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# If both x and y are integers, is √x^2-y^2 an integer?

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If both x and y are integers, is √x^2-y^2 an integer?  [#permalink]

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30 Sep 2018, 10:08
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Difficulty:

35% (medium)

Question Stats:

80% (01:04) correct 20% (00:50) wrong based on 10 sessions

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If both x and y are integers, is √$$x^2$$-$$y^2$$ an integer?
(1) x+y=0
(2)$$x^2-y^2$$equals the cube of an integer.
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 968
Location: India
GPA: 3.64
If both x and y are integers, is √x^2-y^2 an integer?  [#permalink]

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30 Sep 2018, 10:33
1
jalice wrote:
If both x and y are integers, is √$$x^2$$-$$y^2$$ an integer?
(1) x+y=0
(2)$$x^2-y^2$$equals the cube of an integer.

S1 - x+y=0
x=-y
$$\sqrt{x^2-y^2}$$ = $$\sqrt{x^2-x^2}$$ = 0 = Integer
Sufficient.

S2 = $$x^2-y^2$$ = $$a^3$$ where a is an integer
$$\sqrt{x^2-x^2} = \sqrt{a^3}$$, which may or may not be an integer.
E.g. if a=2, not integer, but if a=4, then integer.
Insufficient.
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Re: If both x and y are integers, is √x^2-y^2 an integer?  [#permalink]

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30 Sep 2018, 20:35
jalice wrote:
If both x and y are integers, is √$$x^2$$-$$y^2$$ an integer?
(1) x+y=0
(2)$$x^2-y^2$$equals the cube of an integer.

Discussed here: https://gmatclub.com/forum/if-both-x-an ... 40259.html

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Re: If both x and y are integers, is √x^2-y^2 an integer? &nbs [#permalink] 30 Sep 2018, 20:35
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