Bash + Unix utilities, 28 bytes
dc<<<`grep -c [13579]$`d2-*p
Input is on stdin: one number per line.
Output is on stdout: 0 is truthy, any non-zero value is falsy.
How it works:
- grep counts the number n of lines ending with an odd digit;
- dc then computes and prints n*(n-2), which is 0 iff n equals 0 or 2.