prep 中几道搞不清的题目 3

helenlife · 发表于 2010-7-7 00:18:36

Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

(1) One of the six countries sent 41 representatives to the congress
(2) Country A sent fewer than 12 representatives to the congress

I selected B on this one when the answer is E. I can kind of see why I am not correct, but am not completely sure. Can someone prove this to me mathematically? Thanks!

avalon9527 · 发表于 2010-7-7 00:48:53

A B C D E F 共75。A占据第二多，A是否超过10
1）有一个占据了41（并不能说明是否A占据等于或超过了10）
2）A占据了比12少（也不能说明A是否占据等于或超过了10，比如B占了40，A占了9,C占了8,D占了7，E6,F5或者B占了20，A18,C14,D10,E7,F6）
就算B41，那么A可能9,C8,D7,E6,F4或者B41,A11,C8,D6,E5,F4

allennuli · 发表于 2010-7-7 00:56:15

Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

(1) One of the six countries sent 41 representatives to the congress
(2) Country A sent fewer than 12 representatives to the congress

I selected B on this one when the answer is E. I can kind of see why I am not correct, but am not completely sure. Can someone prove this to me mathematically? Thanks!

-- by 会员 helenlife (2010/7/7 0:18:36)

最简单的方法就是带入数字进行排除
单看B选项的话假设代表人数最少的4个国家分别派了1,2,3,4人，剩下两国加起来等于65，而由于代表人数最多的国家未知，就是多种组合方式， 5+60 或者 11+54都成立，所以无法判断A是否>10
两个选项结合起来看，A+其它四国=34
先看A是否有小于10的可能: 带入发现9+8+7+6+4=34 成立，而当A=11的时候，也很明显地可以组合出34，所以还是没法判断A是否>10

prep 中几道搞不清的题目 3

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