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Question
Club X has more than 10 but fewer than 40 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?
Club X has more than 10 but fewer than 40 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?
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Solution
The correct option is E 5
3 members at one table and 4 members at each of the other tables, means that the total number of members is 3 more than a multiple of 4: x = 4m+3.3 members at one table and 5 members at each of the other tables, means that the total number of members is 3 more than a multiple of 5: x = 5n+3.
Thus x- 3 is a multiple of both 4 and 5, so a multiple of 20. Therefore x is 3 more than a multiple of 20. Since 10<x<40, then x=23.
The remainder when 23 is divided by 6 is 5.Option E
3 members at one table and 4 members at each of the other tables, means that the total number of members is 3 more than a multiple of 4: x = 4m+3.
3 members at one table and 5 members at each of the other tables, means that the total number of members is 3 more than a multiple of 5: x = 5n+3.
Thus x- 3 is a multiple of both 4 and 5, so a multiple of 20. Therefore x is 3 more than a multiple of 20. Since 10<x<40, then x=23.
The remainder when 23 is divided by 6 is 5.
Option E
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