GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 07:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
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]

### Show Tags

31 Aug 2018, 23:02
00:00

Difficulty:

95% (hard)

Question Stats:

29% (01:53) correct 71% (02:12) wrong based on 119 sessions

### HideShow timer Statistics

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: 7978
Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

### Show Tags

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
_________________
Manager
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]

### Show Tags

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.
_________________
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: 253
Re: If |x+2|=|y+2| , what is the value of x+y ? (1) x≠y (2) x−y=16  [#permalink]

### Show Tags

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

### Show Tags

02 Sep 2018, 06:22
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
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]

### Show Tags

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
_________________
Manager
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]

### Show Tags

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]

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
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]

### Show Tags

03 Oct 2019, 02:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
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
Display posts from previous: Sort by