Club X has more than 30 but fewer than 60 members. Sometimes 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. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?  Choices
A) 1  B) 2  C) 3  D) 4  E) 5
The number of members is 4j+3 = 5k+3.   Let's start at 4(7)+3 = 31 and keep adding 4 until we find a number in the form 5k+3.   31, 35, 39, 43 = 5(8) + 3   The club has 43 members.   43/6 = 6(7) + 1   The answer is 1.
<result>A</result>
Club X has more than 30 but fewer than 60 members. Sometimes 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. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?