Club X has more than 10 but fewer than 40 members.

10 < X < 40

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.

3+4N = 3+5M = X

Based on the sequence, 3+5M
THe number of members could be any of the following
13
18
23
28
33
38

Out of these, 23 satisfies the expression 3+4N

If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table

23 = 6a +b
a = Total no of tables -1 = 3
b = No of members sitting on the table with fewer than 6 members = 5



Option E

rachitakapoor wrote:Q. 118 - OG 13

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

3 members at one table and 4 members at each of the other tables.
In other words, the total number of members is 3 more than a multiple of 4:

3 members at one table and 5 members at each of the other tables.
In other words, the total number of members is 3 more than a multiple of 5:

Thus, the total number of members must be 3 more than a multiple of 4 AND 5 -- in other words, 3 more than a multiple of 20.
The only viable option between 10 and 40 is 23.
Since 23/6 = 3 R5, there will be 3 tables of 6 and one table of 5.

The correct answer is E.

rachitakapoor wrote:Q. 118 - OG 13

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

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.

The answer is E