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# Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible

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Math Expert
Joined: 02 Sep 2009
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Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible [#permalink]

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08 Feb 2018, 23:43
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Question Stats:

28% (01:50) correct 72% (00:58) wrong based on 55 sessions

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Is x an even integer?

(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.
[Reveal] Spoiler: OA

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Senior Manager
Joined: 17 Oct 2016
Posts: 327
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible [#permalink]

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08 Feb 2018, 23:55
IMO D.

from statement 1, we can say x² has to be even integer. Hence x has to be an even integer. sufficient.

from statement 2, we can say x^4 has to be even integer. Hence x has to be an even integer. sufficient.
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Senior Manager
Joined: 31 Jul 2017
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Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible [#permalink]

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09 Feb 2018, 03:33
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Bunuel wrote:
Is x an even integer?

(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.

Statement I:

Let $$x = \sqrt{20}, x^2$$ is Divisible by 4.
Let $$x = 2, x^2$$ is Divisible by 4.........So, Insufficient.

Statement II:

$$x = 2(2)^{1/4}, x^4$$ is Divisible by 16.
Let, $$x= 2, x^4$$ is Divisible by 16......So, Insufficient.

Combining I & II:

Let $$x = \sqrt{20},$$
$$x^2$$ is Divisible by 4 and $$x^4$$ is Divisible by 16.

Let $$x = 2$$
$$x^2$$ is Divisible by 4 and $$x^4$$ is Divisible by 16.

So, Insufficient. Hence, E.
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Joined: 01 Aug 2017
Posts: 5
Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible [#permalink]

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09 Feb 2018, 05:22
I agree with rahul16singh28.

In statement 1 is said x^2 is divisible by 4, x^2= a*4 ---> x=a^(1/2)*2 (not considering sings)

so, a could be 1.5 and x= 3 (not an even integer) , but a could be 9 and x= 6 (even integer). Not sufficient

Statement two is no different than statement 1. Also not sufficient

And both together Not sufficient
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Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible [#permalink]

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09 Feb 2018, 23:39
Bunuel wrote:
Is x an even integer?

(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.

I think E is the answer as x could be 4root 3 or 4 we can't saw anything.
Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible   [#permalink] 09 Feb 2018, 23:39
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# Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible

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