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# Is x - x^2 > y - y^2 ? *(1) x > y (2) x^2 > y^2

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Intern
Joined: 14 Jul 2014
Posts: 6
Is x - x^2 > y - y^2 ? *(1) x > y (2) x^2 > y^2  [#permalink]

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Updated on: 22 Apr 2018, 01:00
00:00

Difficulty:

95% (hard)

Question Stats:

47% (03:13) correct 53% (02:41) wrong based on 28 sessions

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Is $$x - x^2 > y - y^2$$ ?

(1) x > y
(2) $$x^2 > y^2$$

Originally posted by Deepit on 29 Mar 2018, 04:05.
Last edited by amanvermagmat on 22 Apr 2018, 01:00, edited 2 times in total.
Renamed the topic and edited the question.
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Joined: 27 Oct 2017
Posts: 1256
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is x - x^2 > y - y^2 ? *(1) x > y (2) x^2 > y^2  [#permalink]

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29 Mar 2018, 06:49
IS $$x - x^2 > y -y^2$$
or, $$x-y>x^2-y^2$$
or, $$(x-y)>(x-y)(x+y)$$
Statement 1:
x>y or (x-y)>0
hence question reduces to is 1>(x+y). No other info
insufficient.

Statement 2:
$$x^2>y^2$$
$$x^2-y^2>0$$
(x-y)(x+y)>0. No other info.
Insufficient.

Combining 1 & 2 we get, (x-y)>0 and $$(x^2-y^2)>0$$
but still we cant find the relative relation between the two

Hence it is insufficient..
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Retired Moderator
Joined: 27 Oct 2017
Posts: 1256
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is x - x^2 > y - y^2 ? *(1) x > y (2) x^2 > y^2  [#permalink]

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29 Mar 2018, 07:00
3
The OA is wrong, it should be E.

suppose (x, y) = (4,3)
it satisfy both statements
here answer to question $$x−x^2>y−y^2$$ shall be NO.

if (x,y) = (0.7, 0.1)
it satisfy both statements
here answer to question $$x−x^2>y−y^2$$ shall be YES.

Hence Answer shall be E

Actually in case of Inequality, only like inequality can only be added,
Subtraction is not valid.

Hence it is not sufficient.
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Re: Is x - x^2 > y - y^2 ? *(1) x > y (2) x^2 > y^2   [#permalink] 29 Mar 2018, 07:00
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# Is x - x^2 > y - y^2 ? *(1) x > y (2) x^2 > y^2

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