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# In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42

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Math Expert
Joined: 02 Sep 2009
Posts: 59623
In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42  [#permalink]

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09 Dec 2019, 02:50
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(N/A)

Question Stats:

100% (02:01) correct 0% (00:00) wrong based on 7 sessions

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In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42 grill their food. If 8 grill and bake, 12 fry and bake and 10 grill and fry and 3 do all the three, how many chefs neither bake, fry, nor grill their food?

A. 23
B. 21
C. 19
D. 17
E. 10

Are You Up For the Challenge: 700 Level Questions

The OA will be automatically revealed on Friday 13th of December 2019 01:50:23 AM Pacific Time Zone
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Re: In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42  [#permalink]

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09 Dec 2019, 09:08
total = A+B+C-(sum of exactly2 )-2* all three+ neither
120=50+45+42-(8+12+10)-2*3+N
120=137-(30)-6+n
120-101 = N
N=19
IMO C

Bunuel wrote:
In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42 grill their food. If 8 grill and bake, 12 fry and bake and 10 grill and fry and 3 do all the three, how many chefs neither bake, fry, nor grill their food?

A. 23
B. 21
C. 19
D. 17
E. 10

Are You Up For the Challenge: 700 Level Questions
Intern
Joined: 27 Nov 2018
Posts: 48
Re: In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42  [#permalink]

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09 Dec 2019, 09:51
Archit3110 wrote:
total = A+B+C-(sum of exactly2 )-2* all three+ neither
120=50+45+42-(8+12+10)-2*3+N
120=137-(30)-6+n
120-101 = N
N=19
IMO C

Bunuel wrote:
In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42 grill their food. If 8 grill and bake, 12 fry and bake and 10 grill and fry and 3 do all the three, how many chefs neither bake, fry, nor grill their food?

A. 23
B. 21
C. 19
D. 17
E. 10

Are You Up For the Challenge: 700 Level Questions

IMO - E

Total = n(A) + n(B) + n(C) -n(A U B) - n(B U C) - n (C U A) + n(AUBUC) + Neither
120 = 50 + 45 + 42 - 8 - 12 - 10 + 3 + Neither
120 = 137 - 30 + 3 + Neither
120 = 110 + Neither
Neither = 120 - 110 = 10 =Option E ... Hit Kudos If solution helped..
Re: In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42   [#permalink] 09 Dec 2019, 09:51
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