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

Question

Is x an even integer?
 
(1) x^2 is divisible by 4.
(2) x^4 is divisible by 16.

Sasindran · Answer

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.

rahul16singh28 · Answer

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.

LucasDinizMiranda · Answer

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

rishabhmishra · Answer

I think E is the answer as x could be 4root 3 or 4 we can't saw anything.

danielarasan · Answer

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

vivapopo · Answer

Would u explain highlighted part ,plz?

Izzyjolly · Answer

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.

Kinshook · Answer

Asked: Is x an even integer?
 
(1) x^2 is divisible by 4.
If x^2 = 8; x = 2root(2); x is NOT an even integer
But if x^2 = 4; x = 2; x is an even integer
NOT SUFFICIENT

(2) x^4 is divisible by 16.
If x^4 = 64; x = 2root(2); x is NOT an even integer
But if x^4 = 16; x = 2; x is an even integer
NOT SUFFICIENT

(1) + (2) 
(1) x^2 is divisible by 4.
If x^2 = 8; x = 2root(2); x is NOT an even integer
But if x^2 = 4; x = 2; x is an even integer
(2) x^4 is divisible by 16.
If x^4 = 64; x = 2root(2); x is NOT an even integer
But if x^4 = 16; x = 2; x is an even integer
NOT SUFFICIENT

IMO E

SatvikVedala · Answer

Statement 1: x^2 is divisible by 4
if x^2 = 4, then it is divisible by 4, x = 2 => so x is an integer
if x^2 = 8, then it is divisible by 4, x = 2^(1/2) => so x is not an integer

Statement 2: x^4 is divisible by 16
if x^4 = 16, then it is divisible by 16, x = 2 => so x is an integer
if x^4 = 32, then it is divisible by 16, x = 2^(1/2) => so x is not an integer

Combining both also gives same cases
So Option E is the answer

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

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