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If z and x are integers is (z^3 + x)(z^4 + x) even?

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If z and x are integers is (z^3 + x)(z^4 + x) even?  [#permalink]

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New post 09 Dec 2019, 00:26
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A
B
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E

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  45% (medium)

Question Stats:

56% (01:45) correct 44% (02:52) wrong based on 16 sessions

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Re: If z and x are integers is (z^3 + x)(z^4 + x) even?  [#permalink]

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New post 09 Dec 2019, 00:46
determine
is \((z^3 + x)(z^4 + x)\) even
possible when both sum is odd / even
#1
\(x^3 + x^2\) is even
value of z is not know ; insufficient
#2
\(\frac{z^2 + x^2}{2}\) is odd
z^2 + x^2 = must be even i.e both are either odd or even
so
\((z^3 + x)(z^4 + x)\) even ; yes
sufficient
IMO B


Bunuel wrote:
If z and x are integers is \((z^3 + x)(z^4 + x)\) even?

(1) \(x^3 + x^2\) is even

(2) \(\frac{z^2 + x^2}{2}\) is odd


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Re: If z and x are integers is (z^3 + x)(z^4 + x) even?   [#permalink] 09 Dec 2019, 00:46
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