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There are 68 children in the cafeteria of a school and all

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There are 68 children in the cafeteria of a school and all [#permalink] New post 04 May 2006, 17:34
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E

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There are 68 children in the cafeteria of a school and all of the children have something for lunch. Thirty-four of the children brought lunches from home, 23 of the children bought a drink from the cafeteria beverage machine, and 32 of the children bought fruit in the cafeteria. If 18 children did at least 2 of these things, how many children did exactly two of these things?

(A) 3
(B) 6
(C) 9
(D) 13
(E) 15
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 [#permalink] New post 04 May 2006, 18:33
Draw a venn diagram with the following:

(# All 3) = x
(# Drink + Home) = w
(# Drink + Fruit) = y
(# Home + Fruit) = z
(# Drink only) = 23-w-x-y
(# Home only) = 34-w-x-z
(# Fruit only) = 32-x-y-z


So:

34-x-w-z + 32-x-y-z + 23-w-x-y + x + y + z + w = 68

89 - w - y - z - 2x = 68

w+y+z = 21-2x ----(1)

We also know:
w+y+z+x = 18
w+y+z = 18-x ---(2)

Equate (1) and (2) to get:

21-2x = 18-x
3 = x

Substitute this to (2)

w+y+z = 15.

So Ans = E
Manager
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 [#permalink] New post 05 May 2006, 14:00
Exellent ywilfred !
OA is E.
  [#permalink] 05 May 2006, 14:00
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There are 68 children in the cafeteria of a school and all

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