2011 AMC 8 Problem 17

shanghai

Member
Let $$w$$, $$x$$, $$y$$, and $$z$$ be whole numbers. If $$2^w \cdot 3^x \cdot 5^y \cdot 7^z = 588$$, then what does $$2w + 3x + 5y + 7z$$ equal?

$$\textbf{(A) } 21\qquad\textbf{(B) }25\qquad\textbf{(C) }27\qquad\textbf{(D) }35\qquad\textbf{(E) }56$$