AFOQT Practice-Arithmetic Reasoning

AFOQT Practice-Arithmetic Reasoning It costs $0.85 to make a single color copy at a copy center. At this 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 clerk 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. 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 afternoon at 1:00 P.M. e. none of the above - ANS d. Both choices a and b can be 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. Based on the passage, how much will movie theater tickets cost for two adults, one 15-yearold 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. 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, or 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%. 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. 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 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. 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. Then 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 21/4 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 two sides squared. 902 + 1202= = 150 miles. What is the estimated product when 157 and 817 are rounded to the nearest hundred and multiplied? a. 16,000 b. 80,000 c. 160,000 d. 180,000 e. 1,600,000 - ANS c. Round 157 to 200 and round 817 to 800: 200 × 800 = 160,000. Mr. James Rossen is just beginning a computer consulting firm and has purchased the following equipment: 3 telephone sets, each costing $125; 2 computers, each costing $1,300; 2 computer monitors, each costing $950; 1 printer, costing $600; and 1 answering machine, costing $50. Mr. Rossen is reviewing his finances. What should he write as the total value of the equipment he has purchased so far? a. $3,025 b. $4,025 c. $5,400 d. $5,525 e. $6,525 - ANS d. It is important to remember to include all three telephone sets ($375 total), both computers ($2,600 total), and both monitors ($1,900 total) in the total value. One lap on a particular outdoor track measures a quarter of a mile around. To run a total of three-and-a-half miles, how many laps must a person complete? a. 7 b. 9 c. 10 d. 13 e. 14 - ANS e. To solve this problem, you must convert 3 1/2 to 7/2 and then divide 7/2 by 1/4. The answer, 28/4 ,is then reduced to the number 14. 5/8 × 4/7 = a. 5/14 b. 20/8 c. 25/32 d. 9/16 e. 10 - ANS a. Cancel factors that are common to the numerator and denominator, then multiply: 5/14 Newly hired nurses have to buy duty shoes at the full price of $84.50, but nurses who have served at least a year get a 15% discount. Nurses who have served at least three years get an additional 10% off the discounted price. How much does a nurse who has served at least three years have to pay for shoes? a. $63.78 b. $64.65 c. $67.49 d. $71.83 e. $72.05 - ANS b. You cannot simply take 25% off the original price, because the 10% discount after three years of service is taken off the price that has already been reduced by 15%. Figure the problem in two steps: After the 15% discount, the price is $71.83. Another 10% off that gives you $64.65. The basal metabolic rate (BMR) is the rate at which our bodies use calories. The BMR for a man in his twenties is about 1,700 calories per day. If 204 of those calories should come from protein, about what percentage of this man's diet should be protein? a. 1.2% b. 8.3% c. 12% d. 16% e. 18% - ANS c. The problem is solved by dividing 204 by 1,700. The answer, 0.12, is then converted to a percentage—12%. How much water must be added to one liter of a 5% saline solution to get a 2% saline solution? a. .5 liter b. 1 liter c. 1.5 liters d. 2 liters e. 2.5 liters - ANS c. Use the equation .05(1) = .02(x), where x is the total amount of water in the resulting 2% solution. Solving for x, you get 2.5. Subtracting the 1 liter of water already present in the 5% solution, you will find that 1.5 liters need to be added. All of the rooms in a building are rectangular, with 8-foot ceilings. One room is 9 feet wide by 11 feet long. What is the combined area of the four walls, including doors and windows? a. 90 square feet b. 160 square feet c. 180 square feet d. 280 square feet e. 320 square feet - ANS e. 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 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. Finally, add 144 and 176 to get 320 square feet. A child has a temperature of 40° C. What is the child's temperature in degrees Fahrenheit? (F = 9 5C + 32) a. 100° F b. 101° F c. 102° F d. 103° F e. 104° F - ANS e. Substituting 40 for C in the equation yields F = (9/5)(40) + 32 = 72 + 32 = 104. A woman drives west at 45 miles per hour. After half an hour, a man starts to follow her. How fast must he drive to catch up to her three hours after he starts? a. 52.5 miles per hour b. 55 miles per hour c. 60 miles per hour d. 65 miles per hour e. 67.5 miles per hour - ANS a. The woman will have traveled 3.5 hours at 45 miles per hour for a distance of 157.5 miles. To reach her in 3 hours, the man must travel at 157.5 miles per 3 hours, or 52.5 mph. Jason is six times as old as Kate. In two years, Jason will be twice as old as Kate is then. How old is Jason now? a. 3 years old b. 6 years old c. 9 years old d. 12 years old e. 15 years old - ANS a. J = 6K. J + 2 = 2(K + 2), so 6K + 2 = 2K + 4, which means K equals 1 2. J equals 6K, or 3. A flash drive shows 827,036 bytes free. If you delete a file of size 542,159 bytes and create a new file of size 489,986 bytes, how many free bytes will the flash drive have? a. 489,986 free bytes b. 577,179 free bytes c. 681,525 free bytes d. 774,863 free bytes e. 879,209 free bytes - ANS e. The 827,036 bytes free on the flash drive plus 542,159 bytes freed when the file was deleted equals 1,369,195 bytes: 1,369,195 bytes minus 489,986 bytes put into the new file leaves 879,209 bytes free. On the cardiac ward, there are 7 nursing assistants. NA Basil has 8 patients; NA Hobbes has 5 patients; NA McGuire has 9 patients; NA Hicks has 10 patients; NA Garcia has 10 patients; NA James has 14 patients; and NA Davis has 7 patients. What is the average number of patients per nursing assistant? a. 6 b. 7 c. 8 d. 9 e. 10 - ANS d. First, add the number of patients to find the total: 63. Then, divide the number of patients by the number of nursing assistants: 63 divided by 7 is 9. A patient's hospice stay cost one-fourth as much as his visit to the emergency room. His home nursing cost twice as much as his hospice stay. If his total health care bill was $140,000, how much did his home nursing cost? a. $10,000 b. $20,000 c. $40,000 d. $60,000 e. $80,000 - ANS c. Let E = emergency room cost; H = hospice cost, which is (1/4)E; N = home nursing cost, which is 2H, or 2(1/4)E. The total bill is E + H + N, which is E + (1/4)E + (2/4)E = 140,000. Add the left side of the equation to get (7/4)E = 140,000. To solve for E, multiply both sides of the equation by (4/7)E = 140,000(4/7), or 80,000. H = (1/4)E, or 20,000, and N = 2H, or 40,000. At a certain school, half of all the students are female and one-twelfth of the students are from outside the state. Half of the out-of-state students are also female. What proportion of the students would you expect to be females from outside the state? a. 1/12 b. 1/24 c. 1/8 d. 1/6 e. 1/3 - ANS b. If half the students are female, then you would expect half of the out-of-state students to be female. One-half of 1/12 is 1/24. Based on the following information, estimate the weight of a person who is 5′5″ tall. Height Weight 5′ 110 lbs. 6′ 170 lbs. a. 125 b. 130 c. 135 d. 140 e. 145 - ANS c. A foot in height makes a difference of 60 pounds, or 5 pounds per inch of height over 5′. A person who is 5′5″ is (5)(5 pounds), or 25 pounds, heavier than the person who is 5′, so add 25 pounds to 110 pounds to get 135 pounds. During exercise, a person's heart rate should be between 60% and 90% of the difference between 220 and the person's age. According to this guideline, what should a 30-year-old person's maximum heart rate be during exercise? a. 114 b. 132 c. 156 d. 171 e. 198 - ANS d. The difference between 220 and this person's age is 190. The maximum heart rate is 90% of this: (0.9)(190) = 171. A certain water pollutant is unsafe at a level of 20 ppm (parts per million). A city's water supply now contains 50 ppm of this pollutant. What percentage of improvement will make the water safe? a. 20% b. 30% c. 40% d. 50% e. 60% - ANS e. An amount equaling 30 ppm of the pollutant would have to be removed to bring the 50 ppm down to 20 ppm (30 ppm is 60% of 50 ppm). A study shows that 600,000 women die each year in pregnancy and childbirth, one-fifth more than scientists previously estimated. How many such deaths did the scientists previously estimate? a. 120,000 b. 240,000 c. 300,000 d. 480,000 e. 500,000 - ANS e. Let E = the estimate. One-fifth more than the estimate would be 6/5, or 120%, of E, so 600,000 = (1.20)(E). Dividing both sides by 1.2 leaves E = 500,000. What is 250 milligrams in terms of grams? a. 0.0250 grams b. 0.250 grams c. 2.50 grams d. 25 grams e. 250,000 grams - ANS b. In terms of grams, 250 milligrams is 250/1000 gram, or 0.250 grams. An Army food supply truck can carry three tons. A breakfast ration weighs 12 ounces, and the other two daily meals weigh 18 ounces each. Assuming each soldier gets three meals per day, on a 10-day trip, how many soldiers can be supplied by one truck? a. 100 soldiers b. 150 soldiers c. 200 soldiers d. 320 soldiers e. 270 soldiers - ANS c. Three tons = 6,000 pounds. At 16 ounces per pound, 6,000 pounds = 96,000 ounces that can be carried by the truck. The total weight of each daily ration is 12 ounces + 18 ounces + 18 ounces = 48 ounces per soldier per day, and 96,000/48 = 2,000. So 2,000/10 days = 200 soldiers supplied. A train must travel 3,450 miles in six days. How many miles must it travel each day? a. 525 b. 550 c. 600 d. 575 e. 625 - ANS d. The total number of miles, 3,450, divided by 6 days is 575 miles. A dormitory now houses 30 men and allows 42 square feet of space per man. If five more men are put into this dormitory, how much less space will each man have? a. 5 square feet b. 6 square feet c. 7 square feet d. 8 square feet e. 9 square feet - ANS b. The present number of men, 30, multiplied by 42 square feet of space is 1,260 square feet of space; 1,260 square feet divided by 35 men is 36 square feet, so each man will have 6 square feet of space less. Ron is half as old as Sam, who is three times as old as Ted. The sum of their ages is 55. How old is Ron? a. 5 years old b. 10 years old c. 15 years old d. 20 years old e. 30 years old - ANS c. Let T = Ted's age; S = Sam's age = 3T; R = Ron's age = S/2 , or 3T/2 . The sum of the ages is 55, which means T + 3T + 3T/2 = 55. To find the common denominator (2), you can add to the left side of the equation: T = 10. If Ted is 10, then Sam is 30, and Ron is 3T/2 , which is 15 years old.