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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?

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 \(y\leq{0}\).

Answer: D.

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 \(y=0\).

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 \(y\leq{0}\).

Answer: D.

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.

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 \(y\leq{0}\).

Answer: D.

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. Please explain. Thanks in advance.

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 \(y\leq{0}\).

Answer: D.

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. Please explain. Thanks in advance.

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

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 )
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

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.

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.

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

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03 Oct 2017, 12:14

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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

\(y\leq{0}\)

Answer D

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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