Is x + y 1?

Question

Is x + y > 1?

(1) x^2 - y^2 > 1
(2) x/y + 1 > 0, where y is positive.

chetan2u · Answer

Hi,

lets see the statements

1)  x^2-y^2>1  
OR (x-y)(x+y)>1..
Insuff

2)  \frac{x}{y}+1>0 , where y is positive 
(x+y)/y>0
since y is positive, x+y is also positive..
but we cannot say if x+y>1
insuff

combined.. 
 x+y is positive , so x-y is also +ive..
which means x>y.. 
Now  x^2-y^2>1....x^2>1+y^2 
so so  x^2>1 
and as x is POSITIVE, x>1 so x+y will be >1
sufficient
C

TheUltimateWinner · Answer

Thanks  chetan2u .
So, what will be the difficulty level of this question?

chetan2u · Answer

hi,
It should be close to 600-650 since it contains two variables and inequality too..

TheUltimateWinner · Answer

how can we be sure that it is close to 600-650 by seeing ''since it contains two variables and inequality too''. I want to know just for curiosity.

stonecold · Answer

Personal Opinion => This is a 650 - 700 level..
Again => This is a personal opinion ..

chetan2u · Answer

Hi,

generally inequalities and two variables Q are considered to be difficult by any average person, BUT since the Q has some straight forward equations, it can be 600-650 level..

However difficulty level is each ones perception. A difficult topic such as prob may be easy for you but very difficult for others

TheUltimateWinner · Answer

Thanks  @chetan2u . I got it

TheUltimateWinner · Answer

GMAT is nothing but all about technique. So could you please give a technique of this problem? Can you share  unconventional method/shortcut way  for THIS problem?
Thanks...

leanhdung · Answer

But x= 1/2 and y = 1/4 --> x^2 - y^2 < 1 --> statement 1 is not satisfied. Hi Bunuel ! From (1) and (2), we have y > 0, x + y > 0 and x - y > 0 (Or x > y). Assume x + y <= 1 --> x - y <= x + y <= 1 --> x^2 - y^2 = (x-y)(x+y) <= 1 --> contradict the statement (1) --> x + y> 1 --> C I think the OA must be C, please confirm! Many thanks ^^

chetan2u · Answer

Hi..

You are absolutely correct OA has to be C..
editing the OA

+1 kudos

ism1994 · Answer

Hi all,

Combining 1) and 2) we have the following conditions:
1-a) x> 1+y
1-b) x> 1-y
2) x> -y

Such conditions are met when
a) -y<x<1-y
b) x > 1+y

Although b) alone would give us answer C, since x also meets condition a), the correct answer is E

Can someone please confirm/ explain what I'm getting wrong?

Thanks!

Is x + y > 1?

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Is x + y > 1?

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