A juice manufacturer organized taste-testing sessions : PS Archive
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# A juice manufacturer organized taste-testing sessions

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30 Sep 2006, 12:59
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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 65 chose brand C. Which of the following could be the number of customers who preferred brand D?

(A) 1 (B) 8 (C) 14 (D) 20 (E) 27
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30 Sep 2006, 19:08
% who prefer either C or D = 100 -(61 +61/2) = 8.5%

# who prefer C = 65
# who prefer D = x

so 65+x = 8.5/100 (total)
Alos RHS has to be an integer as # of people cannot be fractions.

so smallest interger value for RHS = 85
=> x = 20

anyone else?
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