - B is also equal to 0.
So, 0 = 0.
Sufficient.

I'll go with [spoiler][C][/spoiler]

tomada wrote:When you say both are sufficient, do you mean that each one is sufficient, or that the combination of statements is sufficient?

diebeatsthegmat wrote:

gmatusa2010 wrote:Is |X|= A-B?

1) X=A-B
2) X=B-A

Still trying to understand the logic if absolute value DS.

if x> 0 so |x|=A-B but if x<0 |x|=B-A
from above, you can see that both are sufficient

please note: it's absolute value. Ok man!

D for me.

C it is. A should be equal to B

Answer is C

statement 1
X = A-B
If A = 2, B =1
A - B = 2-1 = 1 so is X

|X| |1| = A- B = 1 fine

If A = 1, B =2
A - B = 1-2 = -1 so is X = -1

|X| |-1| = 1 But A- B = -1 Not Fine.

so statement A is not sufficient

similarly for statement B is not sufficient.

combined

A-B = B-A

so A= B
A-B or B-A = 0 always

so |X| =X =0 always.

Answer is C