Last Updated on May 3, 2023
GMAT OFFICIAL GUIDE PS
Solution:
Although this problem appears to be a general word problem it is actually testing us on our understanding of remainders when dividing integers. We are first told that the total number of members, which we can denote as “T”, is between 10 and 40. Next, we are told two important pieces of information:
1) “Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables.”
2) “Sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables.”
Let’s now translate these into two mathematical expressions.
1) T/4 = Quotient + Remainder 3
2) T/5 = Quotient + Remainder 3
Because T is being divided by 4 and 5, we are really looking for the following:
T/20 = Quotient + remainder 3.
Since T must be between 10 and 40, there is only one value in that range which, when divided by 20, produces a remainder of 3. That value is 23. We can now use this value to complete the question. We are finally asked:
“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?”
This is same as asking the following: what is the remainder when 23 is divided by 6? We can see that 6 divides into 23 3 times with a remainder of 5.
Answer: E
