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

Question

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

(1)  x - y = 4

(2)  \frac{x}{y} = -1

Kinshook · Answer

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

JonShukhrat · Answer

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

Since x and y are equal (note: their absolute values are so), let's pick some easy numbers to work with.

ST1   x−y=4
Say x and y are 2 each. 2-2=0 (NO, must be 4). Does not work
Say x and y are (-2) each. (-2)-(-2)=0 (NO, must be 4). Does not work
Say x is (-2) and y is (2). (-2)-2=-4 (NO, must be 4). Does not work
Say x is 2 and y is (-2). 2-(-2)=4,  yes it works . So 2+(-2)= 0 . We have an answer.  Sufficient.

ST2   xy=−1
Let's do similar testing. 
Say x and y are 2 each. 2/2=1(NO, must be (-1)). Does not work
Say x and y are (-2) each. (-2)/(-2)=1 (NO, must be (-1)). Does not work
Say x is (-2) and y is (2). (-2)/2=-1, yes it works. So, we have -2+2=0. We have an answer. 
Say x is 2 and y is (-2). 2/(-2)=-1,  yes it works.  So 2+(-2)=0. Again, we have an answer. (Although two different sets of value works, both yield the same answer)  Sufficient

Hence  D

Ilishar · Answer

Given : |x|=|y|
Find: x+y? (single value should be available)
Analysis: 
if x=y then, values are required
if x= -y then, x+y = 0
if -x = y then, x+y =0
 (1)Statement 1: 
x-y=4
x=y+4 => x not equal to y 
we know |x|=|y| thus, we can have values like x(2), y(-2), implying that x+y = 0
Hence, sufficient

(ii) Statement 2: 
x/y = -1 
x=-y thus, x+y =0
Hence, Sufficient

Final Answer D

RusskiyLev · Answer

It is given that  |x|=|y| . Hence, either  x = y  or  x = - y . 
We need to find out what is  x + y ? 
 If  x = y , then  x + y is 2x or 2y . 
If  x = -y , then  x + y = 0 .

Let us analyze the statements separately first and see if it is required to analyze them together.

Statement 1: 
 x - y = 4.  
From this statement we can conclude that  x = y + 4 , and  x  is not equal to  y . From what we found in the beginning, it means that  x = -y . In this case, we can substitute  y  by  -x  and write an equation  as x + y = x - x = 0 .
Statement is sufficient.

Statement 2:  
 x/y = -1 . 
From this stament, it can be calculated that  x = -1 * y = -y . Here, we can solve it in the same way as we did above in analysis of the first statement. 
Statement 2 is sufficient.

As we have both statements sufficient to solve the question, the Answer is  D .

freedom128 · Answer

|x|=|y| --> x^2 = y^2 --> x^2 - y^2 = 0 --> (x-y)(x+y)=0

QUESTION: x+y=?

(1) x−y=4  
If (x−y)(x+y)=0 and (x−y)=4, then (x+y) must be 0
 (1) is SUFFICIENT

(2) x/y=−1  
x/y=−1 --> x = −y --> x+y = 0
 (2) is SUFFICIENT

Correct answer is  (D)

bebs · Answer

Given: |x|=|y|

Question : x+y=0

St 1: x-y = 4 ==> x = 2, y = -2 ==> 2+(-2)=0 ===> sufficient since we can't find any other set of numbers that satisfies St 1 and |x|=|y|. 
St 2:  \frac{x}{y} =-1 ==> x=-y ==> x+y=0 ==> sufficient

Therefore, the answer is D.

nick1816 · Answer

Statement 1
|x|=|y| and x-y=4
It implies that x and y gas opposite signs
Hence x+y=0
Sufficient

Statement 2
|x|=|y| and xy=-1
Again we get that x and y are equal in magnitude, but have opposite signs
x+y=0
sufficient

IMO D

CareerGeek · Answer

|x|=|y|
--> x = ± y
--> x = y (or) x = -y

(1) x − y = 4
--> x & y can have ONLY opposite sign; x is positive & y is negative
--> x = -y
-y - y = 4
--> -2y = 4
--> y = -2
--> x = -(-2) = 2

x + y = 2 - 2 = 0

Sufficient

(2) x/y=−1
--> x & y are of same value, BUT opposite sign
--> x = -y

x + y = -y + y = 0

Sufficient

IMO Option D

Pls Hit Kudos if you like the solution

GKomoku · Answer

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

(1)  x−y=4, from this we can get that x and y are opposite signs.
If they both were negative, zero: -2--2=-2+2=0.
If they both were positive aslo x-y=0. 
So we infer that both of them need to be opposite signs and x need to be positive. eg: 2--2=2+2=4
We have definite answer, sufficient.

(2)  x/y=−1 from this we get x and y different signs, hence x+y=0, sufficient.

D is the answer.

shridhar786 · Answer

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

|x|^2  =  |y|^2  (squaring both sides)
 x^2  =  y^2 
( x^2 - y^2 ) = 0
(x-y)(x+y) = 0
(x-y)=0 or (x+y) = 0

STATEMENT (1) x−y=4 
this statement tells us that (x-y)  ≠  0
then definitely (x+y) = 0 SUFFICIENT

STATEMENT (2)  \frac{x}{y} =−1
 \frac{x}{y} +1 = 0
  \frac{(x+y)}{y} =0
(x+y)=0 (since y cant be equal to zero)
SUFFICIENT

D is the answer

eakabuah · Answer

If |x|=|y|, then x=y or x=-y
What is x+y?

1. x-y=6
The condition is that x=y or x=-y.
So x-y=6
The values of x and y that satisfy this condition are x=3 and y=-3 and this satisfies the condition x=-y
3-(-3)=6. Hence we can say that x+y=0
Statement 1 alone is sufficient.

Statement 2: x/y=-1
We know that both x and y can be both positive or they both negative or one can be positive while the other is negative. 
So we mutiply both sides by y^2 to ensure the signs don’t change.
y^2+xy=0
y(y+x)=0
either y=0, which makes x=0, or y+x=0 which means that x=-y
And this is true for any pairs of x=-y, such as {1,-1; 2,-2; 3,-3; -4,4}
Hence we can say that x+y=0
Statement 2 is therefore sufficient.
Answer imo is D

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ArtyomYom · Answer

If |x|=|y|, x+y=?
Possibilities:
x and y can be pos and neg:
'+' + '+' = 2x or 2y
'-' + '-' = 2x or 2y
'+' + '-' = 0
'-' + '+' = 0

(1) x−y=4
if x and y:
'+' '+' = no sence, coz |x|=|y|
'-' '-' = no sence, coz |x|=|y|
'+' '-' = can be x = 2 y = -2
'-' '+' = no sense, coz result need to be negative 
SUFFICIENT: '+' + '-' = 0

(2) xy=−1
if x and y:
'+' '+' = no sence, multiple must be positive
'-' '-' = no sence, multiple must be positive
'+' '-' = can be
'-' '+' = can be
SUFFICIENT: 
'+' + '-' = 0
'-' + '+' = 0

Answ D

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

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