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

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
Six people in a company cafeteria for lunch are only eating from the  [#permalink]

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31 Mar 2017, 02:56
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00:00

Difficulty:

95% (hard)

Question Stats:

49% (02:15) correct 51% (03:29) wrong based on 133 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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Senior Manager
Joined: 24 Apr 2016
Posts: 331
Re: Six people in a company cafeteria for lunch are only eating from the  [#permalink]

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31 Mar 2017, 09:45
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Solution attached
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Intern
Joined: 22 Mar 2018
Posts: 19
Location: United States (CA)
Concentration: Strategy, Technology
GMAT 1: 720 Q48 V41
GPA: 3.9
Re: Six people in a company cafeteria for lunch are only eating from the  [#permalink]

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02 Jun 2018, 23:17
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
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.
Senior Manager
Joined: 15 Oct 2017
Posts: 312
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Six people in a company cafeteria for lunch are only eating from the  [#permalink]

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03 Jun 2018, 12:54
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
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.
Director
Joined: 27 May 2012
Posts: 668
Re: Six people in a company cafeteria for lunch are only eating from the  [#permalink]

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16 Nov 2018, 12:09
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

Just a thought:

We have to assume that each person is eating at least one of the three options ( there are only these three options in the cafeteria ). So there is no one that does not eat salad or soup or sandwich, perhaps drinks only tea.
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- Stne

Re: Six people in a company cafeteria for lunch are only eating from the &nbs [#permalink] 16 Nov 2018, 12:09
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