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

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Workers are grouped by their areas of expertise, and are [#permalink]  08 Feb 2010, 20:44
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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?
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Re: Union of three sets formula derivation? [#permalink]  09 Feb 2010, 17:10
Expert's post
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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Re: Workers are grouped by their areas of expertise, and are [#permalink]  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]  27 Dec 2012, 05:38
Expert's post
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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Re: Workers are grouped by their areas of expertise, and are [#permalink]  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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Re: Workers are grouped by their areas of expertise, and are [#permalink]  27 Jun 2013, 11:54
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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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Re: Workers are grouped by their areas of expertise, and are [#permalink]  15 Oct 2013, 01:22
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Solved using Venn diagram attached:
Answer = 40 + 11 + 23 = 74
Attachments

vein.JPG [ 16.98 KiB | Viewed 5312 times ]

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formula or venn diagram? [#permalink]  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: formula or venn diagram? [#permalink]  10 Dec 2013, 03:30
Expert's post
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.

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Re: Workers are grouped by their areas of expertise, and are [#permalink]  11 Dec 2013, 10:43
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.
Attachment:

Problem.jpg [ 31.12 KiB | Viewed 4402 times ]
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Re: Workers are grouped by their areas of expertise, and are [#permalink]  12 Dec 2013, 01:09
Expert's post
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]  29 Apr 2014, 10:06
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]  29 Apr 2014, 22:26
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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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Re: Workers are grouped by their areas of expertise, and are [#permalink]  05 May 2014, 19:55
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.
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Re: Workers are grouped by their areas of expertise, and are [#permalink]  06 May 2014, 04:13
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....
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Re: Workers are grouped by their areas of expertise, and are [#permalink]  06 May 2014, 07:39
Expert's post
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.
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Re: Workers are grouped by their areas of expertise, and are [#permalink]  06 May 2014, 22:26
Expert's post
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/
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Workers are grouped by their areas of expertise, and are [#permalink]  25 Jun 2014, 09:16
[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]  25 Jun 2014, 09:19
Expert's post
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]  09 Jul 2014, 07:58
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

Re: Workers are grouped by their areas of expertise, and are   [#permalink] 09 Jul 2014, 07:58

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