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

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Manager
Joined: 07 Jun 2018
Posts: 52
Location: United States
In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42  [#permalink]

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29 Nov 2018, 18:23
4
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:06) correct 45% (02:46) wrong based on 80 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
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Joined: 02 Aug 2009
Posts: 7756
Re: In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42  [#permalink]

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29 Nov 2018, 21:28
1
1
Jazzmin 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

Let us start from all three..
All three - 3
So, only F and B=12-3=9
Only G and F=10-3=7
Only G and B=8-3=5

Only G= 42-7-5-3=27
Only B= 45-5-9-3=28
Only F=50-9-7-3=31

Total = 3+9+7+5+27+28+31=110..

So neither = 120-110=10

E

Of course you can draw Venn diagram for ease
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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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02 Dec 2018, 23:59
Jazzmin 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

We can also use direct formula :

Total = G1 + G2 + G3 - (Sum of 2-Group Overlaps) + All three + Neither

120 = 50 + 45 + 42 - (8 + 12 + 10) + 3 + Neither

Neither = 120 - 50 - 45 - 42 + 30 - 3

Neither = 10

(E)

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Re: In a survey of 120 chefs, 50 fry their food, 45 bake their food and 42   [#permalink] 02 Dec 2018, 23:59
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