A math teacher has 32 cards, each of which is in 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 re circles.
Select
A) 9	B) 10	C) 11	D) 12	E) 15
a square is a special kind of rhombus (sides are perpendicular)   a square is a special kind of rectangles (sides with same length)   Among the 32 cards with have:   15 rectangles   10 rhombus   8 squares   Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.   Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.   We have 8 squares.   So the minimum different cards that represent a square, a rhombus or a rectangle is   2 + 7 + 8= 
<gadget id="calculator">  2 + 7 + 8</gadget>
<output>17</output>
17   Which means that the maximum number of circles that you could have is  32 - 17= 
<gadget id="calculator"> 32 - 17</gadget>
<output>15</output>
15   Answer (15)
<result>E</result>
A math teacher has 32 cards, each of which is in 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 re circles.