Mo2men wrote:A florist found that 60% of his customers on Valentine's Day bought roses. People had the option that day of buying red roses, yellow roses or orange roses and half of all the people who bought roses bought only red roses. How many people bought all three varieties?
(1) Of the 100 customers the florist had, 12 people bought only yellow and orange roses together.
(2) Of the 100 customers the florist had, no one bought only red roses and one other type of rose.
Total who bought roses = (only R) + (only Y) + (only O) + (only R and Y) + (only R and O) + (only Y and O) + (all 3).
Since both statements indicate a total of 100 customers -- and 60% bought roses -- the total who bought roses = 60.
Since half of the people who bought roses bought only red roses, (only R) = 30.
Thus:
60 = 30 + (only Y) + (only O) + (only R and Y) + (only R and O) + (only Y and O) + (all 3).
Statement 1: (only Y and O) = 12.
Statement 2: (only R and Y) = 0, (only R and O) = 0.
Substituting these values into the blue equation, we get:
60 = 30 + (only Y) + (only O) + 0 + 0 + 12 + (all 3).
Since the values of (only Y) and (only O) are unknown, no way to determine the value of (all 3).
Thus, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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