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At a certain resort, each of the 39 food service employees

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At a certain resort, each of the 39 food service employees [#permalink]

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At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

A. 2
B. 3
C. 4
D. 5
E. 6
[Reveal] Spoiler: OA
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Re: Kaplan free test PS - restraunt [#permalink]

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New post 26 May 2012, 21:28
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have a look at this problem. See how quickly you can solve it. also post the time you took. Will post the OA soon.
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Re: At a certain resort, each of the 39 food service employees [#permalink]

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New post 10 Jul 2012, 22:14
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vibhav wrote:
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

A. 2
B. 3
C. 4
D. 5
E. 6


39 = 19 + 18 + 12 - 4 - 2x
2x = 19 + 18 + 12 - 4 - 39
= 45 - 39
= 6

x = 3

Less than a minute i guess
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Re: At a certain resort, each of the 39 food service employees [#permalink]

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vibhav wrote:
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

A. 2
B. 3
C. 4
D. 5
E. 6



{Total} = {Buffet} + {Dinning room} + {Snack bar} - {Those who work in exactly 2 restaurants} - 2*{Those who work in exactly 3 restaurants} (explained here: formulae-for-3-overlapping-sets-69014.html#p729340);

39=19+18+12-4-2x --> x=3.

Answer: B.
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Re: At a certain resort, each of the 39 food service employees [#permalink]

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New post 26 Sep 2013, 00:11
Bunuel wrote:
vibhav wrote:
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

A. 2
B. 3
C. 4
D. 5
E. 6



{Total} = {Buffet} + {Dinning room} + {Snack bar} - {Those who work in exactly 2 restaurants} - 2*{Those who work in exactly 3 restaurants} (explained here: ;

39=19+18+12-4-2x --> x=3.

Answer: B.


Thanks for the formula and link!
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Re: At a certain resort, each of the 39 food service employees [#permalink]

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New post 17 Jun 2014, 15:38
Hi Bunuel,

I have a dbt regarding this formula.As in this question it is explicitly mentioned that "exactly" 19 employees are trained to work in the family buffet, While 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. So how can we add these 3 values as it is in the formula.I mean 18 and 12 would constitute of some commom values also while 19 wont.
Please help me understand.
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Re: At a certain resort, each of the 39 food service employees [#permalink]

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New post 17 Jun 2014, 15:40
maggie27 wrote:
Hi Bunuel,

I have a dbt regarding this formula.As in this question it is explicitly mentioned that "exactly" 19 employees are trained to work in the family buffet, While 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. So how can we add these 3 values as it is in the formula.I mean 18 and 12 would constitute of some commom values also while 19 wont.
Please help me understand.


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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: At a certain resort, each of the 39 food service employees [#permalink]

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New post 19 Jun 2014, 02:22
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Solved using Venn Diagram. Please refer below:

39 = 19 + 12-(b+c+x) + c + 18-(a+c+x)

a+b+c + 2x = 49 - 39

2x = 6

x = 3

Answer = B
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At a certain resort, each of the 39 food service employees [#permalink]

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New post 30 Apr 2017, 15:26
vibhav wrote:
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

A. 2
B. 3
C. 4
D. 5
E. 6


Equations:
a + b + c = 39 [total people working per restaurants]
a + 2b + 3c = 49 [total people working one or more restaurants]

Substitute "b" = 4:
a + c = 39 - 4 = 35
a + 3c = 49 - 8 = 41

Solve System "subtract to find c = people working in all 3 restaurants":
2c = 41 - 35 = 6
c = 3
At a certain resort, each of the 39 food service employees   [#permalink] 30 Apr 2017, 15:26
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