of 30 cards 15 are rectangles, 10 are rhombuses, and the rest are squares, 8, and circles, x. Hence the circles can be 30-15-10-8=x. Since x returns negative, we can consider squares and rhombuses as rectangles too or as subsets of rectangles, then 15 rectangles include 8 squares and 10 rhombuses, which leaves the maximum possible number of circles, x, as 30-15=15. The closest value to 15 is 13 which is also possible and maximizes the number of circles-> 15 rectangles containing 10 rhombuses and 5 squares, 2 squares and 13 circles.

e

this question is more like a brain-teaser

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

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.