【問題】GWD18-06

[little8]

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

整題看完不知道怎麼下手耶,好像是連題意都搞不清楚,懇請各位大大們幫忙解惑,感謝~

[kwtluck]

題目說 n = xyz [注意]xyz是代表百位,十位,個位,不是乘積喔
又f(m) = 9f(v), 9=3^2, 那就是鎖定 3的位子=> y => 十位
若v有一個y, m就有y+2個y
題目求 m - v = (y+2)-y =2, 又y代表十位數, 所以答案是20

p.s.請記得要附上答案喔!!

**我已經盡力表達了,希望你看得懂**

[chris8888]

我終於搞懂了,

1. f(n) = 2^x * 3^y * 5^z and n = xyz <== 注意, 這不是乘喔(例如 : n = 567)

2. 根據題目的敘述 : f(v) = 2^x * 3^y * 5^z
9 * 2^x * 3^y * 5^z = f(m)
f(m) = 2^x * 3^(y+2) * 5^z

3. 所以 v= xyz and m = x(y+2)z <== 記住不是乘喔(例如 : 345之類的百位數)
m - v => y+2 - y => 2, 因為這是tenth digit, 所以2 * 10 = 20

答案 : D