|y| is always positive. To satisfy the inequality, y must be negative.
Another value of y that satisfies the inequality is 0

Also by POE:

(A) y>0....y can be negative
(B) y>=0....y can be negative
(C) y<0....y can be zero
(E) y=0.....y can be negative


Hence A,B,C,E need not be true or must not be true

Therefore D

Okay:)

To satisfy the condition, we need a condition that meet both Y are negative AND zero.

Thanks!

you got it!

when y + | y | = 0, there are only two possiblities
When y itself = 0 ; then the actual and absolute value of y both would be zero and hence their sum would be zero#
Second possibility is that y is a negative number; in such a case the absolute value will become positive and hence the sum would be a resultant zero; Hence the possibility is that y is less than or equal to zero.
Hence D