Discussion
How many candidates offered B with F?
Answer: C
35 candidates offered B with F.
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.
B and F occur together only in A B F, and F is taken by 35 candidates in all, all of them in A B F, so 35 offered B with F.
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