Praxis Mathematics Practice Questions

E: This question requires that you consider the different ways in which a rectangle and a circle lying on a plane could overlap and determine the maximum number of points of intersection. It might be helpful to sketch various possibilities. If the rectangle is placed so that one side is tangent to the circle, there will be one point of intersection. However, if the rectangle is placed so that each of the four corners overlaps the circumference of the circle, there will be eight points of intersection. It is impossible to sketch a scenario in which the figures share more than eight points of intersection, so choice (E) is correct.

C: To find the average (arithmetic mean) of a set of values, divide the sum of the values by the number of values in the set. In this case, a common denominator must be found before 3/5 and 9/2 can be added; the lowest common denominator is 10: 3/5 = 6/10 = and 9/2 = 45/10
The sum is (6/10) + (45/10) = (51/10)
The average is (51/10/2) = (51/10) x (1/2) = 51/20

A: If a number leaves a remainder of 5 when divided into 137, then two things must be true: the number must be greater than 5, and the number must divide evenly into (137 − 5), or 132. Only (A), 12, is greater than 5 and divides evenly into 132.

E: The easiest way to solve this problem is to count in increments of four hours until the ninth reading, starting at 12:00 PM: 12:00 PM, 4:00 PM, 8:00 PM, 12:00 AM, 4:00 AM, 8:00 AM, 12:00 PM, 4:00 PM, 8:00 PM. Thus, the ninth reading will be taken at 8:00 PM. Choice (E) is correct.

C: Locate on the graph the number of barrels of solvent sold in June 2009, 12, and then locate the number of barrels sold in July 2009, 11. The combined number of barrels sold is 12 + 11 = 23 barrels. Choice (C) is correct.