Problem Solving

The function f is defined for each positive three-digit integer n by f(n) = 2^x3^y5^z, 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), then m-v = ?

A. 8
B. 9
C. 18
D. 20
E. 80

Please explain. Thanks. OA-D[/spoiler]

Hey arocks, a very good and interesting qs to solve. I really liked it. Refer the approach -

f(m) = 9 * f(n)
2^mx3^my5^mz = 9 * 2^vx3^vy5^vz
So 2 ^ (mx - vx) 3 ^ (my - vy) 5 ^ (mz - vz) = 3 ^ 2

So mx = vx
my - vy = 2
mz = vz

Again m - v = 100(mx - vx) + 10(my - vy) + (mz - vz)
= 100 * 0 + 10 * 2 + 0
= 20

So the answer is D. What do u say guys?

well, we say u are right .. but i wouldnt use so many variables ..

Well, we say u are right .. but i wouldnt use so many variables ..

Hey Gabriel, then I would like to know ur approach then ...