Photo AI
In a table quiz, 100 questions were asked - Junior Cycle Mathematics - Question b - 2014
Question b
In a table quiz, 100 questions were asked. Team M answered 72 questions correctly. Team N answered 38 questions correctly. (i) Find, with the aid of the Venn diagra... show full transcript
Worked Solution & Example Answer:In a table quiz, 100 questions were asked - Junior Cycle Mathematics - Question b - 2014
Step 1
Find, with the aid of the Venn diagram, the minimum number of questions answered correctly by both teams.
Answer
To find the minimum number of questions answered correctly by both teams, we can use the principle of inclusion-exclusion.
-
Add the number of questions answered correctly by both teams:
Team M: 72
Team N: 38
Total: 72 + 38 = 110Since the total number of questions is 100, we need to find the overlap:
Questions answered correctly by both teams = Total - 100 = 110 - 100 = 10
-
Thus, the minimum number of questions answered correctly by both teams is 10.
Step 2
Find, with the aid of the Venn diagram, the maximum number of questions answered correctly by both teams.
Answer
To find the maximum number of questions answered correctly by both teams, we consider how to maximize the overlap of the sets:
-
The maximum occurs when we let Team M's questions overlap with Team N's as much as possible. Therefore, we set:
Team N accurately answered 38 questions.
-
The maximum overlap is limited by the size of Team N, which is 38. Hence, the maximum number of questions answered correctly by both teams is:
Maximum = 38.