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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.
(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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02 Jun 2009, 11:51
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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.
(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.
02 Jun 2009, 18:36
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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.
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.
