Author 
Message 
TAGS:

Hide Tags

Intern
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
19 Oct 2016, 19:45
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 =9032+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 =90208 =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 2group overlaps) + (All 3) + Neither "In the formula above, Sum of 2group 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 2group 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
Joined: 12 Nov 2016
Posts: 683
Location: United States
GPA: 2.66

Re: Workers are grouped by their areas of expertise, and are
[#permalink]
Show Tags
12 Oct 2017, 17:44
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
Joined: 05 Mar 2018
Posts: 5

Re: Workers are grouped by their areas of expertise, and are
[#permalink]
Show Tags
30 May 2018, 09:12
alexjoh89 wrote: I have a question. If the formula is:
Total = Group1 + Group2 + Group3  (sum of 2group 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
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
15 Jul 2018, 22:45
alexjoh89 wrote: I have a question. If the formula is:
Total = Group1 + Group2 + Group3  (sum of 2group 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 theseoverlapping 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
Joined: 29 Apr 2019
Posts: 94
Location: India

Re: Workers are grouped by their areas of expertise, and are
[#permalink]
Show Tags
07 Jun 2019, 21:08
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. Bunuel VeritasKarishma IanStewart chetan2u



Math Expert
Joined: 02 Aug 2009
Posts: 8249

Re: Workers are grouped by their areas of expertise, and are
[#permalink]
Show Tags
07 Jun 2019, 22:03
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. Bunuel VeritasKarishma IanStewart chetan2uLet 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 overlapssum 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
Joined: 29 Apr 2019
Posts: 94
Location: India

Workers are grouped by their areas of expertise, and are
[#permalink]
Show Tags
07 Jun 2019, 22:22
Hi chetan2uThanks 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
Joined: 02 Aug 2009
Posts: 8249

Re: Workers are grouped by their areas of expertise, and are
[#permalink]
Show Tags
07 Jun 2019, 22:40
Sourav700 wrote: Hi chetan2uThanks 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
Joined: 02 Sep 2009
Posts: 61396

Re: Workers are grouped by their areas of expertise, and are
[#permalink]
Show Tags
08 Jun 2019, 00:03
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. Bunuel VeritasKarishma IanStewart chetan2uCheck below. 19. Overlapping Sets [*]TheoryOverlapping Sets Made Easy!How to draw a Venn Diagram for problemsADVANCED OVERLAPPING SETS PROBLEMS Formulae for 3 overlapping sets[*]QuestionsThe EGMAT Sets Triad: 3 Exciting Sets Questions!The Word “Or” in GMAT MathDS QuestionsPS Questions
_________________



GMAT Tutor
Joined: 24 Jun 2008
Posts: 2012

Re: Workers are grouped by their areas of expertise, and are
[#permalink]
Show Tags
08 Jun 2019, 10:06
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 ]



