求助GWD30一道数学题！！！！

anikakoko

在GWD第30套第二题

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



实在不知道怎么做啊。。。。。。这么难的题，老外做得出吗。。。。晕死啊。。。

anikakoko

楼上的好厉害！！！！正确答案是D

zhangmeng1988

这个题不难把。。。看上去比较唬人。9f(v)=2^x*3^y*5^Z*3^2=f(m)说的简单点就是f(m)的y 比f(v)的y大2，既9是3的2次方。y是十位数，所以m比v就大20了。

dliu64

答案应该是D咯。。 因为f(m)=9f(v),  那通过题目我们知道f(m) 和 f(v)里面都要包括factor 2,3,5 或者是他们各自的倍数，例如4,9,25... 好，既然F(M)是f(v)x9也就是说在F(m)里面要比f(v)里多一个factor of 9 也就是 3^2.   那知道这些条件都很简单咯。。  既然我们知道m and v are three digits number. then randomly chose  two three digits number for m and v so that m has one factor of 9 more than v.... So, if v is 110, then M has to be 130 to make the f(m)=9f(v) valid.  or if v is 223, then M has to be 242 to make the f(m)=9f(v) valid... thus...  130-110=20,   243-223=20.. so the answer is 20 !!!!

if v is 110 then, f(v)=2^1 x 3^1 x 5^0...             M has to be 130 because in this case, f(m)=2^1 x 3^3 x5^0 .. ... and you can see the value of f(m) is 9f(v).... 花了好长时间写这个答案。。 费时间，希望我写的能让人明白。

未满

答案是什么？A么？><？