Problem Solving

BTGmoderatorLU wrote: ↑

Mon Jul 06, 2020 4:58 am

Source: Princeton Review

A single slice cut from the center of a circular pizza has an edge length (from the center of the pizza to the edge of the crust) of 5", has an arc length of \(1.25\pi"\), and weighs 4 ounces. If a serving weighs 8 ounces, then, to the nearest integer, what is the largest number of serving that 6" diameter pizzas can yield? (Note that servings must weigh 8 ounces, but they do not need to be equal in shape.)

A. 1
B. 4
C. 6
D. 8
E. 9

The OA is D

Solution:

Let’s determine the area of the slice of pizza that weighs 4 ounces. Since the radius of the slice is 5 inches and the arc length is 1.25π inches, the angle of the slice (measuring at the tip) is 1.25π/10π x 360 = 1/8 x 360 = 45 degrees. That is, a 45-degree slice of a pizza that has a radius of 5 inches (or a diameter of 10 inches) weighs 4 ounces. Now, let’s determine its area:

45/360 x 5^2 x π = 1/8 x 25π = 25π/8 sq. in.

That is, if a pizza (or portion of it) has an area of 25π/8 sq. in., it weighs 4 ounces. In other words, a pizza (or portion of it) having an area of 25π/8 x 2 = 25π/4 sq. in. would weigh 8 ounces (or 1 serving).

Now let’s determine the area of a 6-inch diameter (or 3-inch radius) pizza:

3^2 x π = 9π sq. in.

Dividing 9π by 25π/4, we have:

(9π)/(25π/4) = 9/(25/4) = 9 x 4/25 = 36/25

Since 36/25 is more than 1 and less than 2, the largest number of servings in a 6-inch diameter pizza is therefore 1.

Answer: A

Note: This question originally asks for the number of servings that six pizzas with a diameter of 6” can yield and the OA of D belongs to that question. With the current wording, the answer is A.