Workers are grouped by their areas of expertise, and are

Question

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

Show Answer

Official Answer

C

A. 62
B. 78
C. 74
D. 66
E. 72

PareshGmat · Accepted Answer

Solved using Venn diagram attached:
Answer = 40 + 11 + 23 = 74

Bunuel · Answer

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

Show Answer

Official Answer

C

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

piyushpachori · Answer

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.

g106 · Answer

Ans C

alexjoh89 · Answer

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?

Bunuel · Answer

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

elc280 · Answer

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?

Bunuel · Answer

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.

dobrecf · Answer

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) –   + (total in none of the groups) = Overall total

Bunuel · Answer

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.

NGGMAT · Answer

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.

KarishmaB · Answer

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.

NGGMAT · Answer

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....

Bunuel · Answer

This question is discussed here: in-a-consumer-survey-85-of-those-surveyed-liked-at-least-98018.html Hope it helps.

KarishmaB · Answer

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)

GGMAT760 · Answer

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

pLEASE aDVICE...are these two formulas suppose to give same answer right???

Bunuel · Answer

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.

KarishmaB · Answer

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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/09 ... ping-sets/

devbond · Answer

"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

Workers are grouped by their areas of expertise, and are

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Workers are grouped by their areas of expertise, and are

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615 to 715 in 15 Days (Ria's Strategies)

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