In this question on overlapping sets, let the total number of students be 80, since 80 is a common multiple of the denominators of the fractions given. It’s neither too small that it will end up giving fractions nor too large that you have to spend time on calculations.
Keeping 80 as the number of students in Social High, we can draw a Venn diagram like the one below:
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20th Nov 2019 - Reply 1.jpg [ 34.81 KiB | Viewed 40 times ]
Note that the region outside the circles is ZERO since the question says that every student is in at least one club. This is crucial information; always be on the lookout for such statements in an Overlapping sets question because they make your life easy.
3/8th of 80 i.e. 30 are in all the three clubs. The respective number of students in the Albanian, Bardic and Checkmate sets are 40, 50 and 60 respectively.
If we add these values, we get 150. But, this 150 includes repetition of certain regions – a, b and c appear twice; 30 appears thrice. So, we will have to remove a, b and c once and 30 twice. If we do that, we should obtain 80 since that is the actual total number of students in the school.
Therefore, 150 – a – b – c – 60 = 80. Solving this, we get a+b+c = 10. a+b+c represents the number of people who belong to exactly two clubs. Hence, the required fraction = 10/80 = 1/8.
The correct answer option is A.
Hope that helps!
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