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 45 chose brand C. Which of the following could be the number of customers who preferred brand D? Choices
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 = 14....the first time I get an answer that is an option in the question.   14
<result>C</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 45 chose brand C. Which of the following could be the number of customers who preferred brand D?