GWD 18-06

[stwang]

Q6:
The function f is defined for each positive three-digit integer n by f(n) = 2^x 3^y 5^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) = 9 f(v), then m - v =
A.8
B.9
C.18
D.20
E.80

正確答案D

小妹愚笨 看了很多次還是不知道要從何算起
請教各位大大喔....

[clbb]

有點筆誤,5^Zm才對

[waleaaa]

我的想法是─
先假設v為百/十/個位數分別為a, b, c
所以f(v) = 2^a * 3^b * 5^c
又　f(m) = 9 * f(v) = 3^2 * f(v) = 2^a * 3^(b+2) * 5^c
故　m的百/十/個位數分別為a, (b+2), c
所以 m - v = 20

p.s. clbb大大解得更詳細唷...
不好意思我po得太慢~所以重覆啦...

[clbb]

對吼 我幹麼要繞一大圈

果然半夜不該算數學=.=

[stwang]

呵呵.....看了clbb和waleaaa大大精闢的解說
小妹我了解啦....

謝謝兩位大大的解答唷...