Co-prime Integer Selection Count

For $\gcd(x, y) = 1$ for ALL $y \in [2, 40] \setminus \{x\}$, $x$ must have no common prime factor with any other number in the set $[2, 40]$. Therefore, $x$ must be a prime number $p$ such that its smallest multiple $2p > 40 \implies p > 20$. The prime numbers in $[20, 40]$ are: 23, 29, 31, 37. Thus, there are 4 such possible choices for $x$.