Overlapping Sets: Data Analysis - Numerical Analysis

Question

Question was:  In a company of 80 employees, 40% of the employees are in customer care, 50% are in sales, and 30% are in design. If 5 employees are a part of both the sales and design departments, but not in customer care, what is the maximum number of employees who are in both customer care and design, but not sales?

A) 19 - right solution 
 B) 28 
 C) 32 
 D) 36 
 E) 40

So what did I do: 
 CC: 80*0,4 = 32 
 S: 80*0,5 = 40 
 D: 80*0,3 = 24

If there are 5 in both S and D but not CC:  
 CC only stays 32 
 S only: 40-5 = 35  
 D only: 24-5 = 19 
 S and D: = 5 
 Total still over 80: 32+25+19+5= 91

x represents CC and D (employees in both): 35+5+19-x+32-x+x = 80 
 Because employees in both are added and subtracted in the "only categories" 
 x = 11

New distribution: 
 S = 35 
 S/D = 5 
 D = 19-11= 8 
 CC = 32-11 = 21 
 D/CC = 11 
 Lets check: 35+5+8+21+11 = 80

but 11 is not a possible answer, at is point I am stuck

Thanks so much for your help!

Maxsmdt041197 · Answer

Similar question was deleted due to poor answers, an expert answer would be really appreciated!

Krunaal · Answer

In my attached solution, n = neither department, and we want to find x, now we can’t have x more than 19 since it will make people only in D negative, which is not possible. So we check by substituting x = 19, we are getting n = 27, and satisfying our Venn diagram.  Edit:  n = 8, the equation will be 80 - n = 32 - x + 35 + x + 5 + 19 - x =>  80 - n = 91 - x

Maxsmdt041197 · Answer

Sorry I still don't get it. I understand why x can't be greater than 19 due to the Design group which totals at 19 after substituting 5 from both design and sales. But I still don't get your n. 
80-n = 91-2n |+2n
80+n=91 |-80
n= 11

And even if we take off the max 19 we get the following:
Sales: 35
Sales and Design: 5
Design: 0 (19-19)
Design an Customer care: 19
Customer care: 32-19 = 13

Which totals at: 35+5+0+19+13= 72 --> we are still missing 8 employees

Krunaal · Answer

You're right

We assume x = 19, and n will be 8. I missed adding x in my soln. above.

So, the correct answer is 19, and 8 people work in neither department.

Maxsmdt041197 · Answer

I see!

So from knowing that x can be max 19, and adding everything we are missing 8 which have to bei neither of the three categories that it totals to 80.

One more question: how did you got to n=27 because the equation gives me n=11

Krunaal · Answer

I edited it, I got n = 8

80 - n = 91 - x

assuming x = 19

80 - n = 91 - 19

80 - n = 72

n = 8

Maxsmdt041197 · Answer

Perfect, thanks so much

ManishaPrepMinds · Answer

Given:

Total = 80

CC = 40% × 80 = 32

S = 50% × 80 = 40

D = 30% × 80 = 24

S ∩ D only (not CC) = 5

Maximize CC ∩ D (not S) ->we want max

To maximize CC ∩ D only, minimize all other groups within Design.
 
Set "All three depts" = 0 & Set "Design only" = 0

24 (total in D) = 5 (S ∩ D only) + CC ∩ D only
→ CC ∩ D only = 19

Feasibility check: (CC ∩ D only = 19, All three depts = 0) 
- D only = 24 − (5+19+0) = 0 Must be ≥ 0. 
- CC remaining = 32 − 19 − 0 = 13 Must be ≥ 0. 
- S remaining = 40 − 5 − 0 = 35 Must be ≥ 0.
Total = 13 + 35 + 0 + 0 + 19 + 5 + 0 = 72 ≤ 80 (8 employees in none of these departments)

Answer: 19

Overlapping Sets: Data Analysis - Numerical Analysis

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Overlapping Sets: Data Analysis - Numerical Analysis

Prep Toolkit

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

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From 555 to 765: 210-point Improvement

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