[問題]GWD23-2

[honey801106]

Q2

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

(the answer is D)

我搞不懂, 需要幫祝 謝謝

[FIG]

f(m)=2^x * 3^y * 5^z
9f(v)= 9 * 2^x1 * 3^y1 * 5^z1=2^x1 * 3^(y1+2) * 5^z1
兩式相等=>y=y1+2
所以10位數大2 m-v=20