Question 297130: In a box of 40 cookies, 24 of the cookies were round and 20 of them were made of chocolate. If 12 cookies were neither round nor made of chocolate, how many round chocolate cookies were in the box?
(A) 4 (B) 8 (C) 16 (D) 20 (E) 28
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Box contains 40 cookies.
24 of them are round.
20 of them are chocolate.
12 are neither round nor chocolate.
If 24 are round, then 16 must be not round.
If 20 are chocolate, then 20 must be not chocolate.
The count is therefore:
24 round and 16 not round
20 chocolate and 20 not chocolate
Since we have 12 not round and not chocolate, we'll move them to their own category to get:
24 round and 4 not round
20 chocolate and 8 not chocolate
12 not round and not chocolate
The 4 remaining that are not round must be chocolate. Otherwise they would have been counted in the not round and not chocolate.
We'll move them to their own category to get a revised count of:
24 round
16 chocolate and 8 not chocolate
12 not round and not chocolate
4 not round and chocolate
The 8 that are not chocolate must be round. Otherwise they would have been counted in the not round and not chocolate also.
We'll move them to their own category to get a revised count of:
16 round
16 chocolate
12 not round and not chocolate
4 not round and chocolate
8 round and not chocolate = 8
The 16 that are round and the 16 that are chocolate must be the same cookies.
We'll move them to their own category to get a revised count of:
12 not round and not chocolate = 12
4 not round and chocolate = 4
8 round and not chocolate = 8
16 round and chocolate = 16
The total number of cookies is equal to 12 + 4 + 8 + 16 = 40 as it should be.
Your answer is that the number of cookies that are round and chocolate is 16.
That would be selection C.
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