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# If x and y are positive integers

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VP
Joined: 26 Mar 2013
Posts: 1284

Kudos [?]: 296 [0], given: 165

If x and y are positive integers [#permalink]

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24 Sep 2017, 15:55
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Question Stats:

40% (00:35) correct 60% (00:14) wrong based on 5 sessions

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If x and y are positive integers and $$(x+y)^2$$is an odd integer, is x an even integer?

1) $$x^4 - y^3$$ is an odd integer

2) $$0 < y^3-y < 24$$
[Reveal] Spoiler: OA

Kudos [?]: 296 [0], given: 165

Senior Manager
Joined: 02 Jul 2017
Posts: 269

Kudos [?]: 80 [1], given: 65

Location: India
Re: If x and y are positive integers [#permalink]

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24 Sep 2017, 18:55
1
KUDOS
If x and y are positive integers and $$(x+y)^2$$ is an odd integer, is x an even integer?

$$(x+y)^2$$ is an odd integer => as E+O =O => between x and y 1 is even and 1 is odd

1) $$x^4−y^3$$ is an odd integer
as O-E=O or E-O=O => above equation implies that between x and y 1 is even and 1 is odd
=> No extra information
Insufficient

2) $$0<y^3−y<24$$
as x and y are positive integers, so value of y can be 1,2,3....
for above equation only possible value of y=2=> $$0<2^3-2<24$$
=> y is even => by question stem x is odd
Sufficient

Kudos [?]: 80 [1], given: 65

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132646 [0], given: 12326

Re: If x and y are positive integers [#permalink]

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24 Sep 2017, 21:17
Mo2men wrote:
If x and y are positive integers and $$(x+y)^2$$is an odd integer, is x an even integer?

1) $$x^4 - y^3$$ is an odd integer

2) $$0 < y^3-y < 24$$

Discussed here: https://gmatclub.com/forum/if-x-and-y-a ... 16462.html
_________________

Kudos [?]: 132646 [0], given: 12326

Re: If x and y are positive integers   [#permalink] 24 Sep 2017, 21:17
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