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

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Math Expert
Joined: 02 Sep 2009
Posts: 61197
If z and x are integers is (z^3 + x)(z^4 + x) even?  [#permalink]

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09 Dec 2019, 00:26
00:00

Difficulty:

45% (medium)

Question Stats:

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

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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]

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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

Are You Up For the Challenge: 700 Level Questions
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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