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Manager
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All coffee mixtures sold in a store contain colombian, [#permalink]
 20 May 2006, 18:45
All coffee mixtures sold in a store contain colombian, jamaican or brazilian coffee or some combination of these. Of all mixtures, 33 contain Col, 43 contain Jamaican and 42 contain brazilian. Of these, 16 contain at least col and jamaican, 18 contain at least jamaican and brazilian, 8 contain at least brazilian and colombian and 5 contain all three. how many diffrent coffee mixtures are there?
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Manager
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You are correct but how did you come to that answer?
In my calculation, I arrived at 47 multiple mixtures of two or more coffees and 19 mixtures of pure coffee. This totals 66 mixtures. what am i not understanding?
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Director
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These problems can be confusion, so you need to read it backwards.
5 contain all three = 5 mixtures
8 contain at least brazilian and colombian = 8-5 = 3 mixtures (because the 5 mixtures above contact brazilian and colombian as well).
Similarly:
18 contain at least jamaican and brazilian = 18-5 = 13 mixtures
16 contain at least col and jamaican = 16-5 = 11 mixtures
33 contain Colombian = 33-(11+3+5) = 14 mixtures
43 contain Jamaican = 43-(11+13+5) = 14 mixtures
42 contain brazilian = 42-(13+3+5) = 21 mixtures.
Add 'em up: = 81 mixtures.
You could also use Venn Diagrams instead of you are familiar with them.
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Manager
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these type of questions become much simpler using venn diagram. If you are not sure, it is explained in one of the manhattan gmat guides.
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Manager
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Venn diagrams provide a much simpler method to solve this...
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Director
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Not sure but can we solve it this way:
Total= Col+Jam+Bra - ((Col+Jam)+(Jam+Bra)+(Bra+Col))+ All =
118 - 42 + 5 = 81?
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