Is x^2 y^2? (1) x + y

Question

Is x^2 > y^2?

(1) x + y < 0

(2) x - y < 0

Bunuel · Accepted Answer

Is x^2 > y^2?

Is x^2 > y^2? --> is |x| > |y|? So, the question asks whether x is further from 0 than y.

(1) x + y < 0. The sum of two numbers is less than 0. Clearly insufficient to say which one is further from 0.

(2) x - y < 0 --> x < y. One number is less than another. Also, insufficient to say which one is further from 0. For example, if x = 1 and y = 2, then y is further but if x = -2 and y = 1, then x is further. Not sufficient.

(1)+(2) Is x^2 > y^2? Can be rephrased as "is (x - y)(x + y) > 0?" (1) says that x + y < 0 and (2) says that x - y < 0, thus their product, the product of two negative values, must be greater than 0. Sufficient.

Answer: C.

Hope it's clear.

mvictor · Answer

ok so that is how I resolved, but it is not correct:

x + y < 0
x<-y
hence if x must be less than -y, and that must be a negative, and since x is more than negative y, then x^2 must be also more than y^2
but it is incorrect.

can someone explain why?

PS
I did not consider the fact that y can be negative, in this case, x is positive, and since we have 2 outcomes, the statement 1 alone is insufficient.

vards · Answer

Solved this in 30 secs.I happened to learn this concept in e-gmat Quant live prep course..

if we are given that,

a>b and a+b is positive, then a^2 > b^2
a>b and a+b is negative, then a^2 < b^2

if we are given that,

a<b and a+b is positive, then a^2 < b^2
a<b and a^b is negative, then a^2 > b^2

Please press KUDOS if u find my post useful.Thank you.

desaichinmay22 · Answer

Is x^2 > y^2?
x^2-y^2 > 0
(x+y) (x-y) > 0... ?

statement 1 :
x + y < 0
we don't know value of (x-y). statement is insufficient

statement 2 :
x - y < 0
we don't know value of (x+y). statement is insufficient

1+2 combined,
statements are sufficient.

Ans - C

bumpbot · Answer

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Is x^2 > y^2? (1) x + y < 0 (2) x - y < 0

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