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Club X has more than 10 but fewer than 40 members. Sometimes [#permalink]
12 Dec 2012, 05:31

2

This post received KUDOS

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00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

66% (03:51) correct
34% (02:11) wrong based on 928 sessions

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?

Re: Club X has more than 10 but fewer than 40 members. Sometimes [#permalink]
12 Dec 2012, 05:39

17

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Expert's post

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Walkabout 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?

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

3 members at one table and 4 members at each of the other tables, means that the total number of members is 3 more than a multiple of 4: x=4m+3. 3 members at one table and 5 members at each of the other tables, means that the total number of members is 3 more than a multiple of 5: x=5n+3.

Thus x-3 is a multiple of both 4 and 5, so a multiple of 20. Therefore x is 3 more than a multiple of 20. Since 10<x<40, then x=23.

Re: Club X has more than 10 but fewer than 40 members. Sometimes [#permalink]
14 Dec 2012, 02:16

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Ans:

let the number of people be n , now 10<n<40. Also n=(3+ multiple of 4) and n=(3+ multiple of 5). Therefore n-3 is a multiple of both 4 and 5, one such number is 20. N=23, when 6 members sit at tables then people left are 5, therefore the answer is (E). _________________

Re: Club X has more than 10 but fewer than 40 members. Sometimes [#permalink]
27 Aug 2014, 01:58

I did this the long way, wrote out the seating arrangements possible under each scenario and found that 23 people is the only situation which applies to both seat configurations. Then as the others have pointed out 23 / 6 = 3 remainder 5

Re: Club X has more than 10 but fewer than 40 members. Sometimes [#permalink]
11 Sep 2014, 11:27

Walkabout 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?

Re: Club X has more than 10 but fewer than 40 members. Sometimes [#permalink]
30 Oct 2014, 21:54

1

This post received KUDOS

Simple solution quickly would be - E We know that the remainder is 3 in both cases when 4 or 5 people sit --> such one number is 23 (which also is between 20 and 40). And hence, 23/6 gives remainder =5 .

Re: Club X has more than 10 but fewer than 40 members. Sometimes [#permalink]
15 Jun 2015, 17:21

I got 5 as my answer.

For people that are more visual (like me)..

I put a 3 down and another 3 down representing the first two tables, then figured out how many "4s" were needed for the first set and how many "5s" were needed for the second set to add up and equal to the same number for both sets. Since 3 was constant between the two sets, it meant that 4 and 5 needed to have the same number of people, or the LCM, which is 20. Therefore 20 plus 3 is a total of 23 people.

Now you know that the table with a set of 6s needs to add up to 23, but the last table needs to still be less than 6. So the only combination for 6s is 3 tables of 6 people to equal 18 and then a table of 5 people.

Re: Club X has more than 10 but fewer than 40 members. Sometimes [#permalink]
15 Jun 2015, 22:17

1

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Expert's post

TudorM wrote:

I got tricked by "tables" in the problem stem and I considered more than 1 table of 3 person eacg.

Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables...

Isn't the problem poorly worded?

No, it isn't. This is GMAT language - especially considering that the question is official - and hence you will be required to successfully comprehend such questions.

"Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables,"

The statement explains how the members sit at tables: 3 at ONE table and 4 at EACH of the other tables. Practice questions from the official guide to get comfortable with "GMAT language". _________________

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