51. d. Draw altitudes of AE and BF. ᎏ 1 2 ᎏ (b 1 + b 2 )h = ᎏ 1 2 ᎏ (10 + 2)6 = = 36 square units 52. d. Factor x 2 ϩ 2x Ϫ 8 into (x ϩ 4)(x Ϫ 2). If x is either Ϫ4 or 2, then x 2 ϩ 2x Ϫ 8 ϭ 0. 53. a. Set up a proportion. Let x ϭ the total body weight in terms of g. ᎏ w to e t i a g l h b t o o d f y sk w e e le ig to h n t ᎏ = ᎏ 1 7 0 0 , , 0 0 0 0 0 0 g g r r a a m m s s ᎏ = ᎏ x g ᎏ ᎏ 1 7 ᎏ = ᎏ x g ᎏ x = 7g 54. b. Between 1 P.M. and 3:52 P.M., there are 172 minutes. There are three intervals between the classes. Therefore, 3 ϫ 4 minutes, or 12 minutes, is the time spent in passing to classes. That leaves a total of 172 Ϫ 12, or 160, minutes for instruction, or 40 minutes for each class period. 55. e. (Average)(Number of items) ϭ Sum (x)(P) ϭ Px (y)(N) ϭ Ny ᎏ Numb S e u r m of items ᎏ = Average ᎏ P P x + + N Ny ᎏ = Average 56. b. Select the choice in which the value of n is greater than the value of d in order to yield a value of ᎏ n d ᎏ greater than 1. 57. a.mЄc ϩ mЄd ϭ 180 ° ,but mЄc  mЄd. mЄa ϭ mЄd (vertical angles) mЄa ϭ mЄe (corresponding angles) mЄf ϭ mЄb (corresponding angles) mЄf ϭ mЄc (alternate interior angles) 58. b. Sum ϭ (0.6)(4) or 2.4 0.2 ϩ 0.8 ϩ 1 ϭ 2 x ϭ 2.4 Ϫ 2 or 0.4 0 2 4 6 8 10 2 4 6810 12 14 A B C D E F 2 10 6 – THE GRE QUANTITATIVE SECTION– 235 59. c. ϭϭ 60. d. Area of square EFGH ϭ 36 square feet and area of rectangle ABCD ϭ 36 square feet. Since AD ϭ 4, then DC ϭ 9 feet. The perimeter of ABCD is 4 ϩ 9 ϩ 4 ϩ 9 ϭ 26 feet. 61. c. 500 grams of carbohydrates ϭ 2,050 calories 100 grams of carbohydrates ϭ 410 calories 1 gram of carbohydrates ϭ 4.1 calories 62. a. Total calories ϭ 3,390 Calories from protein ϭ 410 ᎏ 3 4 ,3 1 9 0 0 ᎏ ϭ ᎏ 3 4 3 1 9 ᎏ ϭ 12% 63. b. Boys at 17 require 3,750 calories per day. Girls at 17 require 2,750 calories per day. Difference ϭ 3,750 Ϫ 2,750 ϭ 1,000. 64. d. I is true; observe the regular increase for both sexes up to age 11. II is not true; from age 4 to 12, calorie requirements are generally similar for boys and girls. Note that the broken line and the solid line are almost parallel. III is true; boys reach their peak at 17, while girls reach their peak at 13. 65. c. 100 grams of fat ϭ 930 calories 1,000 grams of fat ϭ 9,300 calories To obtain 9,300 calories from carbohydrates, set up a proportion, letting x ϭ number of grams of carbohydrates needed. ϭ 2,050x ϭ (9,300)(500) x ϭ 2,268 (to the nearest gram) 66. d. Since the formula for the area of a circle is ␲r 2 , any change in r will affect the area by the square of the amount of the change. Since the radius is doubled, the area will be four times as much (2) 2 . 67. c. Since OC ϭ BC and OC and OB are radii, triangle BOC is equilateral and the measure of angle BOC ϭ 60 º . Therefore, x ϭ 120 and ᎏ 1 2 ᎏ x ϭ 60. 68. c. Let x ϭ the number and multiply both sides by 6 to eliminate the fractions. ᎏ 2 x ᎏ = ᎏ 3 x ᎏ + 17 3x = 2x + 102 x = 102 x ᎏᎏ 9,300 calories 500 grams ᎏᎏ 2,050 calories a ϩ b ᎏ a – b a ϩ b(a – b) ᎏᎏ (a – b)(a – b) a 2 – b 2 ᎏ (a – b) – THE GRE QUANTITATIVE SECTION– 236 69. b. Let x ϭ amount Ed had. Let y ϭ amount Patricia had. x ϩ $10 ϭ amount Ed now has. y Ϫ $10 ϭ amount Patricia now has. + $4 ϭ y – 10 x + $10 + $20 ϭ 5y – $50 x – 5y ϭ –$80 x – y ϭ $100 –x – y ϭ –100 (multiply by –1) x – 5y ϭ –$80 –6y ϭ –180 (subtraction) y ϭ $30 (amount Patricia had) $30 – $10 ϭ $20 (amount Patricia now has) 70. c. This is a ratio problem. ϭ ᎏ 2 c ᎏ ϭ ᎏ x ? ᎏ c(?) ϭ 2x (?) ϭ ᎏ 2 c x ᎏ 71. c. Four cows produce one can of milk in one day. Therefore, eight cows could produce two cans of milk in one day. In four days, eight cows will be able to produce eight cans of milk. 72. a. Visualize the situation. The amount of pure alcohol remains the same after the dilution with water. 73. e. Note that the question gives information about the transfer of teachers, but asks about the remain- ing teachers. If 20 teachers are transferred, then there are 60 teachers remaining. ᎏ 6 8 0 0 ᎏ ϭ ᎏ 3 4 ᎏ ϭ 75% 74. e. 152 pounds and 4 ounces ϭ 152.25 pounds. 152.25 Ϭ 3 ϭ 50.75 pounds. Therefore, 0.75 pounds ϭ 12 ounces. 75. e. Let x ϭ number of contestants. 0.05x ϭ 30 5x ϭ 3,000 x ϭ 600 76. d. Since the driver’s fee is paid with the car, the charge for n Ϫ 1 person ϭ c(n Ϫ 1) cents; cost of car and driver ϭ 50 cents. Therefore, T ϭ 50 ϩ c (n Ϫ 1). number of items ᎏᎏ cost in cents x + $10 ᎏ 5 – THE GRE QUANTITATIVE SECTION– 237 . (to the nearest gram) 66. d. Since the formula for the area of a circle is ␲r 2 , any change in r will affect the area by the square of the amount of the change. Since the radius is doubled, the. 0.4 0 2 4 6 8 10 2 4 6 810 12 14 A B C D E F 2 10 6 – THE GRE QUANTITATIVE SECTION 235 59. c. ϭϭ 60. d. Area of square EFGH ϭ 36 square feet and area of rectangle ABCD ϭ 36 square feet. Since AD ϭ 4, then. Visualize the situation. The amount of pure alcohol remains the same after the dilution with water. 73. e. Note that the question gives information about the transfer of teachers, but asks about the