Too many tables, too many members!

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rachitakapoor: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Thu Feb 16, 2012 4:40 am; Thanked: 1 times

by rachitakapoor » Tue Sep 11, 2012 7:09 am

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

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Source: Beat The GMAT — Problem Solving | Tue Sep 11, 2012 7:09 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Tue Sep 11, 2012 8:19 am

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

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Sep 11, 2012 9:03 am

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.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Sep 12, 2012 10:56 pm

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

See the post here: https://www.beatthegmat.com/club-members-t116276.html

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GMAT Expert, Admissions and Career Guidance
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1-800-566-4043 (USA)

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Fri May 15, 2015 8:45 am

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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