Club members

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?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

OA: E

Source: OG13

Anurag@Gurome · Answer

ikaplan wrote: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?

Say, the number of members of the club = n
Hence, 10 < n < 40

n = (Multiple of 4 + 3)
n = (Multiple of 5 + 3)

Hence, (n - 3) is multiple of both 4 and 5, i.e. multiple of 20.
Hence, n is 3 more than a multiple of 20.

Only possible value of n is 23.

Now, the remainder when 23 is divided by 6 is 5.

The correct answer is E.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

ikaplan · Answer

I think I had difficulty with understanding the questions stem

Can you please clarify what does "the members sit at tables with 3 members at one table and 4 members" really mean?

I understood that the sitting arrangement is as follows: /3/ /3/ /3/ /3/... /1/ /1/ /1/ /1/
where / / represents a table

Anurag@Gurome · Answer

ikaplan wrote:I think I had difficulty with understanding the questions stem

"3 members at one table and 4 members at each of the other tables"

This means in only one table there are 3 members and all the other tables have 4 members each.
Hence, if there are x tables, then in one table there are 3 members and in the rest (x - 1) tables have 4 members each.
Therefore, total number of members = 3*1 + 4*(x - 1) = (4x - 1) = (Multiple of 4 - 1) = (Multiple of 4 + 3)

Hope that helps.

ikaplan · Answer

Thanks, I get it now.

zeza · Answer

I am confused with the stem. How is the information about number of members (10<n<40) important? What if there is a club with max number of members (40) or min number of members (10)? Is it possible to start from this information?

ToxicAvenger · Answer

This assumes that each time, the number of members that attend the club is constant, while the number of tables available to them varies.

This is not very realistic: it is much more likely that the number of attendees varies every time as opposed to removing some of the tables available to them.

Matt@VeritasPrep · Answer

That's definitely a realistic objection, but not one that the GMAT would heed: the scenario is the scenario, unfortunately.

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Club members

GMAT/MBA Expert

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER