58. If 0.6 is the average of the four quantities 0.2, 0.8, 1.0, and x, what is the numerical value of x? a. 0.2 b. 0.4 c. 0.67 d. 1.3 e. 2.4 59. ᎏ ( a a 2 – – b b 2 ) ᎏ is equal to a. a ϩ b. b. a Ϫ b. c. ᎏ a a + – b b ᎏ . d. ᎏ a a + – b b ᎏ . e. 1. 60. The area of square EFGH is equal to the area of rectangle ABCD.IfGH ϭ 6 feet and AD ϭ 4 feet, the perimeter (in feet) of the rectangle is a. 9. b. 13. c. 24. d. 26. e. 36. Questions 61–65 refer to the following chart and graph. 24681012141618 1,000 2,000 3,000 4,000 CALORIES BOYS GIRLS CALORIES REQUIRED PER DAY BY BOYS AND GIRLS CALORIES COMPOSITION OF AVERAGE DIET CARBOHYDRATES PROTEIN FAT GRAMS CALORIES 500 100 100 2,050 410 930 AGE – THE GRE QUANTITATIVE SECTION– 225 61. How many calories are there in 1 gram of carbohydrates? a. 0.2 b. 2 c. 4.1 d. 10.25 e. 1.025 62. What percent (to the nearest whole number) of the total calories in the average diet is derived from proteins? a. 12 b. 14 c. 22 d. 27 e. 32 63. Approximately how many more calories per day are required by boys than girls at age 17? a. 500 b. 1,000 c. 2,500 d. 3,500 e. 4,000 64. Which of the following can be inferred from the graphs? I. Calorie requirements for boys and girls have similar rates of increase until age 11. II. From ages 4 to 12 calorie requirements for boys and girls are wholly dissimilar. III. Calorie requirements for boys and girls reach their peaks at different ages. a. I only b. II only c. III only d. I and III e. II and III 65. How many grams of carbohydrates (to the nearest gram) are needed to yield as many calories as 1,000 grams of fat? a. 1,110 b. 2,050 c. 2,268 – THE GRE QUANTITATIVE SECTION– 226 d. 4,100 e. 4,536 66. The radius of a circular pool is twice the radius of a circular flowerbed. The area of the pool is how many times the area of the flowerbed? a. ᎏ 1 4 ᎏ b. ᎏ 1 2 ᎏ c. 2 d. 4 e. 8 67. In the figure above, AB is the diameter and OC ϭ BC. What is the value of ᎏ 2 x ᎏ ? a. 20 b. 30 c. 60 d. 90 e. 120 68. One-half of a number is 17 more than one-third of that number. What is the number? a. 51 b. 84 c. 102 d. 112 e. 204 69. Patricia and Ed together have $100.00. After giving Ed $10.00, Patricia finds that she has $4.00 more than ᎏ 1 5 ᎏ the amount Ed now has. How much does Patricia now have? a. $18.67 b. $20.00 c. $21.00 d. $27.50 e. $30.00 A B C 0 x° – THE GRE QUANTITATIVE SECTION– 227 70. If two items cost c cents, how many items can be purchased for x cents? a. ᎏ 2 x c ᎏ b. ᎏ 2 x c ᎏ c. ᎏ 2 c x ᎏ d. ᎏ c 2 x ᎏ e. 2cx 71. If four cows produce 4 cans of milk in 4 days, how many days does it take eight cows to produce 8 cans of milk? a. 1 b. 2 c. 4 d. 8 e. 16 72. A quart of alcohol containing ᎏ 1 2 ᎏ pint of pure alcohol is diluted by the addition of 1 ᎏ 1 2 ᎏ pints of distilled water. How much pure alcohol is contained in the diluted alcohol? a. ᎏ 1 2 ᎏ pint b. 1 ᎏ 1 2 ᎏ pints c. 2 pints d. 3 pints e. 3 ᎏ 1 2 ᎏ pints 73. If 20 teachers out of a faculty of 80 are transferred, what percentage of the original faculty remains? a. 4 b. 16 c. 25 d. 60 e. 75 – THE GRE QUANTITATIVE SECTION– 228 74. The total weight of three children is 152 pounds and 4 ounces. The average weight is 50 pounds and a. ᎏ 1 3 ᎏ pound. b. ᎏ 1 2 ᎏ pound. c. 1 ᎏ 1 3 ᎏ ounces. d. 9 ounces. e. 12 ounces. 75. Thirty prizes were distributed to 5% of the original entrants in a contest. Assuming one prize per person, the number of entrants in this contest was a. 15. b. 60. c. 150. d. 300. e. 600. 76. To ride a ferry, the total cost T is 50 cents for the car and driver and c cents for each additional passen- ger in the car. What is the total cost for a car with n persons in the automobile? a. T ϭ n ϩ c b. T ϭ 50 ϩ nc c. T ϭ cn d. T ϭ 50 ϩ c(n Ϫ 1) e. T ϭ 50 ϩ (n ϩ 1)c 77. Julie wants to make some candy using a recipe that calls for 1 ᎏ 1 2 ᎏ cups of sugar, ᎏ 1 2 ᎏ cup of boiling water and several other ingredients. She finds that she has only 1 cup of sugar. If she adjusts the recipe for 1 cup of sugar, how much water should she use? a. ᎏ 1 6 ᎏ cup b. ᎏ 1 4 ᎏ cup c. ᎏ 1 3 ᎏ cup d. ᎏ 3 4 ᎏ cup e. 1 cup 78. How many pounds of baggage are allowed for a plane passenger if the European regulations permit 20 kilograms per passenger? (1 kg ϭ 2.2 lbs.) a. 11 b. 44 c. 88 – THE GRE QUANTITATIVE SECTION– 229 d. 91 e. 440 79. Which of the following statements is (are) always true? (Assume a, b, and c are not equal to zero.) I. ᎏ 1 a ᎏ is less than a. II. ᎏ a 2 + a b ᎏ equals ᎏ b 2 + b a ᎏ when a equals b. III. ᎏ a b + + c c ᎏ is more than ᎏ a b ᎏ . a. II only b. I and II only c. I and III only d. II and III only e. I, II, and III 80. If bx Ϫ 2 ϭ k, then x equals a. ᎏ b k ᎏ ϩ 2. b. k Ϫ ᎏ 2 b ᎏ . c. 2 Ϫ ᎏ b k ᎏ . d. ᎏ k + b 2 ᎏ . e. k Ϫ 2 Answers 1. b. ᎏ n + 3 7 ᎏ + ᎏ n 4 –3 ᎏ ᎏ 4n +28 1 + 2 3n –9 ᎏ ᎏ 7n 1 + 2 19 ᎏ The numerators are the same, but the fraction in column B has a smaller denominator, denoting a larger quantity. 2. b. 1y + 0.01y = 2.2 10y + 1y = 220 Multiply each term by 100. 11y = 220 – THE GRE QUANTITATIVE SECTION– 230 . 2,2 68 – THE GRE QUANTITATIVE SECTION 226 d. 4,100 e. 4,536 66. The radius of a circular pool is twice the radius of a circular flowerbed. The area of the pool is how many times the area of the. cup 78. How many pounds of baggage are allowed for a plane passenger if the European regulations permit 20 kilograms per passenger? (1 kg ϭ 2.2 lbs.) a. 11 b. 44 c. 88 – THE GRE QUANTITATIVE SECTION 229 d faculty remains? a. 4 b. 16 c. 25 d. 60 e. 75 – THE GRE QUANTITATIVE SECTION 2 28 74. The total weight of three children is 152 pounds and 4 ounces. The average weight is 50 pounds and a. ᎏ 1 3 ᎏ pound. b. ᎏ 1 2 ᎏ pound. c. 1 ᎏ 1 3 ᎏ ounces. d.