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Is x + y > 1?

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Is x + y > 1? [#permalink]

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Is x + y > 1?

(1) x^2 - y^2 > 1
(2) x/y + 1 > 0, where y is positive.
[Reveal] Spoiler: OA

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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.”
― Henry Wadsworth Longfellow


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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New post 09 Apr 2016, 19:54
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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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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Is x + y > 1? [#permalink]

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New post 09 Apr 2016, 22:38
Thanks chetan2u.
So, what will be the difficulty level of this question?
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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.”
― Henry Wadsworth Longfellow

Kudos [?]: 223 [0], given: 179

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Re: Is x + y > 1? [#permalink]

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New post 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..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [0], given: 121

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Re: Is x + y > 1? [#permalink]

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New post 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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“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.”
― Henry Wadsworth Longfellow

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Re: Is x + y > 1? [#permalink]

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New post 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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New post 10 Apr 2016, 00:26
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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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [2], given: 121

Senior Manager
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Re: Is x + y > 1? [#permalink]

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New post 10 Apr 2016, 00:42
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.”
― Henry Wadsworth Longfellow


Last edited by iMyself on 10 Apr 2016, 06:56, edited 1 time in total.

Kudos [?]: 223 [0], given: 179

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Re: Is x + y > 1? [#permalink]

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New post 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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“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.”
― Henry Wadsworth Longfellow

Kudos [?]: 223 [0], given: 179

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Is x + y > 1? [#permalink]

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New post 26 Oct 2017, 02:44
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chetan2u wrote:
Hi,
I think you are subconsciously taking x and y as integers..
but say if x and y are fractions.. :roll: :roll:
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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Last edited by leanhdung on 26 Oct 2017, 04:33, edited 1 time in total.

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Re: Is x + y > 1? [#permalink]

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New post 26 Oct 2017, 03:05
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leanhdung wrote:
chetan2u wrote:
Hi,
I think you are subconsciously taking x and y as integers..
but say if x and y are fractions.. :roll: :roll:
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [1], given: 121

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