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# All of the coffee mixtures sold in a certain store contain either Col

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Math Expert
Joined: 02 Sep 2009
Posts: 45430
All of the coffee mixtures sold in a certain store contain either Col [#permalink]

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05 Feb 2018, 06:34
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:20) correct 29% (02:23) wrong based on 52 sessions

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All of the coffee mixtures sold in a certain store contain either Colombian, Jamaican, or Brazilian coffee or some combination of these. Of all the mixtures, 33 contain Colombian coffee, 43 contain Jamaican coffee, and 42 contain Brazilian coffee. Of these, 16 contain at least Colombian and Jamaican coffees, 18 contain at least Jamaican and Brazilian coffees, 8 contain at least Brazilian and Colombian coffees, and 5 contain all three. How many different coffee mixtures are sold in the store?

(A) 71

(B) 81

(C) 109

(D) 118

(E) 165

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All of the coffee mixtures sold in a certain store contain either Col [#permalink]

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05 Feb 2018, 08:36
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KUDOS
Bunuel wrote:
All of the coffee mixtures sold in a certain store contain either Colombian, Jamaican, or Brazilian coffee or some combination of these. Of all the mixtures, 33 contain Colombian coffee, 43 contain Jamaican coffee, and 42 contain Brazilian coffee. Of these, 16 contain at least Colombian and Jamaican coffees, 18 contain at least Jamaican and Brazilian coffees, 8 contain at least Brazilian and Colombian coffees, and 5 contain all three. How many different coffee mixtures are sold in the store?

(A) 71

(B) 81

(C) 109

(D) 118

(E) 165

The formula for a three set venn diagram is
P(Total) = P(C) + P(J) + P(B) - P(C U J) - P(C U B) - P(B U J) + P(C U B U J)
where
P(C) = Total number of Colombian coffee mixtures
P(J) = Total number of Jamaican coffee mixtures
P(B) = Total number of Brazilian coffee mixtures
P(C U J) = Total number of Colombian and Jamaican coffee mixtures
P(C U B) = Total number of Colombian and Brazilian coffee mixtures
P(B U J) = Total number of Jamaican and Brazilian coffee mixtures
P(C U B U J) = Total number of all three coffee mixtures

P(Total) = $$33 + 43 + 42 - 16 - 18 - 8 + 5 = 81$$

Therefore, the total number of coffee varieties sold in the store is 81 (Option B)
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All of the coffee mixtures sold in a certain store contain either Col   [#permalink] 05 Feb 2018, 08:36
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