2014-11-05 09:00:00

Marie is making cookies and has already rolled out the dough into a 12" by 18" rectangle. She wants to cut out circular cookies using a circular cookie cutter that has a diameter of 1 inch. For the first batch, Marie cuts the maximum number of cookies she can out of the rectangle. She then rolls out the remaining dough to make another batch. How many circular cookies can she make from the excess dough?

(A) 46
(B) 49
(C) 59
(D) 216
(E) 275

The correct choice is A
Explanation: For the first batch of cookies, Marie can make 216 cookies. The rectangle has a total area of 12 x 18 or 216 square inches. This could be divided into 216 one-inch-by-one-inch squares. The one-inch-diameter cookies would fit perfectly into those squares, meaning she could make 216 cookies in the first batch. Each of those cookies would have a radius of 1/2 inch, meaning they would all have areas of (1/2)(1/2)π inches (since the area of a circle is pi times the square of the radius), or π/4 inches. The total amount of dough left would be 216 - (216 x π/4) inches or approximately 46.35 inches. If Marie rolled that out, she could then cut 46 more cookies out of the dough, again based on the logic of one cookie being cut from one-inch-by-one-inch squares. Thus, 46 is correct, making A correct, even though Marie could theoretically roll out the trimmings again to make even more cookies.