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# SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION

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Intern
Joined: 28 Dec 2017
Posts: 6
SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION  [#permalink]

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30 Dec 2017, 12:15
Hi Folks,

Here is my case :

A company has 3 departments : VISA, Education & Reception

VISA : 300 employees
Education : 400 Employess
Reception : 450 Employees

30 employees belong to VISA & EDUCATION
40 employees belong to VISA & RECEPTION
50 employees belongs to RECEPTION & EDUCATION

20 employees belong to all three depts

Neither segment= 0

Working on the question how many employees belong at leat to 1 dept, I would like to understand one property I have noticed on the 3 sets case :

Number of employees belonging at least to 1 dept = VISA or /union EDUCATION or/union RECEPTION = 300 + 400 + 450 - 30 - 40 - 50 + 20 = 1050 employees.

In a 2 sets case, A, B, we know that A or / union B = A + B - A & / Intersection B = Segment A + Segment B + segment A&B

However, When I apply this concept on the 3 sets case above, I obtain different results using both formula (Union VS Segments addition), and UNION result > Segment sum result

UNION result - Segment addition result = 3 times Center segment value (VISA & EDUCATION & RECEPTION)

Obviously, there is something I miss, do not understand properly .... even if I know that I need to apply the union formula, I want to understand the difference between both approach, and when to use the segment one. From what I understand, the Segments addition gives me all different employees working in the company... so all employees working at least in one department ... doing so I miss 60 employees compared with the result of the UNION formula (respectively 990 and 1050)

Hope my case is crytal clear

CHeers,
Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 689
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION  [#permalink]

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30 Dec 2017, 12:54
OPTIMALCAP wrote:
Hi Folks,

Here is my case :

A company has 3 departments : VISA, Education & Reception

VISA : 300 employees
Education : 400 Employess
Reception : 450 Employees

30 employees belong to VISA & EDUCATION
40 employees belong to VISA & RECEPTION
50 employees belongs to RECEPTION & EDUCATION

20 employees belong to all three depts

Neither segment= 0

...

Obviously, there is something I miss, do not understand properly .... even if I know that I need to apply the union formula, I want to understand the difference between both approach, and when to use the segment one. From what I understand, the Segments addition gives me all different employees working in the company... so all employees working at least in one department ... doing so I miss 60 employees compared with the result of the UNION formula (respectively 990 and 1050)

First: this type of problem is very rare on the GMAT. Unless you're already consistently scoring in the high 40s on Quant, I would recommend dropping this and working on something that's higher-value for you.

Try drawing some pictures to understand the difference.

Here are the three groups.

You can't just add 300 + 400, because you'd be counting the employees in the middle twice. You'd be counting them once as VISA, and again as Education.

If you split everything up into segments, your three segments are 270, 30, and 370. 270 + 30 + 370 = 670. (Not 700.)

Or, you can take a shortcut. Count everybody, then subtract the ones you counted twice. 300 + 400 = 700, then subtract 30, to make up for the fact that you counted the ones in the middle twice.

When you look at Reception as well, you have to split things up even further. Otherwise, the employees in the middle end up getting counted three times - once as part of each group. If we just added Reception, plus VISA, plus Education, we'd count those 20 people three times over. But we only want to count them once, so we have to either separate them out like in the above diagram, or we have to subtract the ones we counted too many times.
_________________

Chelsey Cooley | Manhattan Prep | Seattle and Online

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Intern
Joined: 28 Dec 2017
Posts: 6
Re: SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION  [#permalink]

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31 Dec 2017, 05:58

I made a recap to focus on my initial point, maybe it is more clear now.

Cheers,
Attachments

20171231_141557.jpg [ 3.12 MiB | Viewed 1922 times ]

Intern
Joined: 28 Dec 2017
Posts: 6
Re: SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION  [#permalink]

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31 Dec 2017, 06:54
Ok, I need to rest ... just realize my enormous mistake ... taking half of intersections ... lol

Everything is in the box !
Math Expert
Joined: 02 Sep 2009
Posts: 52971
Re: SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION  [#permalink]

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31 Dec 2017, 07:24
OPTIMALCAP wrote:
Ok, I need to rest ... just realize my enormous mistake ... taking half of intersections ... lol

Everything is in the box !

19. Overlapping Sets

For more:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
_________________
Intern
Joined: 28 Dec 2017
Posts: 6
Re: SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION  [#permalink]

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31 Dec 2017, 07:43
Wonderful !! Thanks !
Re: SET THEORY - 3 SET CASE - UNION FORMULA VS SEGMENTS ADDITION   [#permalink] 31 Dec 2017, 07:43
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