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If x and y are positive integers

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If x and y are positive integers [#permalink]

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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) \(0 < y^3-y < 24\)

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

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

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New post 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: if-x-and-y-are-positive-integers-and-x-y-2-is-an-odd-integer-is-x-216462.html

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