Coffee Venn Diagram

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elgrower: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Feb 08, 2010 4:28 pm

by elgrower » Tue Mar 02, 2010 11:32 am

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?

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Source: Beat The GMAT — Problem Solving | Tue Mar 02, 2010 11:32 am

yeahdisk: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Tue Mar 02, 2010 4:27 am; Thanked: 2 times

by yeahdisk » Tue Mar 02, 2010 12:03 pm

I reckon 82

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elgrower: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Feb 08, 2010 4:28 pm

by elgrower » Tue Mar 02, 2010 12:59 pm

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

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yeahdisk: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Tue Mar 02, 2010 4:27 am; Thanked: 2 times

by yeahdisk » Tue Mar 02, 2010 1:20 pm

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

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stufigol: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Wed Feb 03, 2010 12:09 am; GMAT Score:540

by stufigol » Tue Mar 02, 2010 10:30 pm

A:150

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members; Thanked: 47 times

by kstv » Wed Mar 03, 2010 9:51 am

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

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tata: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Tue Nov 03, 2009 11:07 am

by tata » Wed Mar 03, 2010 11:03 am

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

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elgrower: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Feb 08, 2010 4:28 pm

by elgrower » Wed Mar 03, 2010 1:47 pm

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

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

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