0QUESTION
In a college, where every student follows at least one of the three activities- dance, music, or sports- 65% follow dance, 86% follow music, and 57% follow sports. What can be the maximum and minimum percentage of students who follow
A) All three activities
B) Exactly two activities
ANSWER
Here the sum of the three percentage figures is 208%, however since every students is involve in at least one of the three activities, the surplus count is 108%, accounted for by the people engaged in 2 or 3 activities.
A) Exactly 3 activities
Max -> 108% extra is accounted for by 54% ppl, taking 2 extra activities(Total of 3 activities)
Min -> I allocate a 2nd activity to each of the 100%, but I am still left with 8%, which must be born by 8% people having 3 activities
For B)
Max -> 92%, since in worst case scenario 8% ppl must be into all 3 activities
Min -> 0%, In case of 54% ppl being into all 3 activities, as shown in A (Part 1), we end up with 0% ppl being into exactly 2 activities
Max exactly 2 sets cannot be 100%, as total is 208%, we must have a minimum of 8% students who like all three activities, hence only a max of 92% remaining folks can like exactly 2 activities
If you assign all 100% people 2 activities, your total will be 200 and not 208%... Also dint we just conclude that 8% ppl minimum are into 3 activities, So at least these 8% ppl need to be excluded right?
