oh i did this question wrong i thought the answer to this would be B but its not the case i rectified my mistake after looking the solutions posted here.i did it in a hurry and ended up with a wrong answer

can someone provide an easier to understand explanation?

Defn of Absolute Value

X=A-B

and X=-(A-B)

This is a smple problem.

Q. asks if x = a-b AND b-a simultaneously.

1) x= a-b ------->not sufficient.
2) x= b-a (or, -(a-b)--------->not sufficient.

but 1&2 together is sufficient since one states x=a-b and the other states x=b-a.
Hence C.

gmatusa2010 ur method of the trial and error is perfectly right in this sum...

Is |X|= A - B?

1. X = A - B
2. X = B - A

1. INSUFFICIENT. Because, A-B can be positive or negative
2. INSUFFICIENT. Because, B-A can be positive or negative

Note: Negative A-B or B-A will mean that the A-B or B-A will become B-A or A-B if either is negative.

COMBINED, we know X = A - B = B - A ; which means A=B=X=0. (Not sure if there is any other value?)

ANSWER: C.

(C) is the answer.

C !

Is |X|= A-B?

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

As a general Rule of thumb, we know that | x| = x when x >=0 and | x| = - x when x < 0.

So, let's look at the 1st statement
X=A-B
We don't know whether A- B is +ve or -ve.
So, if A-B is +ve then X = A-B
if A- B is -ve then X = B-A

Now, let's look at the 2nd statement
X= B-A
if B-A is +ve then X = B-A
if B-A is -ve then X= A-B

So, individually neither of the statement can answer the question.

Now let's combine them....
So, X= A-B = B-A can only happen if A =B OR X= 0
which means |x| = 0 and A-B = 0
So, together they satisfy the main question or argument.

So, the answer is 'C'.

[x] = A-B?; Rephrase

Is +-X = A - B ?;
is -X = A - B and is X = A - B?
is X = B - A and is X = A - B?

I think you got it from here....

Mod x = A - B

when x > 0

x = A-B

when x < 0

x = B-A

so C !

C!

Because a>b or b<a, both a and b are insufficient. But both together would be sufficient.

E in answer.

Anyone have official answer???

I think it is E

X= a-b OR x = b-a

if we take both statements together it implies both must be true at the same time which can't happen

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

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

Statement 1:
If X = A-B = 1, then |X| = |1| = 1 and A-B = 1, so |X| = A-B.
If X = A-B = -1, then |X| = |-1| = 1 and A-B = -1, so |X| ≠ A-B.
INSUFFICIENT.

Statement 2:
If X = B-A = 1, then |X| = |1| = 1 and A-B = -1, so |X| ≠ A-B.
If X = B-A = -1, then |X| = |-1| = 1 and A-B = 1, so |X| = A-B.
INSUFFICIENT.

Statements combined:
Adding together X = A-B and X = B-A, we get:
X + X = (A-B) + (B-A)
2X = 0
X = 0.

Since X = A-B and X=0, A-B = 0.
Thus, |X| = A-B.
SUFFICIENT.

The correct answer is C.