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

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mbaMission
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 Q47  V21
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In order to play a certain game, 24 players must be split [#permalink] New post   02 Jun 2009, 08:30
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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.


I always struggle with this type of question. Can anyone pls tell me how to approach this kind of question.

Any formula, step or method to follow?

Pls help.



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Re: In order to play a certain game, 24 players must be split [#permalink] New post   02 Jun 2009, 11:51
IMO E.

(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 =27
1 person sits out.
26 players are left .
possible combination is obly one 13-2.
Its given that "If there are more than two teams, and if each team has more than two players"
so , (1) is 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.
24+7 =31
1 person sits out.
30 players are left .
possible combination are :
10 - 3
6 - 5

so (2) is also insufficient.

Using (1) and (2) together also does not help.
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Re: In order to play a certain game, 24 players must be split [#permalink] New post   02 Jun 2009, 18:36
Four possibilities for grouping the teams:

Team-1 \(\Rightarrow\) 3 x 8

Team-2 \(\Rightarrow\) 8 x 3

Team-3 \(\Rightarrow\) 4 x 6

Team-4 \(\Rightarrow\) 6 x 4


(1) 13-1 = 12, which must be multiple of first integer above. Team-2 is ruled out, but still three possibilities exist

(2) 7-1 = 6, which must be multiple of first integer above. Team-2 and 3 is ruled out, but still 2 possibilities exist.

Combining still leaves with two possibilities.
Therefore, NOT SUFFICIENT.

Answer E.
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Re: In order to play a certain game, 24 players must be split [#permalink] New post   02 Jun 2009, 21:49
how to approach this kind of question.
Any formula, step or method to follow?
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Re: In order to play a certain game, 24 players must be split [#permalink] New post   03 Jun 2009, 03:41
I don't think there is a formulaic approach to this.

This problem has more to do LCM concept.
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Re: In order to play a certain game, 24 players must be split [#permalink] New post   03 Jun 2009, 03:55
mbaMission 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.



Combinations are 3/8, 4/6, 6/4, 8/3 - so # of teams is 3/4/6/8.

(1) So we're adding 12 players-- and 12 is divisible by 3/4/6, so # of teams could be 3/4/6. Insufficient.

(2) So we're adding 6 players-- 6 is divisible by 3/6, insufficient.

Combining insufficient, could be 3/6.

E
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Re: In order to play a certain game, 24 players must be split [#permalink] New post   03 Jun 2009, 07:01
Hades wrote:
mbaMission 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.



Combinations are 3/8, 4/6, 6/4, 8/3 - so # of teams is 3/4/6/8.

(1) So we're adding 12 players-- and 12 is divisible by 3/4/6, so # of teams could be 3/4/6. Insufficient.

(2) So we're adding 6 players-- 6 is divisible by 3/6, insufficient.

Combining insufficient, could be 3/6.

E


Bingo. Same approach here. Just take the info they've given and find out how many divisors there are of the number of players. Even considering both statements, you could have 3 teams, or 6 teams.



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Re: In order to play a certain game, 24 players must be split [#permalink]
03 Jun 2009, 07:01
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