adkikani wrote:
Quote:
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?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
pushpitkc niks18 HatakekakashiWhat is wrong with below thinking?
I know my total members in X have to be between 11 and 39.
Quote:
Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables,
9*4 = 36
1*3 = 3
Total = 39 . .. . .(1)
Quote:
and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables
7*5 = 35
1*3 = 3
Total =38 .. ... .(2)
Do i need to perform trial and error to make (1) = (2) ?
adkikaniWithout having a common number of the members of the club, it is not possible to solve this
problem. So, yes it is necessary for us to have a unique number of the members of the club.
However, we don't need to perform trial and error to arrive at such a number.
In the range 10 < x < 40
Case 1: 11,15,19,23,27,31,35,39 are possible of form 3x + 4
Case 2: 13,18,23,28,33,38 are possible of form 5x + 3
The only overlap happens at 23 and can be assumed to be the number of people at the club.
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