Does x + y = 0? (1) xy

Question

Does x + y = 0 ?

(1) xy < 0
(2) x^2 = y^2

DangerPenguin · Accepted Answer

statement 1: insufficient
this only tells us that either x or y is positive and the other is negative

statement 2: insufficient
if x=2 and y=2, then 4=4 and going back to the original question, 2+2 does not equal 0. but if x=-2 and y=2, then we get a yes and it also fits statement 1.

statement 1+2: sufficient
knowing that one is positive and one is negative from statement 1, the only way statement 2 can be true is if the numbers are the same but have opposite symbols positive/negative. since that is the case, x+y will always be 0.

Answer C!

farzana87 · Answer

Answer c.
statement 1: x, y are of opposite sign.
statement 2: |x| and |y| are equal
1 & 2: x= -y 
 x+y=0

mika84 · Answer

1) xy<0, it means that x and y has different signs, but not necessarily equal. NS
2) (x-y)(x+y)=0
either x=y or x=-y, as we are not certain that x+y=0, then it's NS
BOTH
as xy<0, the signs of x and y are different, then x=-y, or x+y=0 Suf

fitzpratik · Answer

Does x + y = 0? (OR is -x=y OR x=-y)

(1) xy<0
(2) x^2 = y^2

So
1: xy<0 so either x OR y <0 Not sufficient

2. x^2 =y^2 . |x| = |y|. But we dont know anything about the sign of either x OR y. Not sufficient

Both together
xy<0 and x^2 =y^2 : So either one of them is negative, and they have same aboslute value. Suffient to answer the question  x+y=0

KanishkM · Answer

Statement 1 
xy < 0 
x can be +ive or -ive, or can be = to y
y can be +ive or -ive, or can be = to x

With those cases in mind, inline are some samples 
x=1, y=-1, will answer the question as Yes 
x=2, y =-1, will answer the question as No

Statement 2
x can be +ive or -ive
y can be +ive or -ive

With those cases in mind, inline are some samples 
x=1, y=-1, will answer the question as Yes 
x=1, y =1, will answer the question as No

Combine both the statements and you will always get a Yes 
If x is +ive, y has to be -ive
If y is +ive, x has to be -ive.

With those cases in mind, inline are some samples 
x=1, y=-1, will answer the question as Yes 
x=-1, y =1, will answer the question as Yes

Correct answer C.

mmshake · Answer

Please correct me if I am wrong but wont the answer be E?
This is because it is not mentioned that x and y are integers. So in case of both the statements combined, the value of x and y could be a decimal for eg., 0.1 which would satisfy both the conditions, but x+y wont be equal to zero

Bunuel · Answer

Think about it, if x = 0.1, what would be the value of y, and what would be the value of x + y?

mmshake · Answer

Oh right! Got it now! Thank you so much!

KanikaJain · Answer

Does x + y = 0 ?

(1) xy < 0
(2) x^2 = y^2

Statement 1:
either x<0 or y<0.
x may or may not equal to -y.

Statement 2:
(x+y)(x-y) = 0
x = -y or x = y
thus x+y may or may not equal to 0

Combing the two statements, x = -y. thus x+y = 0

hence C

bumpbot · Answer

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Does x + y = 0? (1) xy < 0 (2) x^2 = y^2

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