Bunuel wrote:
Of the N students in a certain class, X took a course in biology and Y took a course in history, and Z took neither of the courses. If there were students who took both two courses, in terms of N, X, Y and Z, what fraction of the students took both two courses?
(A) \(1 - \frac{X+Y+Z}{N}\)
(B) \(\frac{X+Y+Z}{N} - 1\)
(C) \(\frac{X+Y-Z-N}{N}\)
(D) \(\frac{N+X+Y-Z}{N}\)
(E) \(\frac{N-X-Y+Z}{N}\)
Are You Up For the Challenge: 700 Level QuestionsIf there are two categories A and B, we have the formula Total = A + B - Both + Neither. To go into detail, the A category includes "A only" and "Both A and B". The B category includes "B only" and "Both A and B". So we double-counted "Both" if we just add everything up, hence we take it away once from the total. Here we want to find both,
Both = A + B + Neither - Total = X + Y + Z - N.
Finally, the fraction out of the total of N would be \(\frac{{X + Y + Z - N} }{ N} = \frac{{X + Y + Z} }{ N} - 1\). The answer would be B.
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65% (02:19) correct 
