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

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00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

65% (04:06) correct
35% (02:07) wrong based on 699 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

13

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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

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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 .

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