请问这题怎么做？

discard

请问这题怎么做？
1/a+1/b+1/c+1/d+1/e=1,a...e 全是不同的正整数，问a+b+c+d+e的least possible value?

maryland

1/3+1/4+1/5+1/6+1/15=61/60不=1啊。
狒狒的解答是：
1/3+1/4+1/5+1/6+1/20=1。
试出来的，没法从理论上论证该值最小，当时叫我们记住答案即可。

redtea

刚才没看第二页，抱歉。
原来还有更小的和，请告知解法。

redtea

我也无法给出general的解法，但大体思路同上，1/2, 1/4, 1/6,1/12之和为1，只要拆开其中一个为1/x,1/y之和，1/6为首选拆成4/24=3/24+1/24=1/8+1/24
2，4，8，12，24要更小。

redwithblack

1/3+1/4+1/5+1/6+1/15=1,且分母的和最小

tongxun

Hope you guys enjoy GMAT。

licheng

TURE, NICE STUFF

discard2

To be honest, I am laughing just now, but actually, your effort is the basement. Nice to dicuss it with you.

discard2

the lemma here could be

1. Try to divide the total value into two parts.
2. Try to keep the value of two parts close to the middle point!

Here the middle point, e.g. in step 4, say 16, since 12 and 24 are closer to 16 than 9 and 72. While I could not give out the general solution. Somehow, need TRY all kinds of possible number combination at the end.

licheng

yup,...
see. someone must have been laughing till teeth fell down
BUT, to get to 12 and 24 really need some luck...doesn;t it?