If $\displaystyle\frac{x^2}{4}$ is an integer greater than 50, then what is the smallest possible value of $x^2$ ?
IMO the answer should be $204$, the next small integer after $50$ is $51$, therefore, $\displaystyle \frac{x^2}4=51$ thus $x^2=204$. But the answer given is $256$, the question's answers considers the below constraint which I do not understand since my answer satisfies the constraints specifically given in the question.
The textbook answer states that given $x^2$ is divisible by $4$, so $x$ must be divisible by $2$ and even, thus answer given is $16\cdot16=256$. I understand that it should be divisible by $2$ but where does question state $x$ should also be an integer?