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# If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16

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Math Expert
Joined: 02 Sep 2009
Posts: 52285
If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

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31 Aug 2018, 22:02
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Difficulty:

95% (hard)

Question Stats:

27% (02:04) correct 73% (02:04) wrong based on 103 sessions

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If |x + 2| = |y + 2|, what is the value of x + y?

(1) x ≠ y
(2) x − y = 16

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7201
Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

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31 Aug 2018, 22:37
Bunuel wrote:
If |x + 2| = |y + 2|, what is the value of x + y?
(1) x ≠ y
(2) x − y = 16

|x + 2| = |y + 2| means x and y are at same distance from -2
so either both x and y are equal or they are on either side of -2..

OR

square both sides..
$$(|x + 2|)^2 = (|y + 2|)^2..............x^2+4x+4=y^2+4y+4.........x^2-y^2+4x-4y=0.......(x-y)(x+y)+4(x-y)+0........(x-y)(x+y+4)=0$$
this means x=y or x+y=-4 or both

(1) x ≠ y
colored portion above tells us that x+y=-4
sufficient

(2) x − y = 16
again this tells us that x ≠ y, otherwise x-Y=0
colored portion above tells us that x+y=-4
sufficient

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 11 May 2018
Posts: 92
Location: India
GMAT 1: 460 Q42 V14
Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

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31 Aug 2018, 22:54
chetan2u wrote:
Bunuel wrote:
If |x + 2| = |y + 2|, what is the value of x + y?
(1) x ≠ y
(2) x − y = 16

|x + 2| = |y + 2| means x and y are at same distance from -2
so either both x and y are equal or they are on either side of -2..

OR

square both sides..
$$(|x + 2|)^2 = (|y + 2|)^2..............x^2+4x+4=y^2+4y+4.........x^2-y^2+4x-4y=0.......(x-y)(x+y)+4(x-y)+0........(x-y)(x+y+4)=0$$
this means x=y or x+y=-4 or both

(1) x ≠ y
colored portion above tells us that x+y=-4
sufficient

(2) x − y = 16
again this tells us that x ≠ y, otherwise x-Y=0
colored portion above tells us that x+y=-4
sufficient

D

Hello chetan2u
I always had this doubt.Even now i am not clear about the OR in the inequalities.could you please explain the functionality of it or posting a thread link explaining that is also fine because it will be time consuming to type it again if explained elsewhere.
Thankyou.
_________________

If you want to Thank me Give me a KUDOS
"I’ve spent months preparing for the day I’d face you. I’ve come a long way, GMAT"- SonGoku

Senior Manager
Joined: 07 Oct 2017
Posts: 260
Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

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31 Aug 2018, 23:39
SonGoku wrote:
chetan2u wrote:
Bunuel wrote:
If |x + 2| = |y + 2|, what is the value of x + y?
(1) x ≠ y
(2) x − y = 16

|x + 2| = |y + 2| means x and y are at same distance from -2
so either both x and y are equal or they are on either side of -2..

OR

square both sides..
$$(|x + 2|)^2 = (|y + 2|)^2..............x^2+4x+4=y^2+4y+4.........x^2-y^2+4x-4y=0.......(x-y)(x+y)+4(x-y)+0........(x-y)(x+y+4)=0$$
this means x=y or x+y=-4 or both

(1) x ≠ y
colored portion above tells us that x+y=-4
sufficient

(2) x − y = 16
again this tells us that x ≠ y, otherwise x-Y=0
colored portion above tells us that x+y=-4
sufficient

D

Hello chetan2u
I always had this doubt.Even now i am not clear about the OR in the inequalities.could you please explain the functionality of it or posting a thread link explaining that is also fine because it will be time consuming to type it again if explained elsewhere.
Thankyou.
Hi SonGoku

Do you want links for modulus functions?

Thank you = Kudos
_________________

Thank you =Kudos
The best thing in life lies on the other side of the pain.

SVP
Joined: 26 Mar 2013
Posts: 2002
Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

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02 Sep 2018, 05:22
2
Bunuel wrote:
If |x + 2| = |y + 2|, what is the value of x + y?

(1) x ≠ y
(2) x − y = 16

Analyzing the stem, we have 2 cases:

x+2 = y+2..........x =y

Or

x+2 = -y-2....... x+y= 4

(1) x ≠ y

This tells as that case 1 is invalid ....we are left with case 2 in that x +y =4

Sufficient

(2) x − y = 16

This tells us that case 1 is invalid because 0 does not equal 16. we are left with case 2 in that x +y =4

Sufficient

Math Expert
Joined: 02 Aug 2009
Posts: 7201
Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

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02 Sep 2018, 07:08
SonGoku wrote:
chetan2u wrote:
Bunuel wrote:
If |x + 2| = |y + 2|, what is the value of x + y?
(1) x ≠ y
(2) x − y = 16

|x + 2| = |y + 2| means x and y are at same distance from -2
so either both x and y are equal or they are on either side of -2..

OR

square both sides..
$$(|x + 2|)^2 = (|y + 2|)^2..............x^2+4x+4=y^2+4y+4.........x^2-y^2+4x-4y=0.......(x-y)(x+y)+4(x-y)+0........(x-y)(x+y+4)=0$$
this means x=y or x+y=-4 or both

(1) x ≠ y
colored portion above tells us that x+y=-4
sufficient

(2) x − y = 16
again this tells us that x ≠ y, otherwise x-Y=0
colored portion above tells us that x+y=-4
sufficient

D

Hello chetan2u
I always had this doubt.Even now i am not clear about the OR in the inequalities.could you please explain the functionality of it or posting a thread link explaining that is also fine because it will be time consuming to type it again if explained elsewhere.
Thankyou.

if an equation is (a-b)(a+b-1)=0..
there are two cases
a-b=0 so a=b or
a+b-1=0.....a+b=1

so if any of the above two cases a=b or a+b=1 then the equation stands. It may also be the case that both are true say a=b=1/2

is there anything else you are wanting to ask
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 11 May 2018
Posts: 92
Location: India
GMAT 1: 460 Q42 V14
Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

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03 Sep 2018, 09:15
chetan2u wrote:
SonGoku wrote:
chetan2u wrote:
[quote="Bunuel"]If |x + 2| = |y + 2|, what is the value of x + y?
(1) x ≠ y
(2) x − y = 16

|x + 2| = |y + 2| means x and y are at same distance from -2
so either both x and y are equal or they are on either side of -2..

OR

square both sides..
$$(|x + 2|)^2 = (|y + 2|)^2..............x^2+4x+4=y^2+4y+4.........x^2-y^2+4x-4y=0.......(x-y)(x+y)+4(x-y)+0........(x-y)(x+y+4)=0$$
this means x=y or x+y=-4 or both

(1) x ≠ y
colored portion above tells us that x+y=-4
sufficient

(2) x − y = 16
again this tells us that x ≠ y, otherwise x-Y=0
colored portion above tells us that x+y=-4
sufficient

D

Hello chetan2u
I always had this doubt.Even now i am not clear about the OR in the inequalities.could you please explain the functionality of it or posting a thread link explaining that is also fine because it will be time consuming to type it again if explained elsewhere.
Thankyou.

if an equation is (a-b)(a+b-1)=0..
there are two cases
a-b=0 so a=b or
a+b-1=0.....a+b=1

so if any of the above two cases a=b or a+b=1 then the equation stands. It may also be the case that both are true say a=b=1/2

is there anything else you are wanting to ask[/quote]

So, That means if there are two statements and if one of the two statements satisfies any one of above cases.can we consider the statement sufficient? OR Do we need to consider both of them to check whether the statement is sufficient?
_________________

If you want to Thank me Give me a KUDOS
"I’ve spent months preparing for the day I’d face you. I’ve come a long way, GMAT"- SonGoku

Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 &nbs [#permalink] 03 Sep 2018, 09:15
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