AFOQT Arithmetic Reasoning

AFOQT Arithmetic Reasoning It cost $0.85 to make a single color copy at a copy center. At his price, how many copies can be purchased with $68.00? a. 9 b. 45 c. 68 d. 72 e. 80 - ANS e. Since the price per copy is $0.85, divide 68 by .85 to find the total number that can be purchased with $68; 68 / .85 = 80 copies that can be purchased. An aquarium has a base length of 12 inches and a width of 5 inches. If the aquarium is 10 inches tall, what is the total volume? a. 480 cubic inches b. 540 cubic inches c. 600 cubic inches d. 720 cubic inches e. 920 cubic inches - ANS c. The volume of the aquarium can be found by using the formula V = l * w * h. Since the length is 12 inches, the width is 5 inches and the height is 10 inches, multiply V = 12 * 5 * 10 to get a volume of 600 cubic inches. A man turns a woman's handbag in to the Lost and Found Department of a large downtown store. The man informs the clerk in charge that he found the handbag on the floor beside an entranceway. The clerk estimates that the handbag is worth approximately $150. Inside, the clerks finds the following items: one leather makeup case valued at $65, one vial of perfume, unopened, valued at $75, one pair of earrings valued at $150, and $178 in cash. The clerk is writing a report to be submitted along with the found property. What should he write as the total value of the found cash and property? a. $468 b. $608 c. $618 d. $658 e. $718 - ANS c. The value of the handbag ($150) must be included in the total. Use the following information to answer questions 4 through 6. The cost of movie theater tickets is $7.50 for adults and $5 for children ages 12 and under. On Saturday and Sunday afternoons until 4:00 p.m., there is a matinee price: $5.50 for adults and $3 for children ages 12 and under. Special group discounts are available for groups of 30 or more people. Which of these can be determined from the information given in the above passage? a. how much it will cost a family of four to buy movie theater tickets on Saturday afternoon b. the difference between the cost of two movie theater tickets on Tuesday night and the cost of one ticket on Sunday at 3:00 p.m. c. how much movie theater tickets will cost each person if he or she is part of a group of 40 people d. the difference between the cost of a movie theater ticket for an adult on Friday night and a movie theater ticket for a 13-year-old on Saturday aftern - ANS d. Both choices a and b can ruled out because there is no way to determine how many tickets are for adults or for children. Choice c can be ruled out because the price of group tickets is not given. Use the following information to answer questions 4 through 6. The cost of movie theater tickets is $7.50 for adults and $5 for children ages 12 and under. On Saturday and Sunday afternoons until 4:00 p.m., there is a matinee price: $5.50 for adults and $3 for children ages 12 and under. Special group discounts are available for groups of 30 or more people. Based on the passage, how much will movie theater tickets cost for two adults, one 15-year-old child, and one 10-year-old child at 7:00 p.m. on a Sunday night? a. $17.00 b. $19.50 c. $25.00 d. $27.50 e. $37.50 - ANS d. Because the 15-year-old requires an adult ticket, there are 3 adult tickets at $7.50 each and one child's ticket at $5. Use the following information to answer questions 4 through 6. The cost of movie theater tickets is $7.50 for adults and $5 for children ages 12 and under. On Saturday and Sunday afternoons until 4:00 p.m., there is a matinee price: $5.50 for adults and $3 for children ages 12 and under. Special group discounts are available for groups of 30 or more people. Using the passage, how can you find the difference in price between a movie theater ticket for an adult and a movie theater ticket for a child under the age of 12 if the tickets are for a show at 3:00 p.m. on a Saturday afternoon? a. Subtract $3 from $5.50. b. Subtract $5 from $7.50. c. Subtract $7.50 from $5.50. d. Add $5.50 and $3 and divide by 2. e. Add $7.50 and $5.50 and divide by 2. - ANS a. The adult price on Saturday afternoon is $5.50; the child's price is $3.00. It takes a typist 0.50 seconds to type one word. At this rate, how many words can be typed in 60 seconds? a. 2.25 b. 50 c. 90 d. 120 e. 220 - ANS d. This problem is solved by dividing 60 by 0.50. 60 / .50 = 120. If the average cadet burns 8.2 calories per minute while riding a bicycle, how many calories will the cadet burn if he or she rides for 35 minutes? a. 286 b. 287 c. 387 d. 980 e. 1,080 - ANS b. This problem is solved by multiplying 35 times 8.2. Dr. Drake charges $36 for an office visit, which is 3/4 of what Dr. Jean charges. How much does Dr. Jean charge? a. $27 b. $38 c. $48 d. $57 e. $68 - ANS c. You know the ratio of Drake's charge to Jean's charge is 3 to 4, of 3/4. To find what Jean charges, you use the equation 3/4 = 36/x, or 3x = 4(36); (4)(36) = 144, which is then divided by 3 to arrive at x = 48. Thirty percent of the cadets at the Air Force Academy are involved in athletics. If 15% of the athletes play lacrosse, what percentage of the whole academy plays lacrosse? a. 4.5% b. 9.0% c. 15% d. 30% e. 40% - ANS a. In this question, you need to find 15% of the 30% of cadet athletes that play lacrosse. To find 15% of 30%, change the percents to decimal form and multiply. Since 30% = 0.30 and 15% = 0.15, multiply (0.30)(0.15) = 0.045. As a decimal, this is equivalent to 4.5%. Use the following information to answer questions 11 and 12. Basic cable television service, which includes 16 channels, costs $15 a month. The initial labor fee to install the service is $25. A $65 deposit is required but will be refunded within two years if the customer's bills are paid in full. Other cable services may be added to the basic service: the movie channel service is $9.40 a month; the news channels are $7.50 a month; the arts channels are $5 a month; the sports channels are $4.80 a month. A customer's cable television bill totaled $20 a month. Using the preceding passage, what portion of the bill was for basic cable service? a. 25% b. 33% c. 50% d. 75% e. 85% - ANS d. The basic cable service fee of $15 is 75% of $20. Use the following information to answer questions 11 and 12. Basic cable television service, which includes 16 channels, costs $15 a month. The initial labor fee to install the service is $25. A $65 deposit is required but will be refunded within two years if the customer's bills are paid in full. Other cable services may be added to the basic service: the movie channel service is $9.40 a month; the news channels are $7.50 a month; the arts channels are $5 a month; the sports channels are $4.80 a month. A custormer's first bill after having cable television installed totaled $112.50. This customer chose basic cable and one additional cable service. Which additional service was chosen? a. the news channels b. the movie channels c. the arts channels d. the sports channels e. none of the above - ANS a. The labor fee ($25) plus the deposit ($65) plus the basic service ($15) equals $105. The difference between the total bill, $112.50, and $105 is $7.50, the cost of the news channels. Out of every 200 shoppers polled, 60 said they buy fresh vegetables every week. How many shoppers out of 40,000 could be expected to buy fresh vegetables every week? a. 3,600 b. 9,000 c. 12,000 d. 24,000 e. 36,000 - ANS c. 60 out of 200 is 30%. Thirty percent of 40,000 is 12,000. Use the following pie chart to answer questions 14 and 15. Classical 4.5% Country 27.5% Jazz 7.5% Rap 15% Rock 45.5% If 400 total songs were downloaded, how many downloads were country music? a. 11 b. 28 c. 55 d. 110 e. 270 - ANS d. 27.5% of 400 is 110. Use the following pie chart to answer questions 14 and 15. Classical 4.5% Country 27.5% Jazz 7.5% Rap 15% Rock 45.5% Based on the pie chart, which types of music represent exactly half of the songs downloaded? a. rock and jazz b. classical and rock c. rap, classical, and country d. jazz, classical, and rap e. jazz and rap - ANS b. Rock is 45.5%; when we add 4.5% for classical we arrive at 50%. Last year, 220 people bought cars from a certain dealer. Of those, 60 percent reported that they were completely satisfied with their new cars. How many people reported being unsatisfied with their new car? a. 36 b. 55 c. 88 d. 132 e. 155 - ANS c. If 60% of the people were satisfied with their new car, 40% were unsatisfied; 40% of 220 is 88. Of 1,125 OTS candidates, 135 speak fluent Spanish. What percentage of the candidates speaks fluent Spanish? a. 7.3% b. 8.3% c. 12% d. 14% e. 16% - ANS c. Divide 135 Spanish-speaking candidates by 1,125 total number of candidates to arrive at .12 or 12%. The perimeter of a rectangle is 268 feet. Its two longest sides add up to 156 feet. What is the length of each of its two shortest sides? a. 43 feet b. 56 feet c. 72 feet d. 80 feet e. 112 feet - ANS b. The first step in solving the problem is to subtract 156 from 268. 268 - 156 = 112. The remainder, 112, is then divided by 2. 112 / 2 = 56. A piece of wire 3 feet 4 inches long was divided into 5 equal parts. How long was each part? a. 6 inches b. 7.5 inches c. 8 inches d. 10 inches e. 1 foot 2 inches - ANS c. Three feet 4 inches equals 40 inches; 40 divided by 5 is 8. A middle school cafeteria has three different options for lunch. For $2, a student can get either a sandwich or two cookies. For $3, a student can get a sandwich and one cookie. For $4, a student can get either two sandwiches or a sandwich and two cookies. If Jimae has $6 to pay for lunch for her and her brother, which of the following is NOT a possible combination? a. three sandwiches and one cookie b. two sandwiches and two cookies c. one sandwich and four cookies d. three sandwiches and no cookies e. three sandwiches and two cookies - ANS a. It will cost $3 for a sandwich and a cookie. To get two additional sandwiches, it would cost another $4. Therefore, it would cost $7 to get three sandwiches and a cookie. Since she only has $6 to spend, this combination is not possible. A bed is 4 feet wide and 6 feet long. What is the area of the bed? a. 10 square feet b. 20 square feet c. 24 square feet d. 30 square feet e. 36 square feet - ANS c. Area = width * length. In this case, 4 * 6 = 24 square feet. Airman Beard's temperature is 98 degrees Fahrenheit. Using the formula C = 5/9(F-32), what is his temperature in degrees Celsius? a. 35.8 b. 36.7 c. 37.6 d. 41.1 e. 59.6 - ANS b. Use the formula beginning with the operation in parentheses: 98 - 32 = 66. The multiply 66 by 5/9, first multiplying 66 by 5 to get 330; 330 divided by 9 is 36.66667, which is rounded up to 36.7. All of the rooms on the main floor of a barracks are rectangular, with 8-foot high ceilings. Captain Keira's office is 9 feet wide by 11 feet long. What is the combined surface area of the four walls of her office, including any windows and doors? a. 99 square feet b. 160 square feet c. 320 square feet d. 792 square feet e. 640 square feet - ANS c. Each 9-foot wall has an area of 9 * 8 or 72 square feet. There are two such walls, so those two walls combined have an area of 72 * 2 or 144 square feet. Each 11-foot wall has an area of 11 * 8 or 88 square feet, and again there are two such walls: 88 * 2 = 176. To find the total surface area, add 144 and 176 to get 320 square feet. A recipe serves four people and calls for 1 1/2 cups of broth. If you want to serve six people, how much broth do you need? a. 2 cups b. 2 1/4 cups c. 2 1/3 cups d. 2 1/2 cups e. 2 3/4 cups - ANS b. 1 1/2 cups equals 3/2 cups. The ratio is 6 people to 4 people, which is equal to the ratio of x to 3/2. By cross-multiplying, we get 6(3/2) equals 4x, or 9 equals 4x. Dividing both sides by 4, we get 9/4, or 2 1/4 cups. Fort Greenville is 120 miles west and 90 miles north of Fort Johnson. How long is a direct straight line route from Fort Greenville to Fort Johnson City? a. 100 miles b. 125 miles c. 150 miles d. 180 miles e. 195 miles - ANS c. The distance between Fort Greenville and Fort Johnson is the hypotenuse of a right triangle with sides of length 90 and 120. The length of the hypotenuse equals the square root of the sum of the other sides squared. 90^2 + 120^2 = radical 22,500 = 150 miles.