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Manager  Joined: 14 Apr 2010
Posts: 170
If у + |y| = 0, which of the following must be true?  [#permalink]

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16 00:00

Difficulty:   35% (medium)

Question Stats: 56% (00:42) correct 44% (00:42) wrong based on 920 sessions

### HideShow timer Statistics 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

Originally posted by bibha on 07 May 2010, 22:05.
Last edited by Bunuel on 09 Jul 2019, 23:38, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 56277
Re: If у + |y| = 0, which of the following must be true?  [#permalink]

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

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bibha 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

Thanks $$y+|y|=0$$ means either $$y=0$$ or $$y<0$$ (in this case $$|y|=-y$$ and $$y + |y| = 0$$ becomes $$y-y= 0$$). So must be true that $$y\leq{0}$$.

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

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banksy wrote:
199. If у + IyI = 0, which of the following must be true?
(A) у > 0
(B) у is no less than 0
(C) у < 0
(D) у is not greater than 0
(E) y = 0

$$y+|y| = 0$$ --> $$|y|=-y$$. Now, LHS is an absolute value which is never negative hence RHS must also be non-negative: $$-y\geq{0}$$ --> $$y\leq{0}$$.

Or you can see right away that in order $$y+|y|=0$$ to hold true y must be either negative number (for example -3+|-3|=0) or zero (0+|0|=0).

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Posts: 92
Re: If у + |y| = 0, which of the following must be true?  [#permalink]

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

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

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

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If у + |y| = 0, which of the following must be true?  [#permalink]

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1
Hi All,

This question is perfect for TESTing VALUES.

We're told that Y + |Y| = 0. We're asked which of the following MUST be true (which means "which of the following is ALWAYS TRUE no matter how many different examples we can come up with?")

The obvious value for Y is 0 (since 0 + |0| = 0)
Eliminate A and C.

Since there are still 3 values remaining, there MUST be other options to consider....

IF....
Y = -1
-1 + |-1| = 0
Eliminate B and E.

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

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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?

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

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

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_________________ Re: If у + |y| = 0, which of the following must be true?   [#permalink] 13 Mar 2019, 00:24
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