Please help me one GWD math question, thanks!

qiuping2006fr

If k, m, and t are positive integers and K/6 +M/4=T/12, do t and 12 have a common factor greater than 1?

1) K is a multiple of 3

2) M is multiple of 3

The answer is A, but I don't know how to get it.

Thanks!

rio

化简：k/2+m/2=t/6

再化简：2k+3m=t

1：当k是3的倍数：k=3n

则：3（2n+m）=t也就是说t是3的倍数，则t与12有公因子。

2：同上：m=3n

2k+9n=t说明不了问题

rio

其实这类题都一个方法，化来化去就化出来了

ptr07

(1) k=3a, 3a/6 + M/4 = (6a+3M)/12 => T=6a+3M , T and 12 at least has 3 as common factor
do same for (2), T = 2 + 9a,

SO answer is A

qiuping2006fr

Thanks a lot to Rio and Ptr07!

fantasy06

 K/6 +M/4=T/12 ----> 2k/12+3M/12= t/12 -----> 2K+ 3M =T  & 1)---> t and 12 have a common factor, 3.

qiuping MM,  you can also post questions on our place.

fantasy06

hehe, just noticed that so many explanations had posted before mine.

rio

感觉晚上比白天人还多

qiuping2006fr

以下是引用fantasy06在2007-1-9 2:49:00的发言：

 K/6 +M/4=T/12 ----> 2k/12+3M/12= t/12 -----> 2K+ 3M =T  & 1)---> t and 12 have a common factor, 3.

qiuping MM,  you can also post questions on our place.

Maybe it is better to post math questions here, then more people, like me who are not good in math, can see the explanations. What do you think, fantasy MM?

In fact, it is my first time posting math question, and I am really surprised by the answer speed.

Thank you!

fantasy MM, where are you now? It's very late in China now.