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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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Bunuel
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If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 [#permalink] New post  31 Aug 2018, 23:02
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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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Mo2men
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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] 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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chetan2u
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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] New post  02 Feb 2021, 20:32
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CEdward 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 chetan, I've seen squaring of the mod quite a bit including this post of yours. I am confused about when we should square the mod versus not? What are the indicators for us to do this? How is squaring the mod different from other techniques of dealing with mods, e.g. critical transition points, opening the mod, or graphically?


Whenever both the sides are positive, you can square them. Here we have modulus on both sides, so we can square.
But say it was |x+2|=|y-2|+x, you should avoid it as you do not know if RHS is positive.
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chetan2u
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If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 [#permalink] New post  31 Aug 2018, 23:37
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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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SonGoku
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If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 [#permalink] New post  31 Aug 2018, 23:54
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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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sumit411
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If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 [#permalink] 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?


Thank you = Kudos
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chetan2u
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If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 [#permalink] New post  02 Sep 2018, 08:08
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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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SonGoku
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If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 [#permalink] New post  03 Sep 2018, 10:15
chetan2u wrote:
SonGoku wrote:
chetan2u wrote:

|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

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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QuantMadeEasy
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If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 [#permalink] New post  03 Nov 2020, 00:29
Quote:
If |x + 2| = |y + 2|, what is the value of x + y?

Step 1: Understanding the question
Lets understand with cases:
Case 1: Both (x+2) and (y+2) are positive, (x + 2) = (y + 2); x = y
Case 2: One positive and other negative, (x + 2) = -( y + 2); x + y = -4

Step 2: Understanding statement 1 alone
(1) x ≠ y
When x ≠ y, therefore case 2 is valid, hence x + y = -4
Sufficient

Step 3: Understanding statement 2 alone
(2) x − y = 16
As difference between x and y is positive, x is greater than y. Hence, x ≠ y, therefore case 2 is valid ie. x + y = -4
Sufficient

D is correct
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If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16 [#permalink] New post  02 Feb 2021, 14:30
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 chetan, I've seen squaring of the mod quite a bit including this post of yours. I am confused about when we should square the mod versus not? What are the indicators for us to do this? How is squaring the mod different from other techniques of dealing with mods, e.g. critical transition points, opening the mod, or graphically?
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Re: If |x+2|=|y+2| , what is the value of x+y ? (1) xy (2) xy=16 [#permalink] New post  25 Nov 2022, 02:20
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