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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (01:58) correct
25%
(03:22)
wrong
based on 76
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History
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In a certain kindergarten, half of the children are allergic to peanuts, 10 children are not allergic to cashew nuts, 10 children are allergic to both peanuts and cashew nuts, and 18 children are allergic to cashew nuts. How many of the kindergarten's children are NOT allergic to peanuts and are NOT allergic to cashew nuts?
A. 14
B. 10
C. 8
D. 6
E. 4
A. 14
B. 10
C. 8
D. 6
E. 4
Fri Jul 01, 2022 2:34 am
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Let the total number of children be x, and the number of children not allergic to any of the nuts is a.
The total number of children allergic to peanuts will be x/2.
Since 10 children are allergic to both peanuts and cashew nuts,
The children allergic to only peanuts will be x/2 - 10.
Also, as the number of children not allergic to cashew nuts = 10
Thus, x/2 - 10 + a = 10
a = 20 - x/2
Now,
x/2 - 10 + a + 10 + 8 = x
x/2 - 10 + 20 - x/2 + 18 = x
x = 28.
Thus, a = 20 - 14 = 6.
Thus, the correct option is D.
The total number of children allergic to peanuts will be x/2.
Since 10 children are allergic to both peanuts and cashew nuts,
The children allergic to only peanuts will be x/2 - 10.
Also, as the number of children not allergic to cashew nuts = 10
Thus, x/2 - 10 + a = 10
a = 20 - x/2
Now,
x/2 - 10 + a + 10 + 8 = x
x/2 - 10 + 20 - x/2 + 18 = x
x = 28.
Thus, a = 20 - 14 = 6.
Thus, the correct option is D.
Sun Jul 03, 2022 10:33 am
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can someone explain this again?
