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If x and y are positive integers

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Joined: 26 Mar 2013
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If x and y are positive integers [#permalink]

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New post 24 Sep 2017, 15:55
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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

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Joined: 02 Jul 2017
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Kudos [?]: 80 [1], given: 65

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

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New post 24 Sep 2017, 18:55
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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

Answer: B

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

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

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New post 24 Sep 2017, 21:17

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

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

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