knight247 wrote:A math teacher has 30 cards, each of which is in the the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that are circles?
(A)9
(B)10
(C)11
(D)12
(E)13
OA E
I received a PM asking me to comment.
To MAXIMIZE the number of circles, we need to MINIMIZE the number of everything else.
To MINIMIZE the number of everything else, we need to MAXIMIZE the overlap among the three noncircular shapes.
A square is both a rhombus (because all 4 sides are equal) and a rectangle (because opposite sides are equal, with four right angles).
Thus, the following distribution will maximize the overlap among the three non-circular shapes:
As the figure shows, the maximum number of circles = 13.
The correct answer is
E.
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