What is the value of y?

(1) 3|x^2 - 4| = y - 2

(2) |3 - y| = 11


OA: C

Why is the answer not B

If you solve this equation you get 2 values for y, y=-8 and y=14

However, if you put y=14 back to the original stem (3-14)=11 -> -11 = 11 and this is not true.

Can somebody please help me out here?








OA from MGMAT:

(1) INSUFFICIENT: Since this equation contains two variables, we cannot determine the value of y. We can, however, note that the absolute value expression |x2 - 4| must be greater than or equal to 0. Therefore, 3|x2 - 4| must be greater than or equal to 0, which in turn means that y - 2 must be greater than or equal to 0. If y - 2 > 0, then y > 2.

(2) INSUFFICIENT: To solve this equation for y, we must consider both the positive and negative values of the absolute value expression:

If 3 - y > 0, then 3 - y = 11
y = -8

If 3 - y < 0, then 3 - y = -11
y = 14

Since there are two possible values for y, this statement is insufficient.

(1) AND (2) SUFFICIENT: Statement (1) tells us that y is greater than or equal to 2, and statement (2) tells us that y = -8 or 14. Of the two possible values, only 14 is greater than or equal to 2. Therefore, the two statements together tell us that y must equal 14.

The correct answer is C.