GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Feb 2020, 18:29 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Workers are grouped by their areas of expertise, and are

Author Message
TAGS:

### Hide Tags

Intern  B
Joined: 07 Jun 2016
Posts: 30
GPA: 3.8
WE: Supply Chain Management (Manufacturing)
Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

jaydevsachdeva wrote:
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.

I completely agree with you in regards to this particular problem. See Below:

Reading through the history of this problem I can see why there is confusion. I understand applying Venn Diagrams and the formulas associated with such. My confusion initially resulted from the GMAT Club Math Book's formula explanation: Pay attention to the description on what it means to sum the intersections - it states to add "g" to every intersection (d, e, and f)...then you subtract from 90, then you add "g" again.
Total = A+B+C - (sum of 2-group overlaps) + (All 3) + Neither
"In the formula above, Sum of 2-group overlaps = AnB+AnC+BnC, where AnB means intersection of A and B (sections d, and g), AnC means intersection of A and C (sections e and g), and BnC means intersection of B and C (sections f and g).
Now, when we subtract AnB (d and g), AnC (e and g), and BnC (f and g) from A+B+C, we are subtracting sections "d, e, and f" ONCE BUT section "g" THREE TIMES (and we need to subtract section "g" only twice), therefore we should add only section "g", which is intersection of A, B, and C (AnBnC) again to get: Total = A+B+C - (sum of 2-group overlaps) + (all three) + Neither

Due to this, I initially obtained 62 as well because I did as it states: I summed AnB+AnC+BnC by adding d and g, e and g, and f and g...THAT is the key...although I now understand the concept, not just memorizing, I did not when I started learning this concept. It did not mention to only sum d, e, and f.....But that is what I had to do to obtain 74. Thus, by adding (5+4)+(6+4)+(9+4) we get 32....subtracting it from 90 = 58, + 4 = 62. Now, in the Mathbook, the second formula is explained well in that you only add what which is common for A and C, which is "e", for example, not "e and g".

I love that mathbook, it has been my favorite prep for formulas and methods, I am eternally grateful....

Going back through I realize now that although it may say to specifically sum d+g, e+g, f+g, I know that when the question asks for "both A and B" I know not to add the "all 3" in it as well because anything shared amongst all 3 will be included in those 2. I may have read to much into the Mathbook but by understanding the concept it just makes sense now. Bunuel did a great job explaining, thank you again.
Director  S
Joined: 12 Nov 2016
Posts: 683
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

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?

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

The thing with this question is that it doesn't say " Only 5 workers are on both the marketing and sales...only 6 are on both the sales and visions" if it said that then the answer would be 62
Intern  B
Joined: 05 Mar 2018
Posts: 5
GMAT 1: 600 Q45 V27
Re: Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

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?

I got this wrong the first time too. I would advise drawing the venn diagram to see it. The problem is when we subtract the overlap between the 3 groups, we already subtracted the center piece thrice. So we need to add a center piece to get what we want. Your reasoning would be correct if the overlapping piece doesn't cover the center piece, in which case we do need to subtract 2*4.
Intern  B
Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 42
Location: Armenia
GPA: 3.4
Re: Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

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?

Never try to memorize the formula! Always try to find the rationale behind any problem in both verbal and math. In these--overlapping set problems, the relatively tricky part is to understand what overlaps what. Precisely, when you draw the diagrams, understand what part overlaps and what part not.
For example, in this question, when the author says that 4 members are on three teams, you should understand that there can be members who are both in two teams and in three teams. When you think in that way, you eliminate the additional overlaps and find the real number of team members.
Attachments overlapping sets.PNG [ 52.36 KiB | Viewed 418 times ]

_________________
Seryozha Sargsyan 21

Contact: sargsyanseryozha@gmail.com

What you think, you become,
What you feel, you attract,
What you imagine, you create.
BSchool Moderator B
Joined: 29 Apr 2019
Posts: 94
Location: India
Re: Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

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

Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+NeitherTotal=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither.

Alright, I'm really really confused on this topic. I'd really appreciate if someone could help me understand the difference between the two.

Math Expert V
Joined: 02 Aug 2009
Posts: 8249
Re: Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

1
Sourav700 wrote:
There are two formulas for 3 overlapping sets:
Total=A+B+C−(sum of 2−group overlaps)+(all three)+NeitherTotal=A+B+C−(sum of 2−group overlaps)+(all three)+Neither.

Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+NeitherTotal=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither.

Alright, I'm really really confused on this topic. I'd really appreciate if someone could help me understand the difference between the two.

Let us look at both the formulas..

A=a+d+e+f
B=b+d+f+g
C=c+e+f+g

Main difference is the definition and contents of sum of 2−group overlaps and sum of EXACTLY 2−group overlaps
sum of 2−group overlaps means (d+f)+(e+f)+(g+f) and sum of EXACTLY 2−group overlaps means d+e+f

(I) Total=A+B+C−(sum of 2−group overlaps)+(all three)+Neither
Here sum of 2−group overlaps are (d+f)+(e+f)+(g+f).. So, you can see the (all three, that is f, is getting added thrice , the net result being 0, so you add one back .
all three = f
Neither =0
So Total=A+B+C−(sum of 2−group overlaps)+(all three)+Neither=A=a+d+e+f+b+d+f+g+c+e+f+g-((d+f)+(e+f)+(g+f))+(f)

(II) Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither
sum of EXACTLY 2−group overlaps means d+e+f..
so you are not subtracting all three even once, and they have been added thrice in A+B+C, so subtract it 2 times
Attachments overlap.png [ 45.86 KiB | Viewed 258 times ]

_________________
BSchool Moderator B
Joined: 29 Apr 2019
Posts: 94
Location: India
Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

Hi chetan2u

Thanks very much for the explanation. Appreciate it.

i'd like to follow up with another question here.

Now i get the difference between the two:
(sum of 2−group overlaps) = (sum of exactly 2) + 3f. correct?

My question is:

when I'm provided with individual values of d, e, f, and g. why do I get an incorrect answer when i use the second formula?

For example:

Example 1: 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?

The answer here is 74 and not 62.

1st equation: 20 + 30 + 40 - ..................

wait, i think i got it.

When we are given the value for d e and g we must subtract the value of f from each of these values for them to be valid in the second equation.

1st equation: 30 + 40 + 20 - (5+9+6) + 4 = 74
2nd equation: 30 + 40+ 20 - (1+5+2) - 2(4) = 74

Thanks a lot chetan2u P.S. If you were in Calcutta, i'd buy you pizza :p
Math Expert V
Joined: 02 Aug 2009
Posts: 8249
Re: Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

Sourav700 wrote:
Hi chetan2u

Thanks very much for the explanation. Appreciate it.

i'd like to follow up with another question here.

Now i get the difference between the two:
(sum of 2−group overlaps) = (sum of exactly 2) + 3f. correct?

My question is:

when I'm provided with individual values of d, e, f, and g. why do I get an incorrect answer when i use the second formula?

For example:

Example 1: 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?

The answer here is 74 and not 62.

1st equation: 20 + 30 + 40 - ..................

wait, i think i got it.

When we are given the value for d e and g we must subtract the value of f from each of these values for them to be valid in the second equation.

1st equation: 30 + 40 + 20 - (5+9+6) + 4 = 74
2nd equation: 30 + 40+ 20 - (1+5+2) - 2(4) = 74

Thanks a lot chetan2u P.S. If you were in Calcutta, i'd buy you pizza :p

Yes, you are correct..
what is given is d+f as 5, so you have to subtract f from it.

I think I can let that Pizza go, even if it means shifting to calcutta. All the best
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 61396
Re: Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

Sourav700 wrote:
There are two formulas for 3 overlapping sets:
Total=A+B+C−(sum of 2−group overlaps)+(all three)+NeitherTotal=A+B+C−(sum of 2−group overlaps)+(all three)+Neither.

Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+NeitherTotal=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither.

Alright, I'm really really confused on this topic. I'd really appreciate if someone could help me understand the difference between the two.

Check below.

19. Overlapping Sets

[*]Theory
How to draw a Venn Diagram for problems
Formulae for 3 overlapping sets
[*]Questions
The E-GMAT Sets Triad: 3 Exciting Sets Questions!
The Word “Or” in GMAT Math
DS Questions
PS Questions
_________________
GMAT Tutor P
Joined: 24 Jun 2008
Posts: 2012
Re: Workers are grouped by their areas of expertise, and are  [#permalink]

### Show Tags

Sourav700 wrote:
Alright, I'm really really confused on this topic. I'd really appreciate if someone could help me understand the difference between the two.

I've never used those formulas once on a GMAT question, and in my experience, a lot of test takers find them confusing, and often use the wrong one, so they aren't very reliable. Even when using a formula is an option, these overlapping set problems tend almost always to be easier and faster to solve just by using a Venn diagram anyway, as Paresh does on the first page of this thread, and since the Venn diagram can easily be adapted to situations where the formulas don't apply (the types of situations you encounter a lot on the GMAT), it's the better method to learn in general.
_________________
GMAT Tutor in Montreal

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Re: Workers are grouped by their areas of expertise, and are   [#permalink] 08 Jun 2019, 10:06

Go to page   Previous    1   2   3   [ 50 posts ]

Display posts from previous: Sort by

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