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Six people in a company cafeteria for lunch are only eating from the

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Six people in a company cafeteria for lunch are only eating from the [#permalink]

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New post 31 Mar 2017, 03:56
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Difficulty:

  85% (hard)

Question Stats:

52% (01:59) correct 48% (03:07) wrong based on 84 sessions

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Six people in a company cafeteria for lunch are only eating from the salad bar and the soup bar, 10 people are only eating from the sandwich station, and 15 people are only eating from the salad bar and the sandwich station. Only 3 people are eating from all three options, while 8 people are eating neither sandwiches nor salads. If no one is eating a combination from the soup bar and sandwich station, how many of the 70 people eating in the cafeteria are consuming salad?

A. 13
B. 24
C. 28
D. 45
E. 52

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Re: Six people in a company cafeteria for lunch are only eating from the [#permalink]

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New post 31 Mar 2017, 10:45
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Answer is E. 52

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Re: Six people in a company cafeteria for lunch are only eating from the [#permalink]

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New post 03 Jun 2018, 00:17
Bunuel wrote:
Six people in a company cafeteria for lunch are only eating from the salad bar and the soup bar, 10 people are only eating from the sandwich station, and 15 people are only eating from the salad bar and the sandwich station. Only 3 people are eating from all three options, while 8 people are eating neither sandwiches nor salads. If no one is eating a combination from the soup bar and sandwich station, how many of the 70 people eating in the cafeteria are consuming salad?

A. 13
B. 24
C. 28
D. 45
E. 52


Trying to see why the formula here doesn't work?
Soup = 8
Sandwich = 10
Salad = X
Exactly Two Overlaps = 6 + 15 = 21
All Three = 3

I get 70 = 10 + 8 + x - 21 - 2(3) which isn't getting me the right answer.

Luckily, I was able to quickly draw out the venn diagram solution to get to the answer, but wanted to see where I went wrong with applying the formula.
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Six people in a company cafeteria for lunch are only eating from the [#permalink]

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New post 03 Jun 2018, 13:54
wchin24 wrote:
Bunuel wrote:
Six people in a company cafeteria for lunch are only eating from the salad bar and the soup bar, 10 people are only eating from the sandwich station, and 15 people are only eating from the salad bar and the sandwich station. Only 3 people are eating from all three options, while 8 people are eating neither sandwiches nor salads. If no one is eating a combination from the soup bar and sandwich station, how many of the 70 people eating in the cafeteria are consuming salad?

A. 13
B. 24
C. 28
D. 45
E. 52


Trying to see why the formula here doesn't work?
Soup = 8
Sandwich = 10
Salad = X
Exactly Two Overlaps = 6 + 15 = 21
All Three = 3

I get 70 = 10 + 8 + x - 21 - 2(3) which isn't getting me the right answer.

Luckily, I was able to quickly draw out the venn diagram solution to get to the answer, but wanted to see where I went wrong with applying the formula.


Because, in the formula we need to put = 17 + 28 + x - 21 - 6 = 70. x = 52.

10 and 8 are individual values only without including the common values for both the sandwiches and soups. It will be 10 + 15 + 3 = total number of sandwiches.
Six people in a company cafeteria for lunch are only eating from the   [#permalink] 03 Jun 2018, 13:54
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