|X+2|=|Y+2| what is the value of X+Y? (1) XY <0 (2) X&g

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richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Fri Sep 16, 2016 6:04 pm

|X+2|=|Y+2| what is the value of X+Y?

(1) XY <0
(2) X>2 Y<2

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Source: Beat The GMAT — Data Sufficiency | Fri Sep 16, 2016 6:04 pm

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by [email protected] » Fri Sep 16, 2016 6:32 pm

Hi richachampion,

We're told that |X+2| = |Y+2|. We're asked for the value of X+Y. Since we're dealing with absolute values, we should consider how NEGATIVE numbers will impact this question. By extension, the two variables are EITHER the same number OR one is positive and the other is negative so that we 'balance out' the equation.

1) XY < 0

With this Fact, we know that one of the variables is POSITIVE and the other is NEGATIVE. Considering the absolute value equation that we were also given, we can TEST VALUES.

IF....
X = 1, Y = -5
then the answer to the question is -4

IF....
X = 2, Y = -6
then the answer to the question is -4

IF....
X = 2.5, Y = -6.5
then the answer to the question is -4

The answer will ALWAYS be -4.
Fact 1 is SUFFICIENT

2) X > 2 and Y < 2

From this Fact, we can see that the two variables CANNOT be the same number, so they have to include one positive and one negative. That is the SAME pattern we faced in Fact 1 (above). No extra work is needed.
Combined, SUFFICIENT

Final Answer: D

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richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Fri Sep 16, 2016 11:02 pm

[email protected] wrote:Hi richachampion,

We're told that |X+2| = |Y+2|. We're asked for the value of X+Y. Since we're dealing with absolute values, we should consider how NEGATIVE numbers will impact this question. By extension, the two variables are EITHER the same number OR one is positive and the other is negative so that we 'balance out' the equation.

1) XY < 0

With this Fact, we know that one of the variables is POSITIVE and the other is NEGATIVE. Considering the absolute value equation that we were also given, we can TEST VALUES.

IF....
X = 1, Y = -5
then the answer to the question is -4

IF....
X = 2, Y = -6
then the answer to the question is -4

IF....
X = 2.5, Y = -6.5
then the answer to the question is -4

The answer will ALWAYS be -4.
Fact 1 is SUFFICIENT

2) X > 2 and Y < 2

From this Fact, we can see that the two variables CANNOT be the same number, so they have to include one positive and one negative. That is the SAME pattern we faced in Fact 1 (above). No extra work is needed.
Combined, SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Thanks see my approach

|X+2|=|Y+2| = Premise or Fact

Statement 1 >
XY <0
That means X & Y has an opposite sign. That means when X is +ve, Y is negative and vice versa.
When X>0
|Y| = |X| + 4; Remember here X is a positive and Y negative.
Thus,
Y = - (|X| + 4) = - (X+4)
X + Y = X -X -4 = -4

When Y>0
|X| = |Y| + 4; Remember here X is a negative and Y is positive.
X = - (|Y| + 4) = - (Y+4)
X + Y = -Y -4 + Y = -4
Thus X + Y will always be "-4".

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Sep 17, 2016 2:15 am

richachampion wrote:|X+2|=|Y+2| what is the value of X+Y?

(1) XY <0
(2) X>2 Y<2

Case 1: Signs unchanged
X+2 = Y+2
X=Y.

Case 2: Signs changed in ONE of the absolute values
X+2 = -Y-2
X+Y = -4.

Statement 1:
Since X and Y have different signs, only Case 2 is possible, with the result that X+Y = -4.
SUFFICIENT.

Statement 2:
Since Xâ‰ Y, only Case 2 is possible, with the result that X+Y = -4.
SUFFICIENT.

The correct answer is D.

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richachampion: Legendary Member; Posts: 698; Joined: Tue Jul 21, 2015 12:12 amFollowed by: 26 members; Location: Noida, India; Thanked: 32 times; GMAT Score:740

by richachampion » Sat Sep 17, 2016 2:32 am

GMATGuruNY wrote:
richachampion wrote:|X+2|=|Y+2| what is the value of X+Y?

(1) XY <0
(2) X>2 Y<2
Case 1: Signs unchanged
X+2 = Y+2
X=Y.

Case 2: Signs changed in ONE of the absolute values
X+2 = -Y-2
X+Y = -4.

Statement 1:
Since X and Y have different signs, only Case 2 is possible, with the result that X+Y = -4.
SUFFICIENT.

Statement 2:
Since Xâ‰ Y, only Case 2 is possible, with the result that X+Y = -4.
SUFFICIENT.

The correct answer is D.

That means my solution was Perfect. Okies?

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Sat Sep 17, 2016 9:40 am

richachampion wrote:|X+2|=|Y+2| what is the value of X+Y?

(1) XY <0
(2) X>2 Y<2

Hi,
It is really good question but can you please edit Fact 2 to be clear. I thought it is 2Y<2 and X>2Y.

thanks

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crackverbal: Master | Next Rank: 500 Posts; Posts: 157; Joined: Mon Aug 16, 2010 7:30 pmFollowed by: 3 members; Location: India; Thanked: 65 times

by crackverbal » Fri Oct 14, 2016 9:28 am

Hi,

Another way to solve this question is to deconstruct the question. Whenever you have a modulus on both sides of an equality you can square both sides and remove the modulus sign. The reason we can square both sides is because of the relationship |x| = root(x^2).

Squaring both sides of |x+2| = |y+2| we get (x+2)^2 = (y+2)^2
Simplifying, x^2 + 4x + 4 = y^2 + 4y + 4 ----> x^2 - y^2 = 4y - 4x

(x - y) (x + y) = -4(x - y). Now we cannot cancel x - y on both sides here as x - y can be 0. So to find the value of x + y we need the statements to give us conditions where x - y is not equal to 0 so that we can cancel the x - y terms on both sides to get x + y = -4.

Statement 1 : Clearly tells us that x - y cannot be 0 as x and y need to be of opposite sign. So sufficient.

Statement 2 : Again tells us that x - y cannot be 0. Sufficient.

OA : D

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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Sat Oct 15, 2016 6:16 am

|X+2|=|Y+2| what is the value of X+Y?
|X+2|=|Y+2|
squaring both sides
X^2 + 4X + 4 = Y^2 + 4Y + 4
X^2 + 4X - (Y^2 + 4Y) = 0
X^2 - Y^2 + 4X - 4Y =0
(X-Y)(X+Y-4) = 0
either X-Y=0 =>X=Y or (X+Y-4)=0 => X+Y = 4

(1) XY <0
X is not equal to Y so as discussed above second situation will be true (X+Y-4)=0
X+Y=4
SUFFICIENT

(2) X>2 Y<2
X is not equal to Y
X+Y=4
SUFFICIENT

so D

Fiza Gupta

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Re: |X+2|=|Y+2| what is the value of X+Y? (1) XY <0 (2) X&g

by Brent@GMATPrepNow » Sat Apr 18, 2020 6:46 am

richachampion wrote: ↑
Fri Sep 16, 2016 6:04 pm
|X+2|=|Y+2| what is the value of X+Y?

(1) XY <0
(2) X>2 Y<2

Given: |x + 2| = |y + 2|
Key property: If |a| = |b|, then EITHER a = b OR a = -b
So, if |x + 2| = |y + 2|, then there are two possible cases:

case i: x + 2 = y + 2
Subtract 2 from both sides of the equation to get: x = y

case ii: x + 2 = -(y + 2)
Simplify: x + 2 = -y - 2
Subtract 2 from both sides of the equation to get: x = -y - 4
Add y to both sides to get: x + y = -4

Target question: What is the value of x + y?

Statement 1: xy < 0
If the product xy is negative, we can conclude that one of the values (x or y) is POSITIVE, and the other value is NEGATIVE.
This means that x cannot equal y, which means case i cannot be true, which means case ii (x + y = -4) MUST BE TRUE
The answer to the target question is x + y = -4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x > 2 and y < 2
Combine inequalities to get: y < 2 < x
This means that x cannot equal y, which means case i cannot be true, which means case ii (x + y = -4) MUST BE TRUE
The answer to the target question is x + y = -4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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