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30 Jun 2022, 19:30
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D
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Difficulty:
35%
(medium)
Question Stats:
77% (01:49) correct
23%
(02:40)
wrong
based on 39
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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
01 Jul 2022, 03:34
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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.
03 Jul 2022, 11:33
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can someone explain this again?
