請教GWD30-2

[marco1002]

The function f is defined for each postive 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 postive integers such that f(m)=9f(v), then m-v=?
a. 8
b. 9
c. 18
d. 20
e. 80

Ans: d
請教各位大大這題怎解啊?小弟我題目有點搞不懂!!拜託啦

[danny214]

xyz 分別為一個三位數 n 的百位十位以及個位數 即 n = 100x+10y+z
假設
v = 100a+10b+c
f(v) = 2^a3^b5^c
f(m) = 9f(v) 可以將9化成3^2帶進去 => f(m) = 2^a3^(b+2)5^c
m = 100a+10(b+2)+c
因此可以得知
v = 100a+10b+c
m = 100a+10(b+2)+c
m-v=100a+10(b+2)+c-100a-10b-c = 20

如果不清楚可以舉個例
v = 123
f(v) =2^1*3^2*5^3
f(m) = 9f(v) = 2^1*3^(2+2)*5^3
m = 143
m-v = 143-123 = 20

[marco1002]

搞懂了~~感恩~~

[daphnejw]

danny214 發表於: 2007-03-18 15:32 文章主題:

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xyz 分別為一個三位數 n 的百位十位以及個位數 即 n = 100x+10y+z
假設
v = 100a+10b+c
f(v) = 2^a3^b5^c
f(m) = 9f(v) 可以將9化成3^2帶進去 => f(m) = 2^a3^(b+2)5^c
m = 100a+10(b+2)+c
因此可以得知
v = 100a+10b+c
m = 100a+10(b+2)+c
m-v=100a+10(b+2)+c-100a-10b-c = 20

如果不清楚可以舉個例
v = 123
f(v) =2^1*3^2*5^3
f(m) = 9f(v) = 2^1*3^(2+2)*5^3
m = 143
m-v = 143-123 = 20

Wow,高手!
Super.