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题库 / Prep2007E1-DS-17
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.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
题目中说：6个国家共派了75名代表，人数各不同，问第二多的A国是否超过10.
条件一：有一个派了41人，那剩余5个国家一共派34人，当有4个国家分别是1，2，3，4人时候，第二多的国家有可能是24人。同时也有可能是9，8，7，6，4这样的组合，所以不一定超过10。
条件二：A国少于12人，那么从5人到12人都有可能。
两个条件结合：有可能是9-12的任意数字，也不充分。
6 countries, 75 people. No 2 countries sent the same number of people.
Stmnt 1: One country sent 41 people.
The other 5 together sent 75 - 41 = 34 people. 'A' sent the most number of people from the remaining 5 countries. Does A need to send at least 10?
34 divided by 5 is approximately 7. On average, every country sent 7 people so we can split it into 4, 6, 7, 8, 9 (try and split around 7 so that the average stays approx 7). A sent 9 people here.
A could have sent more than 10 people of course (say if the other 4 countries sent 1, 2, 3 and 4)
Not sufficient.
Stmnt 2: A sent fewer than 12
A could have sent 9 people (example above) or 11 (Split is 2, 6, 7, 8, 11. Try to make minimum changes to get what you want to minimize the chances of error. Since I want to increase the last number, I just reduce the first one appropriately).
Again, not sufficient.
Using both statements together, A could have sent 9 or 11 people so not sufficient.
Answer (E)
1)當有一個地區是41, 表示剩下的5個區域=75-41=34
故41的那個區域就會是greatest
當A=9時,這34可以分配給剩下的區域 EX: (9,8,7,6,4) 符合題目要求 但A小於10
當A=11時,則可分配成(11,8,7,6,2) 符合題目要求 但A至少等於10
所以(1)不充分
(2)可由上面的舉例發現 A小於12不成立 因為等於9和等於11都可以
所以(2)不對
(1)+(2) 沒有資料可以顯示其餘國家的人數比例,所以資料不充分
41肯定是最多的，设a发了x人，如果要想得出a至少要发多少人的话，且根据题意没有两个国家发的人数相等，剩下的国家分别发了x-1,x-2,x-3,x-4,加起来5x-10=34,x=8.8，也就是说a至少要发9个代表，