Discussion
How many candidates in all appeared for the examination?
Answer: C
140 candidates appeared.
The permitted sets of three are A B C, A B D, A B F and C D E: A and B go together and A excludes E, and without A and B the only set that keeps F away from C and D is C D E. E appears only in C D E, so 70 candidates took C D E. F appears only in A B F, so 35 took A B F. C appears in A B C and C D E, so A B C has 90 − 70 = 20. D appears in A B D and C D E, so A B D has 85 − 70 = 15. Check: A = 20 + 15 + 35 = 70.
Each candidate offered exactly three subjects, and the subject counts add up to 70 + 70 + 90 + 85 + 70 + 35 = 420. So the number of candidates is 420 / 3 = 140. The same total comes from 20 + 15 + 35 + 70 = 140. The figure 380 is the sum of the first five counts, which is not the number of candidates.
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