Data Sufficiency

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

Statement 1: x+y=z, so x=z-y. Replacing x with z-y in the given: |z-y|=y-z. The expression on the left is always non-negative, so this would only by true if y>=z, which we don't know. INSUFFICIENT

Statement 2: This is obviously insufficient by itself since it gives no information about y and z.

Statements 1 & 2: With both statements, we know that x=z-y AND x<0, using substitution, we know z-y<0 or z<y or y>z. As discussed above, |z-y|=y-z whenever y>z, so this is sufficient.

Answer is C

You could also go in the other direction:

Since x + y = z, y - z = -x.

So, we want to know if -x = |x|
We should know that this is true whenever x <= 0.

gmatboost wrote:You could also go in the other direction:

Since x + y = z, y - z = -x.

So, we want to know if -x = |x|
We should know that this is true whenever x <= 0.

Exactly, IMO:C

Experts, is this approach correct?

Since |x| = y-z
when x is positive, x= y-z
when x is negative, x = z-y

therefore, since we don't know the sign of x, x = y-z(when x is positive) OR z-y (when x is negative)

Statement 1

Simply says that x= z-y. But this doesn't give us the sign of x. x can be negative or positive. Hence |x| values will change accordingly.

Statement 2

Tells us nothing about the relationship between x, y and z

Combining the two,

If x=z-y and x= negative then |x| = z-y the second condition in the question stem is satifisfied.

Hence C