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In a group of 120 athletes, the number of athletes who can play Tennis, Badminton, Squash and Table Tennis is 70, 50, 60 and 30 respectively. What is the maximum number of athletes who can play none of the games
- a)40
- b)50
- c)60
- d)70
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a group of 120 athletes, thenumberof athletes who can play Tennis, ...
In order to think of the maximum number of athletes who can play none of the games, we can think of the fact that since there are 70 athletes who play tennis, fundamentally there are a maximum of 50 athletes who would be possibly in the can play none of the games’.
No other constraint in the problem necessitates a reduction of this number and hence the answer to this question is 50.
Most Upvoted Answer
In a group of 120 athletes, thenumberof athletes who can play Tennis, ...
Given Information:
- Total number of athletes = 120
- Number of athletes who can play Tennis = 70
- Number of athletes who can play Badminton = 50
- Number of athletes who can play Squash = 60
- Number of athletes who can play Table Tennis = 30
To find:
The maximum number of athletes who can play none of the games.
Solution:
To find the maximum number of athletes who can play none of the games, we need to determine the number of athletes who can play at least one game and then subtract it from the total number of athletes.
Number of Athletes who can play at least one game:
To find the number of athletes who can play at least one game, we need to find the sum of athletes who can play each game individually and then subtract the athletes who can play multiple games to avoid double counting.
- Number of athletes who can play Tennis = 70
- Number of athletes who can play Badminton = 50
- Number of athletes who can play Squash = 60
- Number of athletes who can play Table Tennis = 30
Number of athletes who can play more than one game:
To find the number of athletes who can play more than one game, we need to find the intersection between different sets of athletes who can play each game.
- Number of athletes who can play Tennis and Badminton = 0 (Given)
- Number of athletes who can play Tennis and Squash = 0 (Given)
- Number of athletes who can play Tennis and Table Tennis = 0 (Given)
- Number of athletes who can play Badminton and Squash = 0 (Given)
- Number of athletes who can play Badminton and Table Tennis = 0 (Given)
- Number of athletes who can play Squash and Table Tennis = 0 (Given)
Calculating the number of athletes who can play at least one game:
We can calculate the number of athletes who can play at least one game by summing up the individual games and subtracting the athletes who can play more than one game.
Total athletes who can play at least one game = (Number of athletes who can play Tennis) + (Number of athletes who can play Badminton) + (Number of athletes who can play Squash) + (Number of athletes who can play Table Tennis) - (Number of athletes who can play more than one game)
Total athletes who can play at least one game = 70 + 50 + 60 + 30 - (0 + 0 + 0 + 0 + 0 + 0)
Total athletes who can play at least one game = 210
Calculating the maximum number of athletes who can play none of the games:
The maximum number of athletes who can play none of the games can be calculated by subtracting the number of athletes who can play at least one game from the total number of athletes.
Maximum number of athletes who can play none of the games = Total number of athletes - Total athletes who can play at least one game
Maximum number of athletes who can play none of the games = 120 - 210
Maximum number of athletes who can play none of the games = -90
Since the number of athletes cannot be negative, the maximum number of athletes who
- Total number of athletes = 120
- Number of athletes who can play Tennis = 70
- Number of athletes who can play Badminton = 50
- Number of athletes who can play Squash = 60
- Number of athletes who can play Table Tennis = 30
To find:
The maximum number of athletes who can play none of the games.
Solution:
To find the maximum number of athletes who can play none of the games, we need to determine the number of athletes who can play at least one game and then subtract it from the total number of athletes.
Number of Athletes who can play at least one game:
To find the number of athletes who can play at least one game, we need to find the sum of athletes who can play each game individually and then subtract the athletes who can play multiple games to avoid double counting.
- Number of athletes who can play Tennis = 70
- Number of athletes who can play Badminton = 50
- Number of athletes who can play Squash = 60
- Number of athletes who can play Table Tennis = 30
Number of athletes who can play more than one game:
To find the number of athletes who can play more than one game, we need to find the intersection between different sets of athletes who can play each game.
- Number of athletes who can play Tennis and Badminton = 0 (Given)
- Number of athletes who can play Tennis and Squash = 0 (Given)
- Number of athletes who can play Tennis and Table Tennis = 0 (Given)
- Number of athletes who can play Badminton and Squash = 0 (Given)
- Number of athletes who can play Badminton and Table Tennis = 0 (Given)
- Number of athletes who can play Squash and Table Tennis = 0 (Given)
Calculating the number of athletes who can play at least one game:
We can calculate the number of athletes who can play at least one game by summing up the individual games and subtracting the athletes who can play more than one game.
Total athletes who can play at least one game = (Number of athletes who can play Tennis) + (Number of athletes who can play Badminton) + (Number of athletes who can play Squash) + (Number of athletes who can play Table Tennis) - (Number of athletes who can play more than one game)
Total athletes who can play at least one game = 70 + 50 + 60 + 30 - (0 + 0 + 0 + 0 + 0 + 0)
Total athletes who can play at least one game = 210
Calculating the maximum number of athletes who can play none of the games:
The maximum number of athletes who can play none of the games can be calculated by subtracting the number of athletes who can play at least one game from the total number of athletes.
Maximum number of athletes who can play none of the games = Total number of athletes - Total athletes who can play at least one game
Maximum number of athletes who can play none of the games = 120 - 210
Maximum number of athletes who can play none of the games = -90
Since the number of athletes cannot be negative, the maximum number of athletes who
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In a group of 120 athletes, thenumberof athletes who can play Tennis, Badminton, Squash and Table Tennis is70,50,60and30respectively.Whatisthemaximum number ofathletes whocanplay noneof the gamesa)40b)50c)60d)70Correct answer is option 'B'. Can you explain this answer?
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