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

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

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11 Dec 2013, 11:43
Hi, unfortunately i got 62 in total as answer. Would anyone plz explain in which case i've made wrong? For your kind reference, i'm uploading the image of my solution.
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Problem.jpg [ 31.12 KiB | Viewed 8434 times ]

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

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12 Dec 2013, 02:09
mn420 wrote:
Hi, unfortunately i got 62 in total as answer. Would anyone plz explain in which case i've made wrong? For your kind reference, i'm uploading the image of my solution.
Attachment:
Problem.jpg

Solving with formula: workers-are-grouped-by-their-areas-of-expertise-and-are-90246.html#p685690
Solving with Venn diagram: workers-are-grouped-by-their-areas-of-expertise-and-are-90246.html#p1278507

Hope this helps.
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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29 Apr 2014, 11:06
Hi

How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2.
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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29 Apr 2014, 23:26
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nandinigaur wrote:
Hi

How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2.

The question will have words such as 'only' or 'exactly' when it wants to specify that n number of people are in exactly 2 teams.
10 people belong to A and B implies that there are 10 people who belong to both. Some of them could belong to another set C too but that information is not available. All we know is that 10 belong to both A and B.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18098 [2], given: 236 Senior Manager Joined: 28 Apr 2014 Posts: 272 Kudos [?]: 40 [0], given: 46 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 05 May 2014, 20:55 VeritasPrepKarishma wrote: nandinigaur wrote: Hi How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2. The question will have words such as 'only' or 'exactly' when it wants to specify that n number of people are in exactly 2 teams. 10 people belong to A and B implies that there are 10 people who belong to both. Some of them could belong to another set C too but that information is not available. All we know is that 10 belong to both A and B. Thanks Karishma .. This was confusing me as well. Kudos [?]: 40 [0], given: 46 Manager Joined: 20 Oct 2013 Posts: 65 Kudos [?]: 3 [0], given: 27 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 06 May 2014, 05:13 VeritasPrepKarishma wrote: nandinigaur wrote: Hi How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2. The question will have words such as 'only' or 'exactly' when it wants to specify that n number of people are in exactly 2 teams. 10 people belong to A and B implies that there are 10 people who belong to both. Some of them could belong to another set C too but that information is not available. All we know is that 10 belong to both A and B. Dear Karishma I thought i understood but then i saw the following qs: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? in this how to know that we r being asked: people in exactly 2 grps + people in exactly 3 grps... no word is mentioned.... _________________ Hope to clear it this time!! GMAT 1: 540 Preparing again Kudos [?]: 3 [0], given: 27 Math Expert Joined: 02 Sep 2009 Posts: 42544 Kudos [?]: 135260 [0], given: 12679 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 06 May 2014, 08:39 nandinigaur wrote: VeritasPrepKarishma wrote: nandinigaur wrote: Hi How to identify when the qs is meaning to say exactly 2 overlaps and when the qs means otherwise? This qs seemed like it meant exactly 2. The question will have words such as 'only' or 'exactly' when it wants to specify that n number of people are in exactly 2 teams. 10 people belong to A and B implies that there are 10 people who belong to both. Some of them could belong to another set C too but that information is not available. All we know is that 10 belong to both A and B. Dear Karishma I thought i understood but then i saw the following qs: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? in this how to know that we r being asked: people in exactly 2 grps + people in exactly 3 grps... no word is mentioned.... This question is discussed here: in-a-consumer-survey-85-of-those-surveyed-liked-at-least-98018.html Hope it helps. _________________ Kudos [?]: 135260 [0], given: 12679 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7788 Kudos [?]: 18098 [0], given: 236 Location: Pune, India Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 06 May 2014, 23:26 nandinigaur wrote: I thought i understood but then i saw the following qs: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products? in this how to know that we r being asked: people in exactly 2 grps + people in exactly 3 grps... no word is mentioned.... If the question wants to tell you the number of people who like 2 products but not all 3, it will say "30% people liked exactly two products." Or "52% people liked only one of these products" when it wants to tell you that 52% people liked just a single product and did not like other two products and so on... In this particular question, you are asked to find the number of people who liked more than one of the three products. This means you want the number of people who liked either 2 of the 3 products or all three products. So you are looking for "people in exactly 2 grps + people in exactly 3 grps". Note that you can calculate this in two ways: Method 1: people in exactly 2 grps + people in exactly 3 grps Method 2: people in 2 grps (including those in all three groups too) - 2* people in 3 grps (because they have been counted 3 times while counting people in 2 groups) Check out this post for more on three overlapping sets: http://www.veritasprep.com/blog/2012/09 ... ping-sets/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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

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25 Jun 2014, 10:16
[quote="Bunuel"]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:

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

Why are we adding (5+6+9) when the formula has subtraction in it : (sum of exactly 2 - group overlaps) ?

Thanks

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

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25 Jun 2014, 10:19
sagnik242 wrote:
Bunuel wrote:
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:

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

Why are we adding (5+6+9) when the formula has subtraction in it : (sum of exactly 2 - group overlaps) ?

Thanks

Because MnS+MnV+SnV gives 2-group overlaps.
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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09 Jul 2014, 08:58
Bunuel wrote:
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

If I use second formula answer comes different.. Am i making any mistake?? Please correct

20+30+40- (20)- 2(4)+0
90-28 = 62

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

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09 Jul 2014, 09:03
GGMAT730 wrote:
Bunuel wrote:
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

If I use second formula answer comes different.. Am i making any mistake?? Please correct

20+30+40- (20)- 2(4)+0
90-28 = 62

They DO give the same answer when applied properly.

As I wrote in my post above: we are applying first formula as we have intersections of two groups and not the number of only (exactly) 2 group members.

You should understand those formulas, know when to apply which and not simply memorize them.
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Re: Workers are grouped by their areas of expertise, and are [#permalink]

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09 Jul 2014, 22:29
GGMAT760 wrote:

If I use second formula answer comes different.. Am i making any mistake?? Please correct

20+30+40- (20)- 2(4)+0
90-28 = 62

You should understand the concept of the two formulas. They will obviously give the same answer but the inputs they require are different.

Bunuel has given two formulas:

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

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

Note that inputs are different.

In formula 1, you subtract sum of 2 group overlaps, it contains all three thrice and hence all three gets completely removed. So you put it back in.

In formula 2, you subtract sum of exactly two groups and hence it contains no elements of all three. All three has been counted three times in A, B and C and hence you subtract it twice.

You can usually solve these questions with venn diagrams if formulas confuse you.

Check out this post for more on three overlapping sets: http://www.veritasprep.com/blog/2012/09 ... ping-sets/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18098 [0], given: 236 Non-Human User Joined: 09 Sep 2013 Posts: 14938 Kudos [?]: 287 [0], given: 0 Re: Workers are grouped by their areas of expertise and are plac [#permalink] ### Show Tags 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Kudos [?]: 287 [0], given: 0 Non-Human User Joined: 09 Sep 2013 Posts: 14938 Kudos [?]: 287 [0], given: 0 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 28 Jul 2015, 12:56 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Kudos [?]: 287 [0], given: 0 Intern Joined: 13 Aug 2015 Posts: 1 Kudos [?]: [0], given: 2 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 21 Aug 2015, 00:27 Answer is 62. Solved by both equations: Hi, for all that are confused as to why there are 2 different answers from the given 2 equations, 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 The answer is supposed to be 62 for both of them. For 1st Equation, as it is a sum of 2 group overlaps, it will also include the common(all three) 4 part with it. Total=A+B+C−(sum of 2−group overlaps)+(all three)+Neither Total= 20+30+40-((5+4)+(9+4)+(6+4))+4+0=62 =90-32+4 =62 For 2nd Equation, as it is a sum of 2 Exactly group overlaps, it will not include the common 4 part with it. Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither =20+30+40-(5+9+6)-2*4+0 =90-20-8 =62 I hope I am right, and I hope everyone got it. Kudos [?]: [0], given: 2 Manager Joined: 10 Jun 2015 Posts: 126 Kudos [?]: 31 [0], given: 0 Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 21 Aug 2015, 04:37 BarneyStinson wrote: 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? Use venn diagram for this problem. Just fill the number of workers in the 7 regions. since 4 workers are on all teams, the workers on both M and S but not V will be 5-4=1 the workers on both S and V but not on M =6-4=2 the workers on both M and V but not on S =9-4=5 M only is 20-(1+4+5)=10 S only is 30-(1+2+4)=23 V only is 40-(2+4+5)=29 therefore, the total workers =4+1+2+5+10+23+29=74 Kudos [?]: 31 [0], given: 0 Intern Joined: 26 May 2014 Posts: 43 Kudos [?]: 61 [0], given: 17 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 26 Jul 2016, 13:39 "20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team" How do we know 20 , 30 and 40 are not intersection values . For eg. if 20 were placed in marketing, 4 out of them could be in Sales also, so how did we assume M=20 ?Likewise for values of S and V Kudos [?]: 61 [0], given: 17 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7788 Kudos [?]: 18098 [0], given: 236 Location: Pune, India Re: Workers are grouped by their areas of expertise, and are [#permalink] ### Show Tags 26 Jul 2016, 22:27 devbond wrote: "20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team" How do we know 20 , 30 and 40 are not intersection values . For eg. if 20 were placed in marketing, 4 out of them could be in Sales also, so how did we assume M=20 ?Likewise for values of S and V M, S and V in the formula are values including intersections. "20 are on the marketing team, ... 5 workers are on both the Marketing and Sales teams" These 5 are a part of the 20. In this formula: $$Total = A + B + C- (sum \ of \ 2 \ group \ overlaps) + (all \ three) + Neither$$ A, B and C include intersections. They represent the whole set. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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

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27 Jul 2016, 07:29
ThankYou! . I overlooked that!

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Re: Workers are grouped by their areas of expertise, and are   [#permalink] 27 Jul 2016, 07:29

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