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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
In a certain kindergarten, half of the children are allergic to peanut  [#permalink]

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25 Sep 2016, 08:57
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:11) correct 32% (02:49) wrong based on 80 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: In a certain kindergarten, half of the children are allergic to peanut  [#permalink]

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25 Sep 2016, 22:26
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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Joined: 26 Mar 2013
Posts: 2068
Re: In a certain kindergarten, half of the children are allergic to peanut  [#permalink]

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15 Apr 2018, 15:14
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

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