16. You are asked to choose two positive integers, $m$ and $n$ with $m>n$, so that as many as possible of the expressions $m+n, m-n, m \times n$ and $m \div n$ have values that are prime. When you do this correctly, how many of these four expressions have values that are prime?
A 0
B 1
C 2
D 3
E 4
16. D All four values cannot be prime. If this were so, both $m \times n$ and $m \div n$ would be prime which can happen only if $m$ is prime and $n=1$. If $m$ is an odd prime then $m+1$ is even and at least 4 , hence not prime, while if $m=2$ then $m-1$ is not prime but $m+1=3$ is. Thus three prime values are the most we can have.