Data Sufficiency

VJesus12 wrote:Is |x|=y+1?

1) y+x=-1
2) x<0

The OA is the option C .

I can't see how to use both statements to get an answer. Experts, may you give me some help, please?

1) y + x = -1

Case 1: x = a negative number; say x = -1, then y + x = -1 => y - 1 = -1 => y = 0.
At x = -1 and y = 0, we have |x| = y + 1 => |-1| = 0 + 1 => 1 = 1. The answer is Yes.

Case 2: Say x = 0, then y + x = -1 => y + 0 = -1 => y = -1.
At x = 0 and y = - 1, we have |x| = y + 1 => |0| = -1 + 1 => 0 = 0. The answer is Yes.

Case 3: x = a positive number; say x = 1, then y + x = -1 => y + 1 = -1 => y = -2.
At x = 1 and y = -2, we have |x| = y + 1 => |1| = -2 + 1 => 1 ≠ - 1. The answer is No.

Question rephrased: Is x ≤ 0?

2) x < 0

We have no information about y. Insufficient.

(1) and (2) combined

Only Case 1 is applicable. Thus, the answer is Yes. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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