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Math Expert V
Joined: 02 Sep 2009
Posts: 59182
If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 61% (01:26) correct 39% (01:23) wrong based on 298 sessions

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If $$|x| = |y|$$, $$x + y = ?$$

(1) $$x - y = 4$$

(2) $$\frac{x}{y} = -1$$ This question was provided by Math Revolution for the Game of Timers Competition _________________
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Joined: 03 Jun 2019
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If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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4
1
Given: |x|=|y|
Question: x+y=?

Statement 1:
x−y=4
Since |x|=|y|
=> x = y or x=-y
x-y=4
x<>y => x=-y
x=2 & y=-2
x+y=0
SUFFICIENT

Statement 2:
x/y=−1
x=-y
x+y=0
SUFFICIENT

IMO D
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Originally posted by Kinshook on 12 Jul 2019, 08:16.
Last edited by Kinshook on 13 Jul 2019, 09:30, edited 1 time in total.
##### General Discussion
Senior Manager  G
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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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A alone is sufficient because the numbers have to be 2 and -2.

B is not sufficient because it could be 1/-1 or -1/1.

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Senior Manager  G
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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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stat A... is just sufficient since as per that x,y takes diff values except for (2,-2) for given conditions
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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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given |x| = |y|, x=y or x=-y

from 1: if x=y, then x-y should be 0, but x-y = 4, so x nad y have opp signs. so, x=-y
we have 2 equations, x+y=0 and x-y=4, these can be solved to find x and y, sufficient

from 2: all we know is x and y have opp signs, so not suff

Senior Manager  P
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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
If |x|=|y|, x+y=?

Given:
|x|=|y|
=> x = y or x = -y

(1) x−y=4 --> correct: x-y = 0, so x-y != 0 i.e x != y, so x = -y => x+y = 0

(2) x/y=−1 --> correct: x = -y, so x+y =0

Manager  G
Joined: 27 May 2010
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If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
If |x|=|y|, x+y=?
this implies x = +/-y
that is x+y=0 or x-y=0

(1) x−y=4
therefore x+y=0

(2) x/y=−1
x=-y, therefore x+y=0

Both statements individually imply that X + y = 0.

Option D

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Originally posted by prashanths on 12 Jul 2019, 08:22.
Last edited by prashanths on 12 Jul 2019, 20:04, edited 1 time in total.
Manager  G
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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
If |x|=|y|, x+y=?

(1) x−y=4

(2) x/y=−1

we are given |x| = |y|
which means x = y or x = -y

1. x - y =4 hence x = y + 4 now from above equation if we substitute here. X = Y will not satisfy x = y + 4.
So only x = -y can be substituted in x = y + 4, which will mean x = 2 and y = -2 hence x + y = 0 - Sufficient

2. x/y = -1, simplifying the equation we will get x = -y and hence x + y = 0. - Sufficient

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GMAT 1: 730 Q51 V36 Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
If |x| = |y|, then either x = y or x = -y

Considering statement (1) alone:
x - y = 4
The only possible values are x = 2 and y = -2
SUFFICIENT

Considering statement (2) alone:
x = -y
SUFFICIENT

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Manager  S
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If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
Statement 1
If |x| and |y| are same.
Only way is 2 - (-2) = 4

Statement 2
2 combinations
X negative y postive
X positive y negative

Either ways x+y will be 0

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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
Quote:
If |x| = |y|, x + y = ?
(1) x - y = 4
(2) x/y = -1

If |x|=|y|, then they have the same value, and either the same sign or alternate signs;
(1) x - y = 4: then x=2 y=-2, or x=-2 y=2, in both cases x+y=0, sufficient.
(2) x/y = -1: then, they have alternate signs, and their sum will always be 0, sufficient.

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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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A

From the given equation, x = y and x = -y.

From st 1: x = y +4, we cant solve this equation with x = y, so we get only one solution, i.e. x = 2 and y = -2. Sufficient
From st 2: x = -y, we will get infinite solutions. Not Sufficient.
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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
If |x|=|y| , x+y=?

(1) x−y=4

If x-y=4 then
x=y+4
|y+4|=|y|
the only possible solution is y=-2
x=-2+4=2
x+y=2-2=0
Sufficient

(2) x/y=-1

This statement tells us that x and y are the same numbers but with different sings.
thus their sum should be equal to 0
Sufficient.

IMO D
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GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33 Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
Given x^2=y^2;
x^2-y^2 =0; (x-y)(x+y)=0

1) x-y=4- Sufficient as 4(x+y)=0 gives x+y=0
2)x=-y Sufficient as -y+y=0

IMO D
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If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
given
|x|=|y|,
so x= y possible when either of them is same or opposite sign viz. x=y or x=-y or-x=y
#1
x−y=4
from given condition its only possible when x=2 and y=-2
sufficient to say that x+y=0
#2
x=-y
so x+y=0 sufficient
IMO D

If |x|=|y|, x+y=?

(1) x−y=4

(2) x/y=−1

Originally posted by Archit3110 on 12 Jul 2019, 08:40.
Last edited by Archit3110 on 13 Jul 2019, 03:48, edited 1 time in total.
Manager  S
Joined: 12 Mar 2019
Posts: 158
Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
Answer C : Both statements are sufficient

Suppose X =2, Y =-2
so |x| =2 and |y|= 2
which gives x-y =2+ -(-2) = 4 , so x+y = 0 , sufficient

again consider same
x/y =-1, -1 can only result if both integers are same and one is negative. In this case x+y = 0
So sufficient

Both are individually sufficient
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Joined: 24 Mar 2019
Posts: 22
Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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From the first statement we know that sign of x and y can't be same. Then if we use y=-x and substitute it in the equation we will get value of x and y. Thus first statement is sufficient.

Second statement only tells us about the sign and not the magnitude and thus we cannot find the value of x+y

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Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
Given |x|=|y|
Hence there are two cases: 1) y=x and 2) y=-x

Question stem:- x+y=?

St1:- x-y=4
When y=x then x-y=0 (So this case is not satisfied)
When y=-x then x-y=2x=4 or x=2 so y=-2. Therefore x+y=0
Sufficient.

St2:- x/y=-1 or x=-y
Now x+y=-y+y=0
Sufficient.

Ans. (D)
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Manager  S
Joined: 17 Apr 2018
Posts: 107
Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
modX = modY
x=y
x=-y
-x=y
-x=-y

From A since X-Y =4, X and y cannot be of same sign as if they are of same sign will x-y=0
possibility
x=-y
-x=y

Adding X+y=0 in both the possibilities hence we can conclude it from A.

From B
x/y = -1
x=-y
so x+y=0

both 1st and 2nd satements can independently answer.
Manager  S
Joined: 18 Sep 2018
Posts: 100
Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1  [#permalink]

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1
IMO D

Given, |x|=|y| => squaring both sides, x^2=y^2 => x^2-y^2=0 => (x+y)(x-y)=0 => Either x+y=0 or x-y=0

From (1) x−y=4 (i.e. not 0), hence x+y=0
Sufficient

From (2) x/y=−1 => x=-y => x+y=0
Sufficient Re: If |x| = |y|, x + y = ? (1) x - y = 4 (2) x/y = -1   [#permalink] 12 Jul 2019, 08:56

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