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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 29% (01:53) correct 71% (02:12) wrong based on 119 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 V
Joined: 02 Aug 2009
Posts: 7978
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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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
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Joined: 11 May 2018
Posts: 102
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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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.
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Joined: 07 Oct 2017
Posts: 253
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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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
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The best thing in life lies on the other side of the pain.
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Joined: 26 Mar 2013
Posts: 2345
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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3
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 V
Joined: 02 Aug 2009
Posts: 7978
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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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
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Manager  S
Joined: 11 May 2018
Posts: 102
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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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]
Thanks for the reply

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?
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Non-Human User Joined: 09 Sep 2013
Posts: 13258
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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_________________ Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16   [#permalink] 03 Oct 2019, 02:25
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