|x| is always positive. Please note some absolute value properties:

1. When x ≤ 0 ,then |x| = −x . For example: |−10|= -(-10) = 10

2. When x ≥ 0 ,then |x|=x , For example |10| = 10

So,in our question we are given y+|y|=0 --> |y| = -y . This implies that y ≤ 0.

This is similar to first property.

Hence, answer must be D.

Exactly Pankaj...when I saw the options I got doubt and I was not happy with answer explanation , but I must appreciate amorphous effort.

We are given that |y| + y = 0.


Now |y| = -y .. note here |y| is always positive now in order to LHS and RHS have to be postive , RHS i.e. -y to be +ve , y values has to be
-ve.

then |y| = -(-Y)... then it'll be correct. Here y has to be < 0 .

Note : 0 is neither +ve or -ve but only even number. In that case only C can be correct. But as per absolute principle, D comes.

I want Experts to validate my explanation.

for y + |y| = 0 y itself must be zero.

This is a must true question.

From A to D any value does not make the sum = 0

regardless if you do know that |y| is always positive. That fact is a bit redundant to a clever student.

Yes msk0657. It is a MUST BE TRUE question so considering CAN BE TRUE is a trap answer while solving these type of questions.

So, as the question is asking for a MUST be true ( NOT a can be true), is the answer E Correct? pls, need undisputed solution .

Answer is D as per gmatclub. Bunuel just nailed it

Reference:
https://gmatclub.com/forum/if-y-y-0-whi ... 31099.html

\(y + |y| = 0\)

We do have two case scenarios

1) if two numbers are added and the result is zero AND considering that y must be positive always

OR the other y is negative and the same of \(|y|\) or \(|y|\) itself is zero.

Therefore y must be \(\leq 0\)

2) \(y = |y |\)

In this case |y| is positive and to cancel out y must be < 0

Or \(y = 0\)

Therefore \(y \leq 0\)

1) + 2) \(y \leq 0\)

The question asks "What must be true?"
So, if an answer choice is not necessarily true, we can ELIMINATE it.

Find a solution to the equation y + |y| = 0
One possible solution is y = -1, since -1 + |-1| = 0

Now check the answer choices....
A. -1 > 0. Not true. ELIMINATE
B. -1 ≥ 0. Not true. ELIMINATE
C. -1 < 0. True. KEEP
D. -1 ≤ 0. True. KEEP
E. -1 = 0. Not true. ELIMINATE

B and C are the REMAINING answer choices.
Now find another solution to the equation y + |y| = 0
Another possible solution is y = 0, since 0 + |0| = 0

Now check the REMAINING answer choices....
C. 0 < 0. Not true. ELIMINATE
D. 0 ≤ 0. True. KEEP

By the process of elimination (POE), the correct answer is D

Cheers,
Brent

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