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Let the operation # be defined for the set of real numbers by: image Which of the following statements are true for all real numbers x, y, and z? I. x # y = y # x II. (x # y) # z = x # (y # z) III. 0 # x = 0

(A)I only

(B) II only

(C) III only

(D) I and III only

(E) II and III only

The Correct Answer

So far, a student has earned the following scores on four 100-point tests this grading period:65,73,81, and 82. What score must the student earn on the fifth and last 100-point test of the grading period to earn an average test grade of 80 for the 5 tests?

(A) 75 (B) 76 (C) 78 (D) 99 (E) The student cannot earn an average of 80.

Correct Answer: D

Violet is baking a mixed berry pie that contains blueberries, cherries, blackberries, and raspberries. She uses three times as many blackberries as cherries, twice as many blueberries as raspberries, and the same number of blackberries and raspberries. If Violet has 10 cherries, how many of each of the other berries must she use? Raspberries Blueberries Blackberries

(A)3 2 3 (B) 30 2 3 (C) 30 2 30 (D) 30 60 10 (E) 30 60 30

Correct Answer: E

As shown in the figure below, with angles as marked, a ramp is being designed that will have a vertical height of 4 feet. Which of the following is closest to the horizontal length of the ramp, in feet?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

Correct Answer: C

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