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If y + |y| = 0, which of the following

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If y + |y| = 0, which of the following [#permalink] New post 03 Jun 2018, 07:20
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If y + |y| = 0, which of the following must be true?

A. y > 0

B. Y ≥ 0

C. Y < 0

D. Y ≤ 0

E. Y = 0



src: Orbit Test Prep
[Reveal] Spoiler: OA
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Re: If y + |y| = 0, which of the following [#permalink] New post 07 Jun 2018, 23:25
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amorphous wrote:
If y + |y| = 0, which of the following must be true?

A. y > 0

B. Y ≥ 0

C. Y < 0

D. Y ≤ 0

E. Y = 0



src: Orbit Test Prep


Please share answer explanation.
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Re: If y + |y| = 0, which of the following [#permalink] New post 08 Jun 2018, 02:03
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From the given eqn take y to the left side of the eqn we get,

|y| = - y

Hence, y = -y; only 0 satisfies the condition
or, -y = -y or y = y; Any no would satisfy the condition.

Only 0 satisfies both the condition hence, 0
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Re: If y + |y| = 0, which of the following [#permalink] New post 08 Jun 2018, 04:04
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|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.
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Re: If y + |y| = 0, which of the following [#permalink] New post 09 Jun 2018, 10:52
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PankajPatel wrote:
|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.
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Re: If y + |y| = 0, which of the following [#permalink] New post 09 Jun 2018, 11:08
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Expert's post
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. :wink:
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Re: If y + |y| = 0, which of the following [#permalink] New post 10 Jun 2018, 09:57
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Yes msk0657. It is a MUST BE TRUE question so considering CAN BE TRUE is a trap answer while solving these type of questions.
Re: If y + |y| = 0, which of the following   [#permalink] 10 Jun 2018, 09:57
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