33. How many different committees can be formed from a group of two women and four men if three people are on the committee and at least one member must be a woman? a. 6 b. 8 c. 10 d. 12 e. 16 34. Susan spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had $5 left over. How much money did she start with? a. $60 b. $80 c. $120 d. $160 e. $180 35. A truck travels 20 miles due north, 30 miles due east, and then 20 miles due north. How many miles is the truck from the starting point? a. 20.3 b. 70 c. 44.7 d. 50 e. 120 36. a. .20 b. .5 c. 2 d. 5 e. 20 1 1 2 2× 1 2 5 2 .04 ϭ – QUANTITATIVE PRACTICE TEST– 378 37. A rectangular swimming pool is 20 feet by 28 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 884 square feet. What is the width of the deck? a. 2 feet b. 2.5 feet c. 3 feet d. 4 feet e. 5 feet 38. If a person randomly guesses on each question of a test with n questions, what is the probability of guessing half of the questions correctly if each question has five possible answer choices? a. 5n b. c. d. e. 39. Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes 1 to 2. Find the larger integer. a. 4 b. 6 c. 12 d. 24 e. 30 40. The measure of the side of a square is tripled. If x represents the perimeter of the original square, what is the value of the new perimeter? a. 3x b. 4x c. 9x d. 12x e. 27x 1 1 5 2 2n 1 1 5 2 n 2 1 1 5 2 n 1 5 2 2n – QUANTITATIVE PRACTICE TEST– 379 Data Sufficiency Questions Directions: Each of the following problems contains a question that is followed by two statements. Select your answer using the data in statement (1) and statement (2), and determine whether they provide enough infor- mation to answer the initial question. If you are asked for the value of a quantity, the information is suffi- cient when it is possible to determine only one value for the quantity. The five possible answer choices are as follows: a. Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself. b. Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself. c. The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2). d. The problem can be solved using EITHER statement (1) only or statement (2) only. e. The problem CANNOT be solved using statement (1) and statement (2) TOGETHER. The numbers used are real numbers. If a figure accompanies a question, the figure will be drawn to scale according to the original question or information, but will not necessarily be consistent with the informa- tion given in statements (1) and (2). 41. What is the value of x + 2y? (1) 2x + 4y = 20 (2) y = 5 – x 42. Is r – 5 a real number? (1) r is a rational number. (2) is an irrational number. 43. Is rectangle ABCD a square? (1) m ∠ABC = 90 (2) AC Ќ CD 44. What is the measure of an interior vertex angle of a pentagon? (1) The measure of each adjacent exterior angle is 72. (2) The pentagon is a regular polygon. 45. What is the value of x? (1) x + y = 6 (2) 2x – y = 9 2 r 1 2 – QUANTITATIVE PRACTICE TEST– 380 46. What is the value of x? (1) m∠ACB =30 (2) m∠A + ∠B = 150 47. It takes Joe and Ted four hours to paint a room when they work together. How long does it take Joe working by himself to paint the same room? (1) The dimensions of the room are 12' by 12' by 8'. (2) It takes Ted seven hours to paint the room by himself. 48. Is xy Ͼ 0? (1) x Ͼ 1 (2) y Ͻ 0 49. Given that C is the center of the circle and passes through C, what is the area of the sector of the circle? (1) The diameter of the circle is 12. (2) m ∠C = 30°. 50. Points A, B, and C are located in the same plane. What is the distance between point A and point C? (1) The distance between A and B is 100 cm. (2) The distance between A and B is twice the distance between B and C. A B C D DB A B C D X NOTE: FIGURE NOT DRAWN TO SCALE ° – QUANTITATIVE PRACTICE TEST– 381 51. In the following figure, p || n.Is x supplementary to y? (1) l ⊥ p (2) l || m 52. Which store has a greater discount, store A or store B? (1) Store B has 20% off all items. (2) Store A has $20 off all items. 53. Is x + 1 a factor of 12? (1) x + 1 is even. (2) x + 1 is a factor of both 2 and 3. 54. What is the value of x? (1) 22 Ͻ 3x + 1 Ͻ 28 (2) x is an integer. 55. If x and y are consecutive even integers, what is the value of xy? (1) x + y = 98 (2) y – x = 2 56. What is the numerical value of x 2 – 25? (1) x – 5 = 3 (2) 4 – x = 5 57. A rectangular courtyard with whole-number dimensions has an area of 60 square meters. Find the length of the courtyard. (1) The width is two more than twice the length. (2) The length of the diagonal of the courtyard is 13 meters. p n l m x y – QUANTITATIVE PRACTICE TEST– 382 58. Is x + y Ͼ 2z ? (1) ᭝ABC is equilateral. (2) AD ⊥ BC 59. The circles in the diagram are concentric circles. What is the area of the shaded region? (1) The area of the inner circle is 25. (2) The diameter of the larger circle is 20. 60. Find the value of x. (1) The length of BC is 2͙ ෆ 3. (2) The length of AC is 4. A B C 30° x A B C D z x y – QUANTITATIVE PRACTICE TEST– 383 . what is the value of the new perimeter? a. 3x b. 4x c. 9x d. 12x e. 27x 1 1 5 2 2n 1 1 5 2 n 2 1 1 5 2 n 1 5 2 2n – QUANTITATIVE PRACTICE TEST– 3 79 Data Sufficiency Questions Directions: Each of. of the questions correctly if each question has five possible answer choices? a. 5n b. c. d. e. 39. Two integers are in the ratio of 1 to 4. If 6 is added to the smaller number, the ratio becomes. is a rational number. (2) is an irrational number. 43. Is rectangle ABCD a square? (1) m ∠ABC = 90 (2) AC Ќ CD 44. What is the measure of an interior vertex angle of a pentagon? (1) The measure