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All coffee mixtures sold in a store contain Columbian (C), [#permalink]

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06 Jul 2006, 18:17

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

All coffee mixtures sold in a store contain Columbian (C), Jamaican (J) or Brazilian (B) coffee of some combination of these. Of all mixtures, 33 contain C coffee, 43 contain J coffee, and 42 contain B coffee. Of these, 16 contain at least C and J coffees. 18 contain at least J and B coffees, 8 contain at least B and C coffees and 5 contain all three. How many different coffee mixtures are there?

It is provided that there are 5 flavors containing all 3 cofee
Thus CBJ = 5....................(1)
Now if we work backwards from here:
It is also provided that
Flavor containing atleast C & J = 16 (This includes CBJ)

Thus Flavors contain ONLY C & J = 16 - 5 = 11.......(2)

Similarly
Flavors containing ONLY B & J = 18 - 5 = 13.........(3)
Flavors containing ONLY C & B = 8 - 5 = 3.........(4)

Again working backwards:
It is provided that
Flavors containing ATLEAST C = 33

Thus,
Flavors containing ONLY C = Flavors containing ATLEAST C -
Flavors containing ATLEAST C & J - Flavors containing ATLEAST C & B - Flavors containing C, B & J
=> Flavors containing ONLY C = 33-11-3-5 = 14..............(5)

Similarly
Flavors containing ONLY B = 21...................(6)
Flavors containing ONLY J = 14...................(7)

Adding all 7 equations should yield 81 which is option D.

This is more easily explained using diagrams.....but I made an effort to explain through text. I hope this helps...........

Having trouble with venn diagrams in general and visualizing the question. Also, I'm not sure when to use a Venn and when to just use probability equations...e.g. P(a or b)=p(a) +p(b) - p(a and b)...

How about these 3 problems:

75% of students in class answered question #1 correct. 55% in class got q#2 correct. 20% got neither correct. How many students answered both q1 and q2 correct?
a. 30%
b. 45%
c. 50%
d. 60%
e. 75%

____________

Of 20 adults, 5 belong to club x, 7 to club y, and 9 to club z. If 2 belong to all three organizations and 3 belong to exactly two organizations, how many belong to none of these organizations?
a. 1
b 2
c 4
d 6
e 11

____________

In a consumer survey, 85% of those surveyed liked at least one of the three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three products, what percentage of the survey participants liked more than one of the three products?
a 5
b 10
c 15
d 20
e 25

Do you guys recommend any good websites to visit for Venn help?