15) How many positive integers $n$ are there for which $8 n+50$ is a multiple of $2 n+1$?
(A) None
(B) 1 (C) 2
(D) 5
(E) 10.
15) The answer is $\mathbf{( B )}$. Since $8 n+50=4(2 n+1)+46, 8 n+50$ is a multiple of $2 n+1$ if and only if 46 is a multiple of $2 n+1$. The only divisor of 46 of the form $2 n+1$ with $n$ positive is 23.