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Workers are grouped by their areas of expertise and are plac

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Workers are grouped by their areas of expertise and are plac [#permalink]

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28 Sep 2011, 22:37
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55% (hard)

Question Stats:

54% (02:25) correct 46% (01:23) wrong based on 123 sessions

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Workers are grouped by their areas of expertise and are placed on at least one team. 20 workers are on team A, 30 are on team B, 40 are on team C. 5 workers are on both team A and B, 6 workers are on both the B and C teams, 9 workers are on both the C and A teams and 4 workers are on all 3 teams. How many workers are there in total?

A. 62
B. 78
C. 74
D. 66
E. 72
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Aug 2013, 11:38, edited 2 times in total.
OA corrected from A to C
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29 Sep 2011, 00:52
Ans. A - 62

I solved this using Venn Diagrams. Attaching the solution for you. This is my first ever attachment in the forum. Not sure if it will display the image of the attachment has to be opened. Please check.
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sets_answer.jpg [ 12.5 KiB | Viewed 3086 times ]

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29 Sep 2011, 00:55
the total no of students will be:
20+30+40 - (5+6+9+2*4) = 62

We have deducted the numbers coz the workers should be counted once, but the workers who are in two teams are counted twice and the workers who are in all three teams are counted thrice,
Eg:
Team A should have 20 workers but, Team B should have 20-5 workers coz the 5 workers are already counted in team A.
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06 Oct 2011, 07:13
total = 20+30+40-5-6-9-2(4) = 62
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06 Oct 2011, 08:50
A only = 20-5-9-4 = 2
B only = 30-5-6-4 = 15
C only = 40-6-9-4 = 21

Total = 2+15+21+24(5+6+9+4)= 62
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06 Oct 2011, 11:25
Hi,

I was going through the following section in this forum to get an understanding of overlapping set:

formulae-for-3-overlapping-sets-69014.html

The above problem has been explained here by Bunnel as well. But the answer is 74.

Can somebody pls verify the answer?

Thank you,
Anu
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08 Oct 2011, 00:28
i got 74:
A=10+[1+4+5]=20
B=23+[1+4+2]=30
C=29+[5+4+2]=40
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08 Oct 2011, 03:44
The correct answer is 74.We can get this by drawing 3 set venn diagram and substituting the values.
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Please click Kudos ,if my post helped you

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09 Oct 2011, 03:57
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Ans C
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04 Dec 2011, 00:38
Total= T(A)+T(B)+T(C)- {A|B+B|C+C|D}+ (A|B|C)
=20+30+40 - (5+6+9) + 4
=74

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04 Dec 2011, 08:55
got 74 also nd not 62
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Re: Workers are grouped by their areas of expertise and are plac [#permalink]

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22 Nov 2014, 10:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Workers are grouped by their areas of expertise and are plac   [#permalink] 22 Nov 2014, 10:53
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