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

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New post 31 Aug 2018, 23:02
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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]

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New post 31 Aug 2018, 23:37
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
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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]

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New post 31 Aug 2018, 23:54
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.
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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]

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New post 01 Sep 2018, 00:39
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?


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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]

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New post 02 Sep 2018, 06:22
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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



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

Answer: D
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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]

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New post 02 Sep 2018, 08:08
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
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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]

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New post 03 Sep 2018, 10:15
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]
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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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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