Data Sufficiency

Is |x| = y - z?

1. x + y = z
2. x < 0

What is the beat approach to solve this question?

From the information that is given: |x|=y-z means
We have to consider 2 cases for x>0 and x<0.

If x>0 |x|=x and If x<0 |x|=-x

#1. x + y = z Hence we get, x = z - y. But we do not know if x>0 or x<0 so depending on that, if x>0 x=z-y else if x<0 -x=z-y and hence x=y-z

#2. x < 0 not sufficient since we do not have any information about y and z.

Combining #1 and #2 we can eliminate the case for x>0 and use x<0 and hence -x = z -y or x= y-z and hence confirm that C.) satisfies the question of |x|=y-z.

- Deepak