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

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Senior Manager
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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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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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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.

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

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09 May 2012, 08:26
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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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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Re: If y + | y | = 0, which of the following must be true? [#permalink]

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

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03 Oct 2017, 17:27
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?

$$y + |y| = 0$$
$$|y| = 0 - y$$
$$|y| = -y$$

The last expression means that $$y\leq{0}$$. That rule can seem odd or counterintuitive.

The variable has a "hidden" negative sign. With the variable, it's hard to remember that there ARE two negative signs on RHS. We just do not (cannot) write the minus sign twice with the variable. These equations are equivalent, where y = -2:

|-2| = -(-2) = 2
|y| = -(y) = -y

So if $$y + |y| = 0$$, then $$|y| = -y$$ and

$$y\leq{0}$$

If none of the above occurs to you or if it makes no sense, pick and list three numbers: negative, 0, and positive.

Use them to try to DISPROVE the answers. Even one example that defies the rule being tested makes "must be true" false.

-2, 0, and 2

A. y > 0
$$y + |y| = 0$$. Try y = 0
$$0 + |0| = 0$$. That works. $$y$$ does not have to be positive. REJECT

B. y≥0. Use -2
$$y + |y| = 0$$
$$-2 + |-2| = 0$$. That works. $$y$$ can be negative. REJECT

C. y < 0. We know from (A) that $$y$$ CAN equal 0. REJECT

D. y≤0. Try 2
$$y + |y| = 0$$
$$2 + |2| \neq{0}$$

We know from (A) that $$y$$ can equal 0.
We know from (B) that $$y$$ can be negative.

And having tested +2, we know that $$y$$ CANNOT be positive.

This expression MUST be true. KEEP

E. y = 0
We know from (B) that $$y$$ can be negative. Yes, $$y$$ can also be 0. But it does not have to be 0 -- it can be negative, e.g. -2. REJECT

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If y + | y | = 0, which of the following must be true?   [#permalink] 03 Oct 2017, 17:27
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