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.

Take $x=1/\pi$. It can't be rational, as then $\pi$ would be as well.  Still, their product is equal to $1$.
