PREP 一道关于数列和不等式的DS

memory09

Six countries in a certain region sent a total of 75represetive to an international congress . and no two counteries sentthe same numbers of representives of the six countries . if country Asent the secondgreatest numbers of representives did country A sent at least 10 representives?

(1)One of six counteries sent 41 representives to congress

(2)Country A sent fewer than 12 representives to congress

直觉是2个条件加起来就可以了。因为题干可知，S1+S2+S3+S4+Sa+S6=75，假设S6为最大，因为每个国家人数不同，那么有S1+S1+S3+S4=75-S6-SA>=1+2+3+4=10，所以S6+Sa<=65,因为S6>=Sa+1,所以2S6+1=<S6+Sa<=65,S6<=32.
条件1给的肯定是S6，因为75-41=35，即其他5个国家的和比41小，所以S1+...Sa=35,可以退出Sa<=25
条件2，Sa<12,所以10=<S1+……S4<=10+9+8+7=34,所以10+5=<S1+……S4+Sa=75-S6<=34+12, 29<S6<=60
没有再细算，但觉得１＋２可以，但是答案是Ｅ。求ＮＮ讲解。多谢