acegmat1 wrote:
St. Francis’s gym coach is planning a kickball tournament for the 40 students in the fourth grade. How many teams are there if the coach wants to evenly divide the students to make sure there are more than 2 teams, with each team having more than 2 students?
(1) If 17 fifth-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the fifth-graders to teams.
(2) If 5 third-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the third-graders to teams.
Given:
1. St. Francis’s gym coach is planning a kickball tournament for the 40 students in the fourth grade.
2. The coach wants to evenly divide the students to make sure there are more than 2 teams, with each team having more than 2 students.
Asked: How many teams are there ?
Let the number of teams be t; where t>2
Each team has 40/t students > 2
40/t >2; t<20
2<t<20
40/t is an integer
t = {4,5,8,10]
(1) If 17 fifth-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the fifth-graders to teams.
If t = 4; Students/team = 10; 4 students can be assigned to a team and 1 will have to server as an alternate.
If t = 5; Students/team = 8; 2 students have to serve as an alternate
If t=8; Students /team = 5; 1 student has to serve as an alternate
If t =10; Students/team = 4; 7 students have to serve as an alternate
t = {4,8}
NOT SUFFICIENT
(2) If 5 third-graders are allowed to play in the tournament, one will have to serve as an alternate to evenly assign the third-graders to teams.
If t=4; 1 has to serve as an alternate
If t =5; 0 has to serve as an alternate
If t=8; 5 have to serve as an alternate
If t=10; 5 have to serve as an alternate
t = 4
SUFFICIENT
IMO B
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com