48 . H Given the area of the circle is 16π square meters, the radius is 4 meters. AC is the longest
chord in the circle, which is the diameter of the circle, so O can be labeled as the midpoint.
OA and OB are each 4 meters, so ΔOAB is an equilateral triangle whose angles measure 60°.
AOB + BOC = 180°, BOC so measures 120°, making the arc degree also 120°. Choice
(F) gives the measure of arc AB rather than BC. Choices (G) and (J) use an incorrect triangle.
49 . A A system of equations has no solutions if the equations have the same slope and different y-
intercepts. Two linear equations have the same slope if they have the same ratio of
coefficients for x and y. Set up a proportion of the coefficients: = . 12b = 24, so b = 2.
Choices (B), (C), (D), and (E) do not give slopes equal to that of the first equation.
50 . F The shading above the horizontal line segment means that the y-values, which represent the
number of pies Rebecca and Scott make, are never less than 1. In other words, they always
make at least 1 pie, which is (F).
51 . D The best way to approach this question, since it asks about the maximum, is check the
endpoints or extremes of the graph: (9,1) and (0,4). Using the provided expression for
weekly profit, 12(9) + 25(1) = $133, which is (B). Check the other extreme to see that 12(0)
+ 25(4) = $100, which is less than $133.
52 . K If Rebecca and Scott made 5 pies at 3 hours each and 3 dozen cookies at 1 hour each, then
they spent 18 hours baking that week. They donated $2 for every hour they spent baking, so
they donated $36. The question asks what percent of that week’s profit they donated, so
calculate that week’s profit. According to the provided expression for weekly profit, 12(3) +
25(5) = $161. The $36 donated, out of $161 earned, is approximately 22%, which is (K).
53 . A Following the formula provided, (w)(10) − (w)(w) = 25. Rearranging, 10w − w^2 = 25
becomes w^2 − 10w + 25 = 0. Factoring the quadratic into (w − 5)(w − 5) = 0, the only
possible value for w is 5, so the answer is (A).
54 . K This formula may look complicated, but if you’re careful with the pieces, this will be basic
golden-rule algebra. If x = B(1 + .2g)n, then divide both sides by (1 + .2g)n to get
= B, which is (K). If you find the algebra daunting, you can also plug in simple numbers and
find a target value for B.
55 . C The main things you know for sure about m and n are that m is negative, and n is positive.
