Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

Updated on: 13 Sep 2017, 18:17

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

let m=number of members assume (m-3)/4-(m-3)/5=1 m=23 23/6 gives a remainder of 5 E

Originally posted by gracie on 15 May 2016, 14:10.
Last edited by gracie on 13 Sep 2017, 18:17, edited 1 time in total.

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

01 Dec 2016, 04:34

1

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

Question boils down to the following:

\(10 < X < 40\), and

\(x = 3 (mod_4)\) ---> dividing X into groups of 4 leaves remainder 3

\(x = 3 (mod_5)\) ---> dividing X into groups of 5 leaves same remainder 3

Then:

\(x = LCM (4, 5) + 3 = 23\)\(\)

Now we need to divide X into groups of 6 and find the remainder for the last table.

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

04 Dec 2016, 01:09

This One is a Great Official Question. Here is my solution => Let the number of members be N As per Question N=> (10,23) N=4k+3 N=5k'+3 Combing the above two Equations => N=20k''+3 N=> 3,23,43,63,83... But N=> (10,23) So N must be 23 Hence N=23 Now 23=> 6k+5 So 5 members will be left out when 6 members are arranged on each table. Hence E _________________

Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

21 Jan 2017, 14:30

Hello All,

1. Members sit as 4m + 3 ( 4 members on all table and 3 on last table) 2. Members sit as 5n + 3 ( 5 members on all table and 3 on last table)

Since 10 < X < 40 - Range of Members.

So only possible number which is divisible by 4 & 5 is 20 and adding 3. Total members are 23. So now sitting with 6 members per table we have 3. 6m + 5 = 23. So remainder on last table are 5

Answer is E.
_________________

Thank You Very Much, CoolKl Success is the Journey from Knowing to Doing

A Kudo is a gesture, to express the effort helped. Thanks for your Kudos.

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

25 Mar 2017, 10:33

from the beginning we know the the number of people sitting by several tables is devisible by 4 and 5, hence it is multiply of 20. There is only one multiply of 20 in the range. 20+3 (since 3 people always set separately) 23/6=3tables +5 left 5 is the answer (E)

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

30 Apr 2017, 08:20

1

Top Contributor

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

This is a nice remainder question in disguise. For this question, we'll use a nice rule that that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Let N = the TOTAL number of members.

Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables... With 4 members at each table, then N is multiple of 4 However, we still have one more table to consider. Since the last table has 3 members, we know that N is 3 greater than a multiple of 4 In other words, when we divide N by 4, the remainder is 3 By the above rule, some possible values of N are: 11, 15, 19, 23, 27, etc NOTE: I started at 11, since we're told that 10 < N < 49

Sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables Using the same logic as above, this question tells us that, when we divide N by 5, the remainder is 3 By the above rule, some possible values of N are: 13, 18, 23, 28, 33, 38

Let's check the two results. First we learned that N can equal 11, 15, 19, 23, 27, 31, 35, 38 Next we learned that N can equal 13, 18, 23, 28, 33, 38 Once we check the OVERLAP, we can see that N equals 23

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? If N = 23, then we'll have 3 tables with 6 members and the remaining 5 members will sit at the other table.

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

10 Jun 2017, 10:51

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

I just did the LCM of 5&4 +3 . So basically 20+3/6 . Not sure if this method will hold if the range of members was to change, but it worked on this instance.

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

09 Sep 2017, 05:34

Bunuel wrote:

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.

The remainder when 23 is divided by 6 is 5.

Answer: E.

Hi Bunuel,

I approached the question like this:

Total members is 40>M>10, so 29 members. Now if each table has 6 members, that is 29/6 then the last table would have 5 (29-24) members on the table. Is this approach right? I did the problem in less than a minute with this approach. Thanks in advance.

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

09 Sep 2017, 05:42

SinhaS wrote:

Bunuel wrote:

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.

The remainder when 23 is divided by 6 is 5.

Answer: E.

Hi Bunuel,

I approached the question like this:

Total members is 40>M>10, so 29 members. Now if each table has 6 members, that is 29/6 then the last table would have 5 (29-24) members on the table. Is this approach right? I did the problem in less than a minute with this approach. Thanks in advance.

How did you get that there must be 29 members from 40>M>10? Does 29 members satisfy ANY of the conditions (3 members at one table and 4 members at each of the other tables and 3 members at one table and 5 members at each of the other tables)?
_________________

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

09 Sep 2017, 05:48

Bunuel wrote:

SinhaS wrote:

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.

The remainder when 23 is divided by 6 is 5.

Answer: E.

Hi Bunuel,

I approached the question like this:

Total members is 40>M>10, so 29 members. Now if each table has 6 members, that is 29/6 then the last table would have 5 (29-24) members on the table. Is this approach right? I did the problem in less than a minute with this approach. Thanks in advance.

How did you get that there must be 29 members from 40>M>10? Does 29 members satisfy ANY of the conditions (3 members at one table and 4 members at each of the other tables and 3 members at one table and 5 members at each of the other tables)?[/quote]

I think my approach was not the right way to solve this problem, I took there can be a max 29 members within the range. Although i came to the same answer, this solution is not right i believe.

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

27 Feb 2018, 09:14

Quote:

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]

Show Tags

27 Feb 2018, 09:58

adkikani wrote:

Quote:

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?

Without having a common number of the members of the club, it is not possible to solve this problem. So, yes it is necessary for us to have a unique number of the members of the club.

However, we don't need to perform trial and error to arrive at such a number. In the range 10 < x < 40 Case 1: 11,15,19,23,27,31,35,39 are possible of form 3x + 4 Case 2: 13,18,23,28,33,38 are possible of form 5x + 3

The only overlap happens at 23 and can be assumed to be the number of people at the club.
_________________

You've got what it takes, but it will take everything you've got

Re: Club X has more than 10 but fewer than 40 members. Sometimes
[#permalink]

Show Tags

27 Feb 2018, 10:29

adkikani wrote:

Quote:

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]

Show Tags

27 Feb 2018, 11:31

adkikani wrote:

Quote:

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?