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# If y + | y | = 0, which of the following must be true?

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Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
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If y + | y | = 0, which of the following must be true? [#permalink]

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21 Apr 2012, 21:15
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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

Why is just E incorrect?
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
Posts: 39622
If y + | y | = 0, which of the following must be true? [#permalink]

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21 Apr 2012, 22:23
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Expert's post
boomtangboy 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

Why is just E incorrect?

Absolute value properties:
When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$;

So, $$y+|y|=0$$ --> $$|y|=-y$$, which means that $$y\leq{0}$$.

As for your doubt: question asks which of the following MUST be true, not COULD be true. Since all negative values of y satisfy $$|y|=-y$$ then it's not necessarily true that $$y=0$$.

Hope it's clear.
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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08 May 2012, 10:03
Bunuel wrote:
boomtangboy 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

Why is just E incorrect?

Absolute value properties:
When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|\leq{-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|\leq{some \ expression}$$. For example: $$|5|=5$$;

So, $$y+|y|=0$$ --> $$|y|=-y$$, which means that $$y\leq{0}$$.

As for your doubt: question asks which of the following MUST be true, not COULD be true. Since all negative values of y satisfy $$|y|=-y$$ then it's not necessarily true that $$y=0$$.

Hope it's clear.

Hi ,

Thanks for the clear and concise explaination.

Just wanted to clarify one thing.

In mods the two conditions I know are applied include; If x<0 or if x>=0. However in the above explaination you have used x<=0. Was that used for some particular reason or my concepts of absolute values are incorrect.

Thanks much
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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08 May 2012, 10:15
If y + | y | = 0, which of the following must be true?

please note that | y | is always POSITIVE. so , in order to make this equation equal to zero, u need either y=0, or y <0.

if y=0 , then you get 0+| 0|=0

if y<0, then you get (-)+| -| =0 or (-)+(+)=0
i
that is why y< or = 0
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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09 May 2012, 08:10
Bunuel wrote:
boomtangboy 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

Why is just E incorrect?

Absolute value properties:
When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|\leq{-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|\leq{some \ expression}$$. For example: $$|5|=5$$;

So, $$y+|y|=0$$ --> $$|y|=-y$$, which means that $$y\leq{0}$$.

As for your doubt: question asks which of the following MUST be true, not COULD be true. Since all negative values of y satisfy $$|y|=-y$$ then it's not necessarily true that $$y=0$$.

Hope it's clear.

Hi Bunuel, why are we considering the case of y=0, as if y=0, then the expression
|y|=-y makes no sense, because |0|=0. and there is no +0 or -0.
Math Expert
Joined: 02 Sep 2009
Posts: 39622
Re: If y + | y | = 0, which of the following must be true? [#permalink]

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09 May 2012, 08:26
piyushksharma wrote:
Bunuel wrote:
boomtangboy 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

Why is just E incorrect?

Absolute value properties:
When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|\leq{-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|\leq{some \ expression}$$. For example: $$|5|=5$$;

So, $$y+|y|=0$$ --> $$|y|=-y$$, which means that $$y\leq{0}$$.

As for your doubt: question asks which of the following MUST be true, not COULD be true. Since all negative values of y satisfy $$|y|=-y$$ then it's not necessarily true that $$y=0$$.

Hope it's clear.

Hi Bunuel, why are we considering the case of y=0, as if y=0, then the expression
|y|=-y makes no sense, because |0|=0. and there is no +0 or -0.

Not, so. You can write |0|=-0 and there is nothing wrong in that.
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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09 May 2012, 08:33
Bunuel wrote:

Not, so. You can write |0|=-0 and there is nothing wrong in that.

hm, absolute value of an integer means how far this integer is from zero.
so, absolute value of zero iz zero, since zero is zero far from zero (sounds like a quote of Alice from Wonderland hehe)
-0 looks weird to me, since zero is neither positive, nor negative, and has no sigh. But still, I wont claim that my way of thinking is right. I will believe to Bunuel )) amazing life, every day is a new discovery )
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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15 May 2012, 04:32
I have a question here.. if the the question was y + |y| = 2y , then can we say y>=0? given then 0+0 = 2(0). Please let me know in case I am doing something wrong. Thanks in advance.
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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15 May 2012, 04:45
pavanpuneet wrote:
I have a question here.. if the the question was y + |y| = 2y , then can we say y>=0? given then 0+0 = 2(0). Please let me know in case I am doing something wrong. Thanks in advance.

$$y+|y|=2y$$ --> $$|y|=y$$ --> $$y\geq{0}$$.
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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03 Oct 2012, 03:31
For me the answer is C. (since the question asks MUST be true?)
Can you anyone tell me why C is not correct
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Posts: 39622
Re: If y + | y | = 0, which of the following must be true? [#permalink]

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03 Oct 2012, 03:36
Ousmane wrote:
For me the answer is C. (since the question asks MUST be true?)
Can you anyone tell me why C is not correct

Check the solution here: if-y-y-0-which-of-the-following-must-be-true-131099.html#p1076758

y<0 (C) is not correct because y+|y|=0 hods true when y=0 too, so y<0 is not necessarily true (not a must true statement).

Hope it's clear.
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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04 Dec 2012, 02:03
Manipulate the equations:
y + | y | = 0
|y| = -y

-y > 0 OR -y = 0

This means y could be 0 or y is less than 0.

D. y≤0
E. y=0

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24 Aug 2014, 04:18
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

why is the answer D and not C?

Thanks!
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Joined: 02 Sep 2009
Posts: 39622
Re: If y + | y | = 0, which of the following must be true? [#permalink]

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24 Aug 2014, 05:47
harshitalall 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

why is the answer D and not C?

Thanks!

Merging similar topics. Please refer to the discussion above.
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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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21 Apr 2016, 05:45
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Re: If y + | y | = 0, which of the following must be true?   [#permalink] 21 Apr 2016, 05:45
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