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All coffee mixtures sold in a store contain Columbian (C), [#permalink]
06 Jul 2006, 17:17
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)
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
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)
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?
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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?
Do you guys recommend any good websites to visit for Venn help?