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# Is x + y > 1?

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Senior Manager
Joined: 23 Feb 2015
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GMAT 1: 720 Q49 V40
Is x + y > 1?  [#permalink]

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Updated on: 26 Oct 2017, 03:07
2
00:00

Difficulty:

75% (hard)

Question Stats:

35% (02:14) correct 65% (02:01) wrong based on 77 sessions

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Is x + y > 1?

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

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Originally posted by AsadAbu on 09 Apr 2016, 14:31.
Last edited by chetan2u on 26 Oct 2017, 03:07, edited 3 times in total.
Corrected the OA
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Re: Is x + y > 1?  [#permalink]

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09 Apr 2016, 19:54
2
iMyself wrote:
is x+y>1?

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

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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is x + y > 1?  [#permalink]

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09 Apr 2016, 22:38
Thanks chetan2u.
So, what will be the difficulty level of this question?
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Re: Is x + y > 1?  [#permalink]

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09 Apr 2016, 22:41
iMyself wrote:
Thanks chetan2u.
So, what will be the difficulty level of this question?

hi,
It should be close to 600-650 since it contains two variables and inequality too..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is x + y > 1?  [#permalink]

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09 Apr 2016, 22:47
chetan2u wrote:
iMyself wrote:
Thanks chetan2u.
So, what will be the difficulty level of this question?

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

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.
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Re: Is x + y > 1?  [#permalink]

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09 Apr 2016, 23:59
iMyself wrote:
chetan2u wrote:
iMyself wrote:
Thanks chetan2u.
So, what will be the difficulty level of this question?

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

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.

Personal Opinion => This is a 650 - 700 level..
Again => This is a personal opinion ..
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Re: Is x + y > 1?  [#permalink]

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10 Apr 2016, 00:26
2
iMyself wrote:
chetan2u wrote:
iMyself wrote:
Thanks chetan2u.
So, what will be the difficulty level of this question?

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

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.

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
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 23 Feb 2015
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GMAT 1: 720 Q49 V40
Re: Is x + y > 1?  [#permalink]

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Updated on: 10 Apr 2016, 06:56
Thanks @chetan2u. I got it
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“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
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Originally posted by AsadAbu on 10 Apr 2016, 00:42.
Last edited by AsadAbu on 10 Apr 2016, 06:56, edited 1 time in total.
Senior Manager
Joined: 23 Feb 2015
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Re: Is x + y > 1?  [#permalink]

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10 Apr 2016, 11:05
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...
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Is x + y > 1?  [#permalink]

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Updated on: 26 Oct 2017, 04:33
1
chetan2u wrote:
Hi,
I think you are subconsciously taking x and y as integers..
but say if x and y are fractions..
x= 1/2 and y = 1/4 ..
x+ y <1..

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 ^^
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Originally posted by leanhdung on 26 Oct 2017, 02:44.
Last edited by leanhdung on 26 Oct 2017, 04:33, edited 1 time in total.
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Joined: 02 Aug 2009
Posts: 6979
Re: Is x + y > 1?  [#permalink]

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26 Oct 2017, 03:05
1
leanhdung wrote:
chetan2u wrote:
Hi,
I think you are subconsciously taking x and y as integers..
but say if x and y are fractions..
x= 1/2 and y = 1/4 ..
x+ y <1..

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^2 - y^2> 1

--> C

I think the OA must be C, please confirm! Many thanks ^^

Hi..

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

+1 kudos
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is x + y > 1? &nbs [#permalink] 26 Oct 2017, 03:05
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