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Teams

by sparkles3144 » Mon Jun 17, 2013 10:56 am
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

I didn't really get the statements.
Can someone please explain?
What is the answer?
Thanks!
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by fcabanski » Mon Jun 17, 2013 11:27 am
Alternate means someone else has to drop before the "alternate" person is an active team member. In other words, the alternate doesn't count.

1. Understand the info the original problem gives.

There must be three or more teams.
Each team must have three or more students on it.

Each team must have a factor of 40 students on it, because the students are divided evenly onto the teams. The factors of 40 are:

2 - out, because there must be more than 2 students per team
20
10
4
5
8
40
1 - out, because there must be more than 2 students per team

Which work with the more than 2 teams stipulation?

40 students per team - only 1 team - out
20 students per team - only 2 teams - out
10 students per team - 4 teams
4 students per team - 10 teams
5 students per team - 8 teams
8 students per team - 5 teams


2. Anticipate the info needed to answer the question.

- Number of teams
- Number of students per team
- Some fact that specifies the 10, 4, 5, or 8 students per team, or the 4, 10, 8, or 5 teams


3. Evaluate Statement 1: 17 5th graders, 1 alternate. That means there are 16 5th graders to assign (evenly) to the teams.

4 teams - each with 4 5th graders.
10 teams - cannot evenly distribute the 16 5th graders
8 teams - each with 2 5th graders
5 teams - cannot evenly distribute the 16 5th graders.

This is not sufficient since there are still two possibilities. Eliminate A and D. B, C or E are the possible answers.


3. Evaluate Statement 2: 5 third graders, 1 alternate. That means there are 4 3rd graders to assign (evenly) to teams.

4 teams - each with 1 3rd grader.
10 teams - not enough 3rd graders
8 teams - not enough 3rd graders
5 teams - if one of the 3rd graders is an alternate, there are not enough 3rd graders to assign as full team members.

Since the only possibility is 4 teams, statement 2 is sufficient.

Eliminate C and E. The answer is B.
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