GMAT
题目
A society has more than 10 but fewer than 40 members. The members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. The members now sit at tables with 6 members at each table except one and fewer than 6 members at that one table.
Quantity A
Number of members who will be at the table that has fewer than 6 members
Quantity B
4
解析
设按3人一桌和4人一桌安排座位时，4人一桌的有\(x\)桌；按3人一桌和5人一桌安排座位时，5人一桌的有\(y\)桌。社团总人数为\(N\)。
根据两种不同的座位安排方式可得两个方程：
\(N = 3+4x\)（\(10\lt N\lt40\)），所以\(N\)可能的值为\(11,15,19,23,27,31,35,39\)；
\(N=3 + 5y\)（\(10\lt N\lt40\)），所以\(N\)可能的值为\(13,18,23,28,33,38\)。
综合两种情况，\(N = 23\)。
\(23\div6 = 3\cdots\cdots5\)，即当每张桌子坐6人时，可以坐满3桌，还剩下5人坐在最后一张桌子上。
所以数量\(A = 5\)，而数量\(B=4\)
综上，数量\(A\)大于数量\(B\)，答案是A。
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