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

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New post 08 Feb 2018, 23:43
1
12
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A
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D
E

Difficulty:

  95% (hard)

Question Stats:

36% (01:39) correct 64% (01:20) wrong based on 162 sessions

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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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New post 09 Feb 2018, 03:33
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1
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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New post 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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Re: Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible  [#permalink]

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New post 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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New post 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.
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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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New post 27 Feb 2018, 05:44
1
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.

Answer: 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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New post 10 Aug 2018, 15:44
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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New post 11 Aug 2018, 06:21
2
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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Is x an even integer? (1) x^2 is divisible by 4 (2) x^4 is divisible &nbs [#permalink] 11 Aug 2018, 06:21
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