A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 64 chose brand C. Which of the following could be the number of customers who preferred brand D?	Select the correct option
A) 1  B) 8  C) 14  D) 20  E) 27
I get D, but I'm not sure that my method is sound.   You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.   x = total number of testers   A + B + C + D   .61x + (.5)(.61x) + 65 + D = x   .61x + .305x + 65 + D = x   I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.   x = 400   A = 244, B = 122, C = 65..also over 400   x = 600   A = 366, B = 183 C = 65....also over 600   x = 800   A = 488, B = 244, C = 65...D = 3...not an option on the list.   x = 1000   A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.   27
<result>E</result>
A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 64 chose brand C. Which of the following could be the number of customers who preferred brand D?