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In a certain kindergarten, half of the children are allergic to peanut

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Joined: 02 Sep 2009
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In a certain kindergarten, half of the children are allergic to peanut  [#permalink]

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New post 25 Sep 2016, 09:57
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D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:39) correct 33% (02:22) wrong based on 76 sessions

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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

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Re: In a certain kindergarten, half of the children are allergic to peanut  [#permalink]

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New post 25 Sep 2016, 23:26
1
Bunuel wrote:
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


We are given children allergic to cashew nuts as 18 and not allergic to cashew nuts as 10, so total =10+18=28...

Children allergic to both are 10...
18 are allergic to cashew nuts, so and half or 28/2=14 are allergic to peanuts..
So children allergic to at least one of the TWO are 18+14-10=22..

Therefore children NOT allergic to any of the TWO are 28-22=6

D
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Re: In a certain kindergarten, half of the children are allergic to peanut  [#permalink]

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New post 15 Apr 2018, 16:14
Bunuel wrote:
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


We can use double matrix method

The questions info are in black. The deduction are in red. Final answer is in green.

From the matrix, we can deduce the total number of kids = 28

Half of the children are allergic to peanuts = 14.

The number of kids who are allergic to peanuts but NOT allergic to cashew = 4

Hence, total number umber of kids who are NOT allergic to peanuts and NOT allergic to cashew = 6

Answer: D
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Re: In a certain kindergarten, half of the children are allergic to peanut &nbs [#permalink] 15 Apr 2018, 16:14
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