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# Workers are grouped by their areas of expertise, and are

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

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08 Feb 2010, 21:44
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55% (hard)

Question Stats:

63% (02:05) correct 37% (01:14) wrong based on 209 sessions

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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, 12:41, edited 1 time in total.
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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09 Feb 2010, 18:10
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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:

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

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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28 Sep 2011, 22:37
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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, 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.
Attachments

sets_answer.jpg [ 12.5 KiB | Viewed 5595 times ]

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p!yu$h http://gmatclub.com/forum/from-620-to-710-my-gmat-story-test-date-30-oct-122547.html#p995276 Intern Joined: 27 Jul 2011 Posts: 27 Followers: 0 Kudos [?]: 10 [0], given: 3 Re: Overlapping Set Problem [#permalink] ### Show Tags 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. Senior Manager Status: mba here i come! Joined: 07 Aug 2011 Posts: 270 Followers: 44 Kudos [?]: 1085 [0], given: 48 Re: Overlapping Set Problem [#permalink] ### Show Tags 06 Oct 2011, 07:13 total = 20+30+40-5-6-9-2(4) = 62 _________________ press +1 Kudos to appreciate posts Director Status: No dream is too large, no dreamer is too small Joined: 14 Jul 2010 Posts: 651 Followers: 44 Kudos [?]: 924 [0], given: 39 Re: Overlapping Set Problem [#permalink] ### Show Tags 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 _________________ Collections:- PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html Intern Joined: 28 Feb 2011 Posts: 35 Followers: 0 Kudos [?]: 7 [0], given: 1 Re: Overlapping Set Problem [#permalink] ### Show Tags 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 Senior Manager Joined: 13 May 2011 Posts: 317 WE 1: IT 1 Yr WE 2: Supply Chain 5 Yrs Followers: 21 Kudos [?]: 260 [0], given: 11 Re: Overlapping Set Problem [#permalink] ### Show Tags 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 Manager Status: :) Joined: 29 Jun 2010 Posts: 121 WE: Information Technology (Consulting) Followers: 1 Kudos [?]: 44 [0], given: 51 Re: Overlapping Set Problem [#permalink] ### Show Tags 08 Oct 2011, 03:44 The correct answer is 74.We can get this by drawing 3 set venn diagram and substituting the values. _________________ Thanks, GC24 Please click Kudos ,if my post helped you Manager Joined: 21 Aug 2010 Posts: 188 Location: United States GMAT 1: 700 Q49 V35 Followers: 2 Kudos [?]: 99 [3] , given: 141 Re: Overlapping Set Problem [#permalink] ### Show Tags 09 Oct 2011, 03:57 3 This post received KUDOS Ans C Attachments Ans C.jpg [ 46.5 KiB | Viewed 5202 times ] _________________ ------------------------------------- Senior Manager Joined: 13 May 2011 Posts: 317 WE 1: IT 1 Yr WE 2: Supply Chain 5 Yrs Followers: 21 Kudos [?]: 260 [0], given: 11 Re: Overlapping Set Problem [#permalink] ### Show Tags 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 Edited: check the link: confused-aubuc-79404.html Intern Joined: 07 Nov 2011 Posts: 31 Followers: 0 Kudos [?]: 3 [0], given: 9 Re: Overlapping Set Problem [#permalink] ### Show Tags 04 Dec 2011, 08:55 got 74 also nd not 62 Intern Joined: 17 Sep 2012 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 27 Dec 2012, 06:31 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? Math Expert Joined: 02 Sep 2009 Posts: 37552 Followers: 7391 Kudos [?]: 99222 [0], given: 11009 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 27 Dec 2012, 06:38 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 _________________ Intern Joined: 29 May 2013 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 27 Jun 2013, 12:49 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? Math Expert Joined: 02 Sep 2009 Posts: 37552 Followers: 7391 Kudos [?]: 99222 [1] , given: 11009 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 27 Jun 2013, 12:54 1 This post received KUDOS Expert's post 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. _________________ SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 50 Kudos [?]: 2047 [4] , given: 193 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 15 Oct 2013, 02:22 4 This post received KUDOS 1 This post was BOOKMARKED Solved using Venn diagram attached: Answer = 40 + 11 + 23 = 74 Attachments vein.JPG [ 16.98 KiB | Viewed 11350 times ] _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 27 May 2013 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 10 Dec 2013, 03:22 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 Math Expert Joined: 02 Sep 2009 Posts: 37552 Followers: 7391 Kudos [?]: 99222 [0], given: 11009 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 10 Dec 2013, 04:30 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. _________________ Re: Workers are grouped by their areas of expertise, and are [#permalink] 10 Dec 2013, 04:30 Go to page 1 2 3 Next [ 46 posts ] Similar topics Replies Last post Similar Topics: 1 In a group of 25 factory workers, 15 have brown eyes. Six of the women 5 18 Nov 2015, 23:27 4 If$936 are divided between worker A and worker B in the rat 5 17 Feb 2013, 18:49
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