Answer must be D. The absolute value of anything is going to be positive. If y were positive, adding another positive number to it would make the value greater than 1, so y must be negative. But, if y = 0, the 0 + |0| = 0 also. There actually seems to be multiple answers below that MUST be true.
If y + | y | = 0, which of the following must be true?
(A) y > 0 y = 2...2 + |2| = 4, not 0
(B) y≥0 y = 0 works, but if y = positive, then same as A which is incorrect
(C) y < 0 This is true, but it doesn't account for y = 0
(D) y≤0 The takes into account all values of y that will make the equation true.
(E) y = 0 This doesn't include all negative numbers, so it is not complete.
I, durgesh, and a few others had a great discussion about the exact same type of question and what does it mean "If [equation], then which of the following MUST be true?" Essentially what we came up with (meaning Durgesh successfully explained to us) is that when you have an equation, treat all values that make that equation true as your "universe". Then pick the answer that includes all possible values of that "universe". Here, D satisfies that.
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.