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

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Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, 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?

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

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Last edited by Vyshak on 29 Jul 2016, 11:41, edited 1 time in total.
Added options and OA
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Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, 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?

Translating:
"are placed on at least one team": members of none =0;
"20 are on the marketing team": M=20;
"30 are on the Sales team": S=30;
"40 are on the Vision team": V=40;
"5 workers are on both the Marketing and Sales teams": MnS=5, note here that some from these 5 can be the members of Vision team as well, MnS is sections d an g on the diagram (assuming Marketing = A, Sales = B and Vision = C);
"6 workers are on both the Sales and Vision teams": SnV=6 (the same as above sections f an g);
"9 workers are on both the Marketing and Vision teams": MnV=9.
"4 workers are on all three teams": MnSnV=4, section 4.

Question: Total=?

Applying first formula as we have intersections of two groups and not the number of only (exactly) 2 group members:

\(Total=M+S+V-(MnS+MnV+SnV)+MnSnV+Neither=20+30+40-(5+6+9)+4+0=74\).

Answer: 74.

For more check ADVANCED OVERLAPPING SETS PROBLEMS
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Workers are grouped by their areas of expertise and are plac [#permalink]

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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

Last edited by Bunuel on 14 Aug 2013, 10:38, edited 2 times in total.
OA corrected from A to C
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Re: Overlapping Set Problem [#permalink]

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New post 28 Sep 2011, 23:52
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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New post 28 Sep 2011, 23:55
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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New post 06 Oct 2011, 06:13
total = 20+30+40-5-6-9-2(4) = 62
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New post 06 Oct 2011, 07:50
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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Re: Overlapping Set Problem [#permalink]

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New post 06 Oct 2011, 10:25
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,
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New post 07 Oct 2011, 23:28
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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Re: Overlapping Set Problem [#permalink]

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New post 08 Oct 2011, 02:44
The correct answer is 74.We can get this by drawing 3 set venn diagram and substituting the values.
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New post 03 Dec 2011, 23:38
Total= T(A)+T(B)+T(C)- {A|B+B|C+C|D}+ (A|B|C)
=20+30+40 - (5+6+9) + 4
=74

Edited: check the link: confused-aubuc-79404.html
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New post 04 Dec 2011, 07:55
got 74 also nd not 62
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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New post 27 Dec 2012, 05:31
I have a question. If the formula is:

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

why is it then + 4 instead of -2*4?
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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New post 27 Dec 2012, 05:38
alexjoh89 wrote:
I have a question. If the formula is:

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

why is it then + 4 instead of -2*4?


There are two formulas for 3 overlapping sets:
\(Total = A + B + C - (sum \ of \ 2-group \ overlaps) + (all \ three) + Neither\).

\(Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither\).

For more check here: ADVANCED OVERLAPPING SETS PROBLEMS
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New post 27 Jun 2013, 11:49
Can you give an example of a problem where you would know to use the 2nd equation? Would the problem say something like "5 workers are in Marketing and Sales but not Vision, 4 are in Sales and Vision but not marketing," etc., so you know that each number does not include members that belong to all three sets?
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elc280 wrote:
Can you give an example of a problem where you would know to use the 2nd equation? Would the problem say something like "5 workers are in Marketing and Sales but not Vision, 4 are in Sales and Vision but not marketing," etc., so you know that each number does not include members that belong to all three sets?


All examples are here: ADVANCED OVERLAPPING SETS PROBLEMS

DS questions on Overlapping Sets: search.php?search_id=tag&tag_id=45
PS questions on Overlapping Sets: search.php?search_id=tag&tag_id=65

Hope it helps.
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Solved using Venn diagram attached:
Answer = 40 + 11 + 23 = 74
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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New post 10 Dec 2013, 02:22
Workers are grouped by their areas of expertise and are placed on at least one

team. There are 20 workers on the Marketing team, 30 on the Sales team, and 40

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?

How do you solve it using the formula:(Total in Group 1) + (Total in Group 2) + (Total in Group 3) – (Overlap of 1 and 2) – (Overlap of 1 and 3) – (Overlap of 2 and 3) – [2 * (Overlap of 1, 2, and 3)] + (total in none of the groups) = Overall total
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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New post 10 Dec 2013, 03:30
dobrecf wrote:
Workers are grouped by their areas of expertise and are placed on at least one

team. There are 20 workers on the Marketing team, 30 on the Sales team, and 40

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?

How do you solve it using the formula:(Total in Group 1) + (Total in Group 2) + (Total in Group 3) – (Overlap of 1 and 2) – (Overlap of 1 and 3) – (Overlap of 2 and 3) – [2 * (Overlap of 1, 2, and 3)] + (total in none of the groups) = Overall total


Merging similar topics. Please refer to the solutions above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules, 1, 2, 3, 7, 8, and 10. Thank you.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Workers are grouped by their areas of expertise, and are   [#permalink] 10 Dec 2013, 03:30

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