GWD30-2

[雲淡風清]

Q2:
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), then m-v = ?

A. 8
B. 9
C. 18
D. 20
E. 80
Answer: (D)

麻煩大家..謝謝

[navywhite0425]

f(n)=2^x*3^y*5^z
你應該是題目看錯了
醬才對^______________^
so,
(100x+10y+z)-{100x+10(y+2)+z}=20

[navywhite0425]

哈哈

小弟一早起床突然發現好像不對
應該是醬子
n=xyz
看y就好 因為9=3^2
所以f(m) = 9f(v)
m-v=10( y+2 )-10y=20

抱歉抱歉
昨晚寫太快了
更正一下
懇請原諒^o^

[youngerwu]

引述cd網看到解答
Q2:
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), then m-v = ?
A. 8
B. 9
C. 18
D. 20
E. 80

f(m) = 2xm3ym5zm
m=100xm+10ym+zm
f(v) = 2xv3yv5zv
v=100xv+10yv+zv
由于f(m) =9f(v),即 2xm3ym5zm= 9*2xv3yv5zv= 2xv3yv+25zv
由于2,3,5互质,所以xm=xv,ym=yv+2,zm=zv
问m-v=100xm+10ym+zm-100xv+10yv+zv=10(ym-yv)=20