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# In order to play a certain game, 24 players must be split in

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In order to play a certain game, 24 players must be split in [#permalink]

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19 Jan 2012, 17:14
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In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.
(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.

[Reveal] Spoiler:
As the OA is not provided, I would like to double check my solution for this problem. This is how I solved it.

Considering the Question Stem

Total players = 24
Number of Teams > 2
Players in each Team > 2
Number of Teams ---> We have to find.

Considering Statement 1

13 players join. So total players = 24+13 = 37. 1 sit out, so total players 36. So now the number of teams can be 18, 12, 9. Therefore insufficient

Considering Statement 2

7 new players join. So total players = 24 + 7 = 29. 1 sit out, so total players 28. Again, the number of teams can be 14, 7, 4. Therefore insufficient.

Combining the two statements - > We can't calculate the exact number of teams and therefore my answer is E. Can you please check and let me know your thoughts guys?
[Reveal] Spoiler: OA

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19 Jan 2012, 18:53
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In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

Given: n>2 and 24/n>2, so basically n is a factor of 24 satisfying both requirements (2<n<12). n can take the following values: 3, 4, 6, and 8. Question: n=?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+13)-1=36 is also multiple of n --> n can be: 3, 4, or 6. Not sufficient.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+7)-1=30 is also a multiple of n --> n can be: 3, or 6. Not sufficient.

(1)+(2) n can still be: 3 or 6. Not sufficient.

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Re: In order to play a certain game, 24 players must be split in [#permalink]

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20 Jan 2012, 06:33
n has to be between 2 and 24 (2<n<24) as two restrictions are given:

First: n>2 more than 2 teams
Second: 24/n>2 more than 2 Player per team
Additionally: To get a fair split n needs to be a factor of 24

1: 37-1 = 36 --> N = 3, 4, 6, 9 --> Not sufficient
2: 31-1= 30 --> N = 3, 6, --> Not sufficient

Even though if both Statements are taken together, it is not sufficient.

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16 Feb 2012, 22:52
when looking at each statement they give new scenarios but the we can only look at number of teams that match the original number of teams example in stmt 2 there's 30 ppl to make teams and factors are 3,5,6 but 5 is not a factor of 24
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Re: In order to play a certain game, 24 players must be split in [#permalink]

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17 Feb 2012, 02:03
enigma123 wrote:
In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.
(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.

As the OA is not provided, I would like to double check my solution for this problem. This is how I solved it.

Considering the Question Stem

Total players = 24
Number of Teams > 2
Players in each Team > 2
Number of Teams ---> We have to find.

Considering Statement 1

13 players join. So total players = 24+13 = 37. 1 sit out, so total players 36. So now the number of teams can be 18, 12, 9. Therefore insufficient

Considering Statement 2

7 new players join. So total players = 24 + 7 = 29. 1 sit out, so total players 28. Again, the number of teams can be 14, 7, 4. Therefore insufficient.

Combining the two statements - > We can't calculate the exact number of teams and therefore my answer is E. Can you please check and let me know your thoughts guys?

Grouping theory of divisibility helps you solve many questions very quickly, very easily and by just using a little bit of imagination. I would strongly advise you to check it out:
http://www.veritasprep.com/blog/2011/04 ... unraveled/

I will show you how it is applicable in this question:

"In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players."
There are 24 people. They are divided into groups with equal no. of people. They could be divided into 3 groups (8 people each) or 4 groups (6 people each) or 6 groups (4 people each) or 8 groups (3 people each). Once we know how many people were there in each group, we can find out the number of groups.

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.
1 player sits out so the rest of the 12 people can also be divided into groups of 6 people each or 4 people each or 3 people each. It is not sufficient to know how many people were there in each group.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.
6 people can also be made to form a group of 6 people or two groups of 3 people each.

Using both statements, we see that the groups could consist of 6 people each or 3 people each. So together they are not sufficient.
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Re: In order to play a certain game, 24 players must be split in [#permalink]

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21 Apr 2013, 16:17
Thank you for the descriptions. I did not think of the factor approach. It makes sense to think of this problem as they are asking for N which is 2 < N < 24, and N are the factors of 24, which are 3, 4, 6, 8. Now statement 1 can have 12 divisible by 3, 4, 6 so not suff. and statement 2 has 6 divisible by 3, and 6 so not sufficient. Thank you.

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23 Apr 2013, 18:13
Bunuel wrote:
In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

Given: n>2 and 24/n>2, so basically n is a factor of 24 satisfying both requirements (2<n<12). n can take the following values: 3, 4, 6, and 8. Question: n=?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+13)-1=36 is also multiple of n --> n can be: 3, 4, or 6. Not sufficient.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+7)-1=30 is also a multiple of n --> n can be: 3, or 6. Not sufficient.

(1)+(2) n can still be: 3 or 6. Not sufficient.

Can You please explain me how (1)+(2) will appears? I mean what is the statement after combining (1)+(2)

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24 Apr 2013, 05:34
mannava189 wrote:
Bunuel wrote:
In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

Given: n>2 and 24/n>2, so basically n is a factor of 24 satisfying both requirements (2<n<12). n can take the following values: 3, 4, 6, and 8. Question: n=?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+13)-1=36 is also multiple of n --> n can be: 3, 4, or 6. Not sufficient.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+7)-1=30 is also a multiple of n --> n can be: 3, or 6. Not sufficient.

(1)+(2) n can still be: 3 or 6. Not sufficient.

Can You please explain me how (1)+(2) will appears? I mean what is the statement after combining (1)+(2)

From (1) we have that n could be: 3, 4, or 6.
From (2) we have that n could be: 3, or 6.

So, when we combine we get that n could be 3 or 6.
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Re: In order to play a certain game, 24 players must be split in [#permalink]

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24 Apr 2013, 17:45
VeritasPrepKarishma wrote:
enigma123 wrote:
In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.
(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.

As the OA is not provided, I would like to double check my solution for this problem. This is how I solved it.

Considering the Question Stem

Total players = 24
Number of Teams > 2
Players in each Team > 2
Number of Teams ---> We have to find.

Considering Statement 1

13 players join. So total players = 24+13 = 37. 1 sit out, so total players 36. So now the number of teams can be 18, 12, 9. Therefore insufficient

Considering Statement 2

7 new players join. So total players = 24 + 7 = 29. 1 sit out, so total players 28. Again, the number of teams can be 14, 7, 4. Therefore insufficient.

Combining the two statements - > We can't calculate the exact number of teams and therefore my answer is E. Can you please check and let me know your thoughts guys?

Grouping theory of divisibility helps you solve many questions very quickly, very easily and by just using a little bit of imagination. I would strongly advise you to check it out:
http://www.veritasprep.com/blog/2011/04 ... unraveled/

I will show you how it is applicable in this question:

"In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players."
There are 24 people. They are divided into groups with equal no. of people. They could be divided into 3 groups (8 people each) or 4 groups (6 people each) or 6 groups (4 people each) or 8 groups (3 people each). Once we know how many people were there in each group, we can find out the number of groups.

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.
1 player sits out so the rest of the 12 people can also be divided into groups of 6 people each or 4 people each or 3 people each. It is not sufficient to know how many people were there in each group.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.
6 people can also be made to form a group of 6 people or two groups of 3 people each.

Using both statements, we see that the groups could consist of 6 people each or 3 people each. So together they are not sufficient.

;
The question would had been solvable in case the statement were like ; 4 people joined and were accommodated or 4 people joined and 1 had to sit out for even distribution.
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Re: In order to play a certain game, 24 players must be split in [#permalink]

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25 Apr 2013, 00:49
aceacharya wrote:
The question would had been solvable in case the statement were like ; 4 people joined and were accommodated or 4 people joined and 1 had to sit out for even distribution.

Yes, that's right.
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Re: In order to play a certain game, 24 players must be split in [#permalink]

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25 Apr 2013, 10:59
Bunuel/Karishma,

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Re: In order to play a certain game, 24 players must be split in [#permalink]

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25 Apr 2013, 19:46
debayan222 wrote:
Bunuel/Karishma,

I will stick with 600-700

Some people could start off thinking it's a Permutation Combination problem.
You cannot make an equation and solve it.
You can imagine the scenario and see the answer quickly if you understand the concept of division - it may not be that clear otherwise.
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Re: In order to play a certain game, 24 players must be split in [#permalink]

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02 Jun 2013, 13:18
Bunuel

Can we solve it using the remainders concept :

I started off with :

1) 24+13 = mq+1
24 = mq-12

2) 24+7 = np+1
24 = np-6

Taking both together :

0 = mq-np-6

After this I got lost.....

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Re: In order to play a certain game, 24 players must be split in [#permalink]

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03 Jun 2013, 04:24
karjan07 wrote:
Bunuel

Can we solve it using the remainders concept :

I started off with :

1) 24+13 = mq+1
24 = mq-12

2) 24+7 = np+1
24 = np-6

Taking both together :

0 = mq-np-6

After this I got lost.....

You are using too many variables. Use only as many as you actually need.

Question says 24/n = an integer

Statement 1: 24+13 = 37 gives remainder 1. This means 36/n is an integer. Common factors of 24 and 36 are 3, 4, 6 which can equal n. Hence, not sufficient.

Statement 2: 24+7 = 31 gives remainder 1. This means 30/n is an integer. Common factors of 24 and 30 are 3, 6 which can equal n. Hence not sufficient.

Together, n can be 3 or 6. So answer (E)
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Re: In order to play a certain game, 24 players must be split in [#permalink]

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17 Aug 2013, 11:21
Stiv wrote:
In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.

hey..
24 players to be split into n teams with m players each....

1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.
Total no. of players now: 24+13= 37
One must sit out, hence no. of players: 36
With 36 players:
n=6, m=6;
n=3, m=12;
n=12, n=3;
i.e there are many ways for the team to be arranged..
Hence, INSUFFICIENT.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.
Total no. of players now: 24+7= 31
One must sit out, hence no. of players: 30
There is more than one possibility for the team:
n=5, m=6;
n=6, m=5.
Hence, INSUFFICIENT.

1 and 2 together: There are no common values.. Hence, INSUFFICIENT.
ANS:E

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Re: In order to play a certain game, 24 players must be split in [#permalink]

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17 Aug 2013, 11:30
Stiv wrote:
In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.

conditions:
1).24 players.
2).each team having an equal number
3). more than two teams
4) each team has more than two players

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams.

total players now = 24+13 =37
remove 1 = 36
this cab be divided in 9 x 4...and ...12 X 3 ....6x6....4x9....3x12....9x4.......(teams x player)
NOT SUFFICIENT

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams.
Total players now = 24 + 7 =31
remove 1 = 30
options available = 3x10 5x6 6x5 10x3 (teams x player)
more than options available
not sufficient.

combining also we have 2 options.
not sufficient

hence E
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Re: In order to play a certain game, 24 players must be split in [#permalink]

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10 Nov 2017, 09:34
Bunuel wrote:
In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

Given: n>2 and 24/n>2, so basically n is a factor of 24 satisfying both requirements (2<n<12). n can take the following values: 3, 4, 6, and 8. Question: n=?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+13)-1=36 is also multiple of n --> n can be: 3, 4, or 6. Not sufficient.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+7)-1=30 is also a multiple of n --> n can be: 3, or 6. Not sufficient.

(1)+(2) n can still be: 3 or 6. Not sufficient.

Hi Bunuel,

I do not understand how we can get n =3 as an option for statement B. If earlier with 24 people we could make 3 teams of 8 members each and 6 more people get added, how will we distribute those six people evenly among 8 teams? seems like 5 or 6 seems are the only option and since 3, 4, 6 and 8 were the only options from the main stem of the questions, only n = 6 seems to be satisfying this equation.

Please tell me where I am going wrong.

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Re: In order to play a certain game, 24 players must be split in [#permalink]

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10 Nov 2017, 10:19
ashikaverma13 wrote:
Bunuel wrote:
In order to play a certain game, 24 players must be split into n teams, with each team having an equal number of players. If there are more than two teams, and if each team has more than two players, how many teams are there?

Given: n>2 and 24/n>2, so basically n is a factor of 24 satisfying both requirements (2<n<12). n can take the following values: 3, 4, 6, and 8. Question: n=?

(1) If thirteen new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+13)-1=36 is also multiple of n --> n can be: 3, 4, or 6. Not sufficient.

(2) If seven new players join the game, one must sit out so that the rest can be split up evenly among the teams --> (24+7)-1=30 is also a multiple of n --> n can be: 3, or 6. Not sufficient.

(1)+(2) n can still be: 3 or 6. Not sufficient.

Hi Bunuel,

I do not understand how we can get n =3 as an option for statement B. If earlier with 24 people we could make 3 teams of 8 members each and 6 more people get added, how will we distribute those six people evenly among 8 teams? seems like 5 or 6 seems are the only option and since 3, 4, 6 and 8 were the only options from the main stem of the questions, only n = 6 seems to be satisfying this equation.

Please tell me where I am going wrong.

(2) implies that 30 is a multiple of n. From the stem we got that n could be 3, 4, 6, and 8. Out of those only 3 and 6 are divisors of 30. So, from (2) n could be 3 or 6.
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Re: In order to play a certain game, 24 players must be split in   [#permalink] 10 Nov 2017, 10:19
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