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Math Expert V
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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13 00:00

Difficulty:   85% (hard)

Question Stats: 37% (01:40) correct 63% (01:22) wrong based on 179 sessions

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Is x an even integer?

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

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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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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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Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

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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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Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

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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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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.
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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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The trick in this question is that it wants us to think of x in terms ox multiples of 2, such as 2, 4, 8 ... If you plug in any of these numbers, for sure they are divible by 4 (in statement I) or by 16 (in statement II)

We should ask ourselves if there is a non integer number x that when x^2 is divisible by 4 or when x^4 is divisible by 16.

(2√2)^2 is equal to 8 and 8 is divisible by 4
(2 * 2^1/4) ^ 4 is equal to 32 and 32 is divisible by for.

Together, (2 * 2^1/4) ^ 2 is not divisible by 4, so there is at least one number that is sufficient for statements I and II but is not an integer.

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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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rahul16singh28 wrote:
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.

Would u explain highlighted part ,plz?
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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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vivapopo wrote:
rahul16singh28 wrote:
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.

Would u explain highlighted part ,plz?

I think what he means is that
Statement II:
Let, $$x = 2*2^\frac{1}{4}$$ (not an even integer) --> $$x^4 = 2^4 * 2 = 16*2$$ --> $$x^4$$ is divisible by 16
Let, $$x= 2$$ (an even integer), $$x^4$$ is Divisible by 16
--> Insufficient.
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