Got wrong...solution plz..

if we go as per the corrct answerr given here. E/E can be odd or can be even but never an interger. non integers are not considered even or odd in GRE. so
i think the C is wrong choice.

What we can be certain is this that J is divisible by K. Please elucidate me here if I am wrong.

Here \(\frac{j^2}{k}\) is odd that is a given so the statement 'E/E can be odd or can be even ' is irrelevant.

\(\frac{j^2}{k}\) is an integer and that too odd. So what are values (even or odd) of k if j is even (given)

You have to go backwards it is already given that the fraction is an odd integer.
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Please explain with an example?

Here let us consider the option one at a time:

Option A ::: j and k are both even: It may not be true because if j=1 and k=1 then we can get \(\frac{j^2}{k}= Odd\)

OPtion B::: j = k: it may not be true because if j=5 and k=1; it still satisfy the equation \(\frac{j^2}{k} = Odd\)

Option C ::: If j is even, k is even , this may be true \(\frac{j^2}{k} = odd\) or \(j^2\) = k*Odd, so if j = even then k has to be even to satisfy the equation (Even * Odd = Even)

Option D::: If j is divisible by k this may not be true because if j = 3 , k = 9 , it still satisfy the equation \(\frac{j^2}{k} = Odd\)

Option E ::: \(j^2 > k\) It may not be true, because if j = 1 and k = 1 then \(j^2 = k\) and it still satisfy the equation \(\frac{j^2}{k} = Odd\)
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j^2/k is odd implies that both j^2 and k are odd or both are even. So it is like, if j is odd, k is also odd or if k is even then j is even. It cannot be the case that j^2 is odd and k is even or vice versa, because in such a case you will not get an integer.

Now look at the options:
A) j and k are both even - but they can be odd also. so this is not certain and hence out
B) there is no evidence of j and k being equal. so this is not certain and hence out
C) Compare it with option A. Here it is given that j is even and hence k is even, this is exactly what we have concluded above
D) j is divisible by k. Not necessarily. consider j=4 and k=16
E) j^2 > k : this may not always be the case, consider j = 4 and k = 16

So the correct answer is C

Sippose j=4 and k=4 then ?it will be 16/4=4 how come C is the right answer

J^2/K is odd, this has multiple options:
j^2 = k For example (2^2)/4 =1 and 3^3/27=1
J and K are both can be even or odd numbers, as the example above
For this answer b,d,e should be ignored

Answer (A) it is not necessarily true j and k could be odd too.
answer is (C).