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
Question:
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
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
Options
Answer: 47
Explanation:
Step 1: Maximum number who like all three To make the number who like all three as large as possible, we assume maximum overlap between the groups. So, the maximum possible number = smallest of the three = 52 Step 2: Minimum number who like all three To make it as small as possible, we assume least overlap. Even if we combine all three groups, we can have at most 100 students. So extra students (overlap) = (73 + 80 + 52) – 100 = 205 – 100 = 105 Each student counted twice extra → those 105 must be shared among the overlaps. To make overlap minimum, put as much as possible in two-way overlaps first, and the least in three-way overlap Minimum who like all three = (73 + 80 + 52) – 2×100 = 5 Step 3: Difference Maximum – Minimum = 52 – 5 = 47
Explanation:
Step 1: Maximum number who like all three To make the number who like all three as large as possible, we assume maximum overlap between the groups. So, the maximum possible number = smallest of the three = 52 Step 2: Minimum number who like all three To make it as small as possible, we assume least overlap. Even if we combine all three groups, we can have at most 100 students. So extra students (overlap) = (73 + 80 + 52) – 100 = 205 – 100 = 105 Each student counted twice extra → those 105 must be shared among the overlaps. To make overlap minimum, put as much as possible in two-way overlaps first, and the least in three-way overlap Minimum who like all three = (73 + 80 + 52) – 2×100 = 5 Step 3: Difference Maximum – Minimum = 52 – 5 = 47
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