老ＪＪ一问

assurance

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

选 d

moderation

f(n) = 2^x3^y5^z

f(m) = 9f(v)=3^2f(v)

if f(m)=2^a*3^b*5^c, then f(v)=2^a*3^(b-2)*5^c

m=a*100+b*10+c

v=a*100+(b-2)*10+c

m-v=b*10-(b-2)*10=20