quantum wrote:

The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?

(A) 8

(B) 9

(C) 18

(D) 20

(E) 80

Please explain also your logic

Thank you!

I assume f(n) = (2^x)*(3^y)*(5^z)

since f(m) = 9*f(v) = (3^2)*f(v) -> first and third digits of m and v are the same: x(m) = x(v), z(m) = z(v) and second digit of m is higher than v by 2: y(m) = y(v) + 2 -> m-v = 20 -> D