Can $x\pi$ be rational? When I was solving a math test, I came across this problem -

Let $x$ be an irrational number. What type of number is $x\pi$?
a) Rational only
b) Irrational only
c) Could be rational or irrational

I was surprised to see that the answer was option c.
Can anyone tell me for what value of $x$ is $x\pi$ rational? Note that $x$ is a irrational number.

If $x=\frac{1}{\pi}$ then they multiply to give $1$.
