At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red? 
(A) 20%
(B) 25%
(C) 50%
(D) 75%
(E) 80%
Answer
For an overlapping set problem we can use a double-set matrix to organize our information and solve. The boldfaced values were given in the question. The non-boldfaced values were derived using the fact that in a double-set matrix, the sum of the first two rows equals the third and the sum of the first two columns equals the third. The variable p was used for the total number of pink roses, so that the total number of pink and red roses could be solved using the additional information given in the question.

  Red Pink White TOTAL
Long-stemmed     0 80
Short-stemmed 5 15 20 40
TOTAL 100 — p p 20 120

The question states that the percentage of red roses that are short-stemmed is equal to the percentage of pink roses that are short stemmed, so we can set up the following proportion:

5

100 – p

15

p

5p = 1500 – 15p 
p = 75
This means that there are a total of 75 pink roses and 25 red roses. Now we can fill out the rest of the double-set matrix:

  Red Pink White TOTAL
Long-stemmed 20 60 0 80
Short-stemmed 5 15 20 40
TOTAL 25 75 20 120

Now we can answer the question. 20 of the 80 long-stemmed roses are red, or 20/80 = 25%.

The correct answer is B.

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