MathNet 2006 — Part 02 Question 149

If $x$, $y$ and $z$ are positive integers such as $x y z = 240$, $x y + z = 46$ and $x + y z = 64$, what is the value of $x + y + z$?


A) 19

B) 20

C) 21

D) 24

E) 36