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In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is
- a)52
- b)53
- c)48
- d)47
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a class of 100 students, 73 like coffee, 80 like tea and 52 like le...
Let n, s, d and t be the number of students who likes none of the drinks, exactly one drink, exactly 2 drinks and all three drinks, respectively.
It is given,
n + s + d + t = 100 ...... (1)
s + 2d + 3t = 73 + 80 + 52
s + 2d + 3t = 205 ...... (2)
(2)-(1), we get
d + 2t - n = 105
Maximum value t can take is 52, i.e. t = 52, d = 1 and n = 0
Minimum value t can take is 5, i.e. t = 5, d = 95 and n = 0 (This also satisfies equation (1))
Difference = 52 - 5 = 47
Most Upvoted Answer
In a class of 100 students, 73 like coffee, 80 like tea and 52 like le...
Solution:
To find the maximum and minimum possible number of students who like all three drinks, we need to use the inclusion-exclusion principle.
Total number of students = 100
Number of students who like coffee = 73
Number of students who like tea = 80
Number of students who like lemonade = 52
Number of students who like coffee and tea = (73 + 80) - 100 = 53
Number of students who like tea and lemonade = (80 + 52) - 100 = 32
Number of students who like coffee and lemonade = (73 + 52) - 100 = 25
Number of students who like all three drinks = Number of students who like coffee + Number of students who like tea + Number of students who like lemonade - Number of students who like coffee and tea - Number of students who like tea and lemonade - Number of students who like coffee and lemonade
= 73 + 80 + 52 - 53 - 32 - 25
= 95
Therefore, the maximum possible number of students who like all three drinks is 95.
To find the minimum possible number of students who like all three drinks, we assume that all the students who like coffee, tea, and lemonade also like all three drinks. Then,
Number of students who like all three drinks = minimum (Number of students who like coffee, tea, and lemonade)
= minimum (73, 80, 52)
= 52
Therefore, the minimum possible number of students who like all three drinks is 52.
The difference between the maximum and minimum possible number of students who like all three drinks is:
95 - 52 = 43
However, the question asks for the difference between the maximum and minimum possible number of students who like all three drinks, given that it is possible that some students do not like any of these three drinks. Therefore, we need to subtract the number of students who do not like any of these three drinks from both the maximum and minimum possible numbers.
Let the number of students who do not like any of these three drinks be x.
Then, x = 100 - (73 + 80 + 52 - 53 - 32 - 25)
x = 37
Maximum possible number of students who like all three drinks with some students not liking any of these three drinks = 95 - 37 = 58
Minimum possible number of students who like all three drinks with some students not liking any of these three drinks = 52 - 37 = 15
Therefore, the difference between the maximum and minimum possible number of students who like all three drinks with some students not liking any of these three drinks is:
58 - 15 = 43
Hence, the correct answer is option D.
To find the maximum and minimum possible number of students who like all three drinks, we need to use the inclusion-exclusion principle.
Total number of students = 100
Number of students who like coffee = 73
Number of students who like tea = 80
Number of students who like lemonade = 52
Number of students who like coffee and tea = (73 + 80) - 100 = 53
Number of students who like tea and lemonade = (80 + 52) - 100 = 32
Number of students who like coffee and lemonade = (73 + 52) - 100 = 25
Number of students who like all three drinks = Number of students who like coffee + Number of students who like tea + Number of students who like lemonade - Number of students who like coffee and tea - Number of students who like tea and lemonade - Number of students who like coffee and lemonade
= 73 + 80 + 52 - 53 - 32 - 25
= 95
Therefore, the maximum possible number of students who like all three drinks is 95.
To find the minimum possible number of students who like all three drinks, we assume that all the students who like coffee, tea, and lemonade also like all three drinks. Then,
Number of students who like all three drinks = minimum (Number of students who like coffee, tea, and lemonade)
= minimum (73, 80, 52)
= 52
Therefore, the minimum possible number of students who like all three drinks is 52.
The difference between the maximum and minimum possible number of students who like all three drinks is:
95 - 52 = 43
However, the question asks for the difference between the maximum and minimum possible number of students who like all three drinks, given that it is possible that some students do not like any of these three drinks. Therefore, we need to subtract the number of students who do not like any of these three drinks from both the maximum and minimum possible numbers.
Let the number of students who do not like any of these three drinks be x.
Then, x = 100 - (73 + 80 + 52 - 53 - 32 - 25)
x = 37
Maximum possible number of students who like all three drinks with some students not liking any of these three drinks = 95 - 37 = 58
Minimum possible number of students who like all three drinks with some students not liking any of these three drinks = 52 - 37 = 15
Therefore, the difference between the maximum and minimum possible number of students who like all three drinks with some students not liking any of these three drinks is:
58 - 15 = 43
Hence, the correct answer is option D.
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Community Answer
In a class of 100 students, 73 like coffee, 80 like tea and 52 like le...
Let n, s, d and t be the number of students who
likes none of the drinks, exactly one drink,
exactly 2 drinks and all three drinks, respectively.
It is given,
n+s+d+t=100.....(1)
1s+2d+3t= 73+80+52
1s+2d+3t=205.....(2)
(2)-(1), we get
d+2t-n=105
Maximum value t can take is 52, i.e. t = 52, d= 1
and n=0
Minimum value t can take is 5, i.e.t= 5, d= 95
and n = 0 (This also satisfies equation (1)
Difference= 52-5 = 47
answer= D
likes none of the drinks, exactly one drink,
exactly 2 drinks and all three drinks, respectively.
It is given,
n+s+d+t=100.....(1)
1s+2d+3t= 73+80+52
1s+2d+3t=205.....(2)
(2)-(1), we get
d+2t-n=105
Maximum value t can take is 52, i.e. t = 52, d= 1
and n=0
Minimum value t can take is 5, i.e.t= 5, d= 95
and n = 0 (This also satisfies equation (1)
Difference= 52-5 = 47
answer= D
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In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer?
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In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer?.
In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer?.
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In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks isa)52b)53c)48d)47Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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