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# If |x+5|=|y+5|, what is the value of x+y?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If |x+5|=|y+5|, what is the value of x+y? [#permalink]

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29 Aug 2017, 00:42
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43% (01:06) correct 57% (01:35) wrong based on 93 sessions

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If |x+5|=|y+5|, what is the value of x+y?

1) xy<0
2) x>3 and y<3
[Reveal] Spoiler: OA

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Manager
Joined: 07 Jun 2017
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Re: If |x+5|=|y+5|, what is the value of x+y? [#permalink]

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29 Aug 2017, 01:41
Can anyone explain the statement 2?

For the statement 1, I got
x>0; y<0
then x+5=-y-5
x+y=-10
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Re: If |x+5|=|y+5|, what is the value of x+y? [#permalink]

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29 Aug 2017, 02:09
MathRevolution wrote:
If |x+5|=|y+5|, what is the value of x+y?

1) xy<0
2) x>3 and y<3

$$|x+5| = |y+5| \implies x+5 = y+5$$ or $$x+5 = - (y+5)$$
$$\implies x=y$$ or $$x+y=0$$

(1) $$xy<0$$

If $$x=y \implies xy=x^2 >0$$. Hence, this case is insufficient to the statement.

If $$x+y=0 \implies x=-y \implies xy = -y^2 < 0$$. This expression is true for any $$y \neq 0$$.

Hence $$x+y=0$$. Sufficient.

(2) Since $$x> 3 > y \implies x \neq y$$. Hence $$x+y=0$$. Sufficient.

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If |x+3|=|y+3|, what is the value of x+y? 1) xy<0 2) x>3 and y<3 [#permalink]

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30 Aug 2017, 00:26
Expert's post
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If |x+3|=|y+3|, what is the value of x+y?

1) xy<0
2) x>3 and y<3
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Re: If |x+3|=|y+3|, what is the value of x+y? 1) xy<0 2) x>3 and y<3 [#permalink]

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30 Aug 2017, 02:02
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Expert's post
MathRevolution wrote:
If |x+3|=|y+3|, what is the value of x+y?

1) xy<0
2) x>3 and y<3

Hi...

|x+3|=|y+3|...

Two possibilities

1) Both same sign... x=y
2) different sign...... x+y=-(3+3)=-6

Let's see the statements..
1) xy<0...
So X and y are of OPPOSITE sign..
x+y=-6

2) x>3 and y<3..
Again opposite sign..
x+y=-6

D
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: If |x+5|=|y+5|, what is the value of x+y? [#permalink]

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31 Aug 2017, 00:22
=>Condition 1)
|x+5|=|y+5| is equivalent to $$(x+5)^2=(y+5)^2 or (x+5)^2-(y+5)^2 = 0.$$
$$(x+5)^2-(y+5)^2 = (x+y+10)(x-y) = 0.$$
Then $$x = y or x + y + 10 = 0.$$
Since x cannot be equal to $$y, x + y = -10.$$
This is sufficient.

Condition 2)
|x+5|=|y+5| is equivalent to $$(x+5)^2=(y+5)^2 or (x+5)^2-(y+5)^2 = 0.$$
$$(x+5)^2-(y+5)^2 = (x+y+10)(x-y) = 0.$$
Then x = y or x + y + 10 = 0.
Since x > 3 and y < 3, x is not equal to y.
Thus x + y = -10.
This is sufficient.

Ans: D
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Joined: 29 Jun 2017
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If |x+5|=|y+5|, what is the value of x+y? [#permalink]

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31 Aug 2017, 00:53
broall wrote:
MathRevolution wrote:
If |x+5|=|y+5|, what is the value of x+y?

1) xy<0
2) x>3 and y<3

$$|x+5| = |y+5| \implies x+5 = y+5$$ or $$x+5 = - (y+5)$$
$$\implies x=y$$ or $$x+y=0$$

(1) $$xy<0$$

If $$x=y \implies xy=x^2 >0$$. Hence, this case is insufficient to the statement.

If $$x+y=0 \implies x=-y \implies xy = -y^2 < 0$$. This expression is true for any $$y \neq 0$$.

Hence $$x+y=0$$. Sufficient.

(2) Since $$x> 3 > y \implies x \neq y$$. Hence $$x+y=0$$. Sufficient.

broall

you have written
|x+5|=|y+5| implies (x+5)= (y+5) or (x+5) = -(y+5) which should mean x+y = - 10 , you have written x+y =0??
Can you enlighten me x+y = 0?? in case when x not equal to y

it should be x+y = -10

AND i can see in your solution everywhere is x+y = 0 ??
guess you have mistakenly forgot -10..

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Senior Manager
Joined: 29 Jun 2017
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GMAT 1: 570 Q49 V19
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If |x+5|=|y+5|, what is the value of x+y? [#permalink]

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31 Aug 2017, 01:03
pclawong wrote:
Can anyone explain the statement 2?

For the statement 1, I got
x>0; y<0
then x+5=-y-5
x+y=-10

2) x>3 and y <3
i guess you must be confused what if y=2 then x will be x+2=-10 , x= -12
but do tell me : is the solution x= -12 > or < 3, if it does not satisfy you condition 2 then it is not your solution and you can not take this value.
on other hand
Let x=4 y = -10-4 , y =-14
means this value is satisfying your condition 2 hence they are correct values.
you cant take 0,0 either as x is > 3 so we cant take those values as well
Therefore sufficient
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Math Revolution GMAT Instructor
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Re: If |x+5|=|y+5|, what is the value of x+y? [#permalink]

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01 Sep 2017, 02:17
=> 1) xy < 0
We can assume x > 0 and y < 0 without loss of generality.
Then we have x + 3 = -y - 3
x + y = -6
This is sufficient.

2) x > 3 and y < 3
Then we have x + 3 = -y - 3
x + y = -6
This is sufficient.

Ans: D
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Re: If |x+5|=|y+5|, what is the value of x+y?   [#permalink] 01 Sep 2017, 02:17
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