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MGMAT World Translation Question - Venn Diagrams

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by david2008 » Thu Jul 02, 2009 7:55 am
Hi All,

I have a quick question on a problem that appears in the MGMAT Word Translation book around Venn Diagrams. (for reference it's on page 133 of the 3rd edition; Guide # 4):

"Workers are grouped by their areas of expertise and are placed on at least one team. 20 workers are on the marketing team, 30 are on the sales teams, and 40 are on the Vision team. 5 workers are on both the marketing and sales teams, 6 workers are on both the sales and vision teams, 9 workers are on both the marketing and vision teams, and 4 workers are on all three teams. How many workers are there in total?"

So instead of using a Venn diagram, i was using the general formula:

Total # = A + B + C - (A and B) - (B and C) - (A and C)- 2 * (A & B & C) + other

Since we know each person is in at least one team, the last term is 0. by that formula:

Total # = 20 + 30 + 40 - 5 - 6 - 9 - 2 * (4) = 62

But the official answer works out to be 74 using the Venn diagram method. The Venn way makes sense but now sure what I'm doing wrong in getting the wrong answer w/ the formula?

Thanks!
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by Robinmrtha » Thu Jul 02, 2009 9:58 am
Hi david...
your formula is wrong

Total # = A + B + C - (A and B) - (B and C) - (A and C)- 2 * (A & B & C) + other

it should be

Total # = A + B + C - (A and B) - (B and C) - (A and C) + (A & B & C) + other
=20 + 30+ 40-5-6-9+4 + 0(no others)
=74
Hope this helps
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by shibal » Thu Jul 02, 2009 4:18 pm
why add back 4 (A,B,C)? when it says that it has 4 in all of them, shouldn't we take them off as well from the original 20mkt, 30sales, 40vision totals?
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by tohellandback » Fri Jul 03, 2009 1:25 am
well I use the vein diagram and am getting 62.
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The powers of two are bloody impolite!!
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by rah_pandey » Fri Jul 03, 2009 1:35 am
I think formula used by Robin and David is one and the same thing.i.e One can be derived from the other
It is interesting to note however that interpretation of (AandB) is different
n=> intersection
=> (AandB)= AnB-AnBnC----DAVID
=> (AandB)= AnB-------Robin

It is also important to note that a statement like the one below
5 workers are on both the marketing and sales teams
means that we are also speaking about the people who are part of Marketing,Vision and Sales team

if the statement was
5 workers are on both the marketing and sales teams ONLY
than it would have meant only members who are part of Marketing and Sales and not of Vision team
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Re: MGMAT World Translation Question - Venn Diagrams

by ssmiles08 » Fri Jul 03, 2009 5:27 am
david2008 wrote:Hi All,

I have a quick question on a problem that appears in the MGMAT Word Translation book around Venn Diagrams. (for reference it's on page 133 of the 3rd edition; Guide # 4):

"Workers are grouped by their areas of expertise and are placed on at least one team. 20 workers are on the marketing team, 30 are on the sales teams, and 40 are on the Vision team. 5 workers are on both the marketing and sales teams, 6 workers are on both the sales and vision teams, 9 workers are on both the marketing and vision teams, and 4 workers are on all three teams. How many workers are there in total?"

So instead of using a Venn diagram, i was using the general formula:

Total # = A + B + C - (A and B) - (B and C) - (A and C)- 2 * (A & B & C) + other

Since we know each person is in at least one team, the last term is 0. by that formula:

Total # = 20 + 30 + 40 - 5 - 6 - 9 - 2 * (4) = 62

But the official answer works out to be 74 using the Venn diagram method. The Venn way makes sense but now sure what I'm doing wrong in getting the wrong answer w/ the formula?

Thanks!
I think in the WT book, they tell you to work with "all three" value first and then work your way up subtracting numbers.

S+M+V = 4
M+V = (9-4) = 5
S+V = (6-4) = 2
M+S = (5-4) = 1

V =40 -[ (V+S) + (M+V) + (S+M+V) ] = 40 - (11) = 29
S = 30 -[ (M+S) +(S+V) + (S+M+V) ] = 30 - (7) = 23
M = 20 - [ (M+S) + (M+V) + (S+M+V) ] = 20 - (10) = 10


now we have: 4+5+2+1+29+23+10 = 74
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