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A project has three test cases. Three te...

A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to at all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 6 members, then what is the exact number of researchers required?

A

10

B

12

C

14

D

16

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the total number of researchers required for the project, given that there are three teams, each with six members, and James is assigned to all three teams. ### Step-by-Step Solution: 1. **Identify the number of teams and their members**: - There are 3 teams formed for the project. - Each team consists of exactly 6 members. 2. **Account for James**: - James is a member of all three teams. Therefore, he is counted in each team's total of 6 members. 3. **Calculate the number of additional members needed for each team**: - Since James is already a member of each team, we need to find out how many additional members are required for each team. - Each team needs 6 members, and since James is one of them, each team requires 5 additional members. - Thus, for each team: - Team 1: 5 additional members - Team 2: 5 additional members - Team 3: 5 additional members 4. **Calculate the total number of additional members**: - Total additional members needed = 5 (Team 1) + 5 (Team 2) + 5 (Team 3) = 15 additional members. 5. **Add James to the total count**: - Now, we include James in the total count of researchers: - Total researchers = 15 (additional members) + 1 (James) = 16 researchers. ### Conclusion: The exact number of researchers required for the project is **16**. ---
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