Math

Quantitative Skills Directions: For questions 11–20, choose the best answer.
11. 40% of what number is 60% of
12? A 18 B 48 C 26 D 12 12. A certain number divided by 3 is 15. If you subtract 15 from the original number, the result is A 15 B 30 C 22.5 D -10
13. What number is the product of 27 and the cube root of 27? A 108 B 9 C 81 D 27
14. What is the next number in the following series: 5, -5, 10, -10, 15, -15, . . . ? A 20 B 10 C 25 D -20
15. What is the missing number in the following series: 2, 3, 6, 7, __, 11, 14? A 12 B 9 C 8 D 10
16. What are the next two numbers in the following series: 2, 0, 1, 5, 3, 4, 8, 6, . . . ? A 9, 7 B 7, 10 C 8, 7 D 7, 11
17. Compare the following three expressions, and then choose the correct answer. (a) 0.025 (b) 0.5 × 0.05 (c) (0.05)2 A (a) is equal to (b), and (b) is equal to (c) B (c) is equal to (a), and (c) is less than (b) C (a) is equal to (b) and greater than (c) D (b) is less than (a) and greater than (c)
18. Compare the following three expressions, and then choose the correct answer. (a) the arithmetic mean (simple average) of -4 and 8 (b) the least common denominator of (c) the greatest prime factor of 48 A (a) < (b) < (c) B (a) < (c) < (b) C (b) > (a) > (c) D (c) = (b) < (a) 3/4 and 3/2

 19. Examine figures (a), (b) and (c), and then choose the correct statement.

A The number of white squares in figure (a) is equal to the number of black squares in figure (c).
B The number of black squares in figure (b) is greater than the number of white squares in figure (a). C The number of white squares in figure (b) is equal to the number of black squares in figure (c).
 D The number of black squares in figure (a) is greater than the number of black squares in figure (c).

20. Examine the figure below, and then choose the correct answer. A c > a > b B a < b < d C b > a > d D c > d > a

Answers and Explanations
Quantitative Skills
11. A Convert the verbal expression to an algebraic equation, and then solve: 0.4x= 0.6x12 0.4x= 7.2 x=18
12. B The original number is 15 × 3 = 45. Subtract 15 from this number: 45 - 15 = 30.
13. C The cube root of 27 is 3 (3 × 3 × 3 = 27). To find the product of 27 and 3, multiply: 27 × 3 = 81.
14. A Each pair of successive terms provides the next positive and negative multiple of 5. Thus, the next two numbers in the series would be 20 followed by -20.
15. D To progress from each term to the next, alternate between two operations: adding 1 and adding 3.
16. D Each group of three terms contains three consecutive integers. The greatest number is listed first, followed by the smallest number, which is followed by the middle number. Each successive group of three numbers contains the next three integers: (2, 0, 1), (5, 3, 4), (8, 6, 7), (11, 9, 10), . . . 17. C 0.5 × 0.05 = 0.025; (0.05)2 = (0.05)(0.05) = 0.0025. Thus, (a) = (b), and (a) and (b) are both greater than (c).
18. B The average of -4 and 8 = (-4+8)/2 = 2 The least common denominator of 3/4 and 3/2 is 4. The greatest prime factor of 48 is 3.

19. C The number of white and black squares in each of the three figures are as follows: Figure (a): 12 black, 13 white Figure (b): 13 black, 12 white Figure (c): 12 black, 12 white As you can see, the number of white squares in figure (b) is equal to the number of black squares in figure (c).

20. D Angle d is supplementary to 65° and 55° angles. In other words, the three angles combine to form a straight line, and their measures must total 180°. Thus, d = 60. Also, each angle in the figure is congruent to its vertical angle (the angle directly across the common vertex). Thus, b = 50, c = 65, and a = 55.


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