Coffee Venn Diagram

[elgrower]

All coffee mixtures sold in a store contain Colombian, Jamaican or Brazilian coffee or some combination of these. Of all 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, and 8 contain at least Brazilian and Colombian coffees and 5 contain all three. How many different coffee mixtures are there?

[yeahdisk]

I reckon 82

[elgrower]

Can you please help me solve this question? Also 82 is not one of the answer choices...

[yeahdisk]

Sorry - can't add up. Its 81.

[Common to 3 sets] 5
+
[Common at 2 sets] (11) + (13) + (3)
+
[Common to 1 set] (14) + (14) + (21)

= 81

[stufigol]

A:150

[kstv]

The Q is incomplete without the options. Please provide them if you can.

[tata]

My guess is 66, whats the OA?
Here is my approach
For 3 Sets ABC
True # of objects = (total # A) + (total # B) + (total #C) - (# only AB) - (# only AC) - (# only BC) - 2(# ABC)
So let T be total

T = 33+43+42 - (16+18+8) -2(5) = 118 - 42 - 10 = 66

[elgrower]

A) 45 B) 56 C) 76) D)81 E)86

Correct answer was D...[spoiler][/spoiler]