mrr0821 wrote:
There are three courses to be taken and 32 students on average in each course. 5 students take two courses only and 3 students take all three courses. How many students are there in total?
(a) 91
(b) 88
(c) 94
(d) 85
(e) 92
Since average in each course is 32, the total instances of course-student pairing is 32*3 = 96. This includes double/triple counting for those students who are taking 2/3 courses.
Each person would lie in one of the a - g regions.
Attachment:
SetsThree_1_23Sept-2.jpg [ 20.19 KiB | Viewed 687 times ]
5 students take exactly 2 courses (in d, e and f) so they have been double counted. So we should take away 5 from 96 to get the number of people.
3 students take all 3 courses (in g) so they have been triple counted. So we should take away 3*2 = 6 instances from 96 to get the number of people.
Number of students = 96 - 5 - 6 = 85
Answer (D)
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