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15 Sep 2020, 22:53
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:07) correct
38%
(02:16)
wrong
based on 336
sessions
History
Date
Time
Result
Not Attempted Yet
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, 10 grill and fry, and 3 do all three, how many chefs neither bake, fry, nor grill their food?
A) 23
B) 21
C) 19
D) 17
E) 10
A) 23
B) 21
C) 19
D) 17
E) 10
15 Sep 2020, 23:53
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The total number of chefs = 120
Let Grill = G, Fry = F and Bake = B
G U B U C (all three) = 3
G \(\cap\) B = 8. Therefore Only G \(\cap\) B = 8 - 3 = 5
F \(\cap\) B = 12. Therefore Only F \(\cap\) B = 12 - 3 = 9
G \(\cap\) F = 10. Therefore Only G \(\cap\) F = 10 - 3 = 7
Only Grill = Those who grill - Those who only Grill and Bake - Those who Grill and Fry - all 3 = 42 - 5 - 7 - 3 = 27
Only Bake = Those who Bake - Those who only Bake and Grill - Those who Bake and Fry - all 3 = 45 - 5 - 9 - 3 = 28
Only Fry = Those who Fry - Those who only Fry and Grill - Those who Fry and Bake - all 3 = 50 - 7 - 9 - 3 = 31
Total = Only Bake + Only Grill + Only Fry + Only B \(\cap\) G + Only B \(\cap\) F + Only G \(\cap\) F + All three - Neither 3
120 = 27 + 28 + 31 + 5 + 9 + 7 + 3 + Neither 3
Neither 3 = 120 - 110 = 10
Option E
Arun Kumar
Let Grill = G, Fry = F and Bake = B
G U B U C (all three) = 3
G \(\cap\) B = 8. Therefore Only G \(\cap\) B = 8 - 3 = 5
F \(\cap\) B = 12. Therefore Only F \(\cap\) B = 12 - 3 = 9
G \(\cap\) F = 10. Therefore Only G \(\cap\) F = 10 - 3 = 7
Only Grill = Those who grill - Those who only Grill and Bake - Those who Grill and Fry - all 3 = 42 - 5 - 7 - 3 = 27
Only Bake = Those who Bake - Those who only Bake and Grill - Those who Bake and Fry - all 3 = 45 - 5 - 9 - 3 = 28
Only Fry = Those who Fry - Those who only Fry and Grill - Those who Fry and Bake - all 3 = 50 - 7 - 9 - 3 = 31
Total = Only Bake + Only Grill + Only Fry + Only B \(\cap\) G + Only B \(\cap\) F + Only G \(\cap\) F + All three - Neither 3
120 = 27 + 28 + 31 + 5 + 9 + 7 + 3 + Neither 3
Neither 3 = 120 - 110 = 10
Option E
Arun Kumar
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15 Jan 2022, 20:08
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Set Neither of those three as X
120-X = 50+45+42 - 8-12-10 + 3
X = 10
120-X = 50+45+42 - 8-12-10 + 3
X = 10
