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 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.