AFOQT: Arithmetic Reasoning
Rock - 45.5%; Country - 27.5%; Rap - 15%; Jazz - 7.5%; Classical - 4.5% Based on the pie chart (metrics above), which type of music represents 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
b
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
b
solve the proportion for x: (5x-8)/3 = (x+4)/2 a. 3 b. 4 c. 5 d. 6 e. 7
b
A baker sells muffins in boxes of 4 and cupcakes in boxes of 6. He does an inventory at the end of he day and determines that he sold 30 boxes of baked goods containing 140 cupcakes and muffins. How many boxes of muffins did he sell? a. 10 b. 15 c. 20 d. 25 e. 30
c
A bed is 4 feet wide by 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
c
A cadet spent three days studying for the Arithmetic Knowledge section of the AFOQT, two days studying vocabulary for the Word Knowledge section, and a total of six days studying for the physical science section. What percentage of study time did the cadet spend preparing for the word knowledge section? a. 0.48% b. 83% c. 18% d. 26% e. 28%
c
A card is drawn from a standard deck. What is the probability that the card is either red or a king? a. 2/13 b. 4/13 c. 7/13 d. 8/13 e. 10/13
c
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 entrance way. 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
c
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
c
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
c
An aquarium has a base length of 12 inches and a width of 5 inches. if the aquarium is 10 inches tall, what is its total volume. a. 480 cubic inches b. 540 cubic inches c. 600 cubic inches d. 720 cubic inches e. 920 cubic inches
c
An organization is recruiting volunteers for a fundraiser. The volunteers can either set-up tables before the event or hand out flyers during the event. Each person can set up 6 tables per hour or hand out 20 flyers per hour. If each volunteer works for 3 hours, how many volunteers will the organization need to set up 180 tables and distribute 300 flyers. a. 5 b. 10 c. 15 d. 20 e. 25
c
Andrew needs to save $50 to buy his girlfriend a birthday present. He will put aside some of the money he makes in tips over the next month in order to save enough. Assuming Andrew makes $20 in tips every day that he works and he works 5 days a week, what percentage of his weekly earnings will he need to save? a. 0.13% b. 0.10% c. 13% d. 15% e. 23%
c
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
c
Entrees-43, Desserts-36, Appetizer-13, salads-8, soups-5 Which will change the most if a chapter with 25 side dishes is added to the book: the range, mean, or median number of recipes per chapter? a. range b. mean c. median d. all values are changed by the same amount e. there is no change in values
c
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
c
If |x-5| = 35, what are possible values for x? a. 20, 30 b. -25, 30 c. -30, 40 d. 30, 45 e. 45, 50
c
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
c
Lauren budgeted $200 for new school clothes. She spent $36 on a skirt, $27 on a blouse, $73 on a dress, and $45 on shoes. Assuming there is no sales tax, how much will she receive in change? a. 12 b. 17 c. 19 d. 32 e. 36
c
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%
c
Out out 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
c
Ralph has taken three tests in history class and he wants to calculate his average test score so far. If he scored 70% on the first test, 85% on the second test, and 80% on the third test which of the following is closest to his average score? a. 71 b. 72 c. 73 d. 82 e. 83
c
Rent - 48%; Food - 24%; Savings - 14%; Other 14% According to this budget, how much money will an individual who makes $2000 a month save in one year? a. $30 b. $300 c. $3,360 d. $36,000 e. nothing
c
The probability of drawing a blue marble from a bag of marbles is 1/10 and the probability of drawing a white marble from the same is 7/10. What is the probability of drawing a blue or white marble? a. 6/10 b. 6/20 c. 8/10 d. 8/20 e. 7/100
c
The smallest angle of a non-right triangle is 5° and the largest is 100°. If the longest side of the triangle is 20", what is the length of the shortest side? a. 75" b. 0.75" c. 1.77" d. 0.56" e. 17.90"
c
Which of the following represents 3/5? a. 5/6 b. 0.5 c. 0.6 d. 5% e. 6%
c
Which of the following sequences is an example of exponential growth? a. (1/2), (3/2), (5/2), (7/2), (9/2) b. (2/3), (4/9), (8/27), (16/81), (32/243) c. (3/2), (9/4), (27/8), (81/16), (243/32) d. 4, 8, 12, 16, 20 e. 5, 15, 45, 135, 405
c
A cook prepared a total of 50 hot dogs and hamburgers for his customers. Half of the hot dogs were eaten; 10 were leftover. How many hamburgers were prepared? a. 10 b. 25 c. 5 d. 30 e. 20
d
At East Valley High School, the ratio of boys to the entire student population is 3:7. If there are 1,200 girls in the school, how many boys are there a. 300 b. 400 c. 700 d. 900 e. 1100
d
The probability of drawing a white marble from a bag of marbles is 1/4. The probability of drawing a black marble from the same bag is also 1/4. What is the probability of drawing a white or black marble? a. 1/10 b. 1/8 c. 1/6 d. 1/4 e. 1/2
e
Tom and Alice left their home in separate vehicles at the exact same time. Tom arrived at their destination in 28 minutes and 32 seconds. Alice arrived in 32 minutes and 28 seconds. what was the difference in driving time. a. 4'0" b. 4'4" c. 3'4" d. 3'54" e. 3'56"
e
in 2013, there were 784 students in Jose's school. In 2014, there were 835 students. What was the percentage increase between 2013 and 2014, rounded to the nearest tenth of a percent? a. 5.5% b. 5.7% c. 6% d. 6.2% e. 6.5%
e
one third can be expressed as which of the following ratios? a. 0 b. 33:11 c. 3:1 d. 1:1 e. 11:33
e
Jenna needs to bake 240 cookies for her catering job. If Jenna can bake two dozen cookies in 30 minutes, approximately how long will it take her to fill this order? a. 3 hours b. 5 hours c. 6 hours d. 7 hours e. 8 hours
b
Kylie noticed that her golden retriever puppy has gained 30% more weight than her Labrador puppy. When she first got the dogs, they both weighed 20 lbs, but the retriever now weighs 46 lbs. how much the lab weigh? a. 35.4 lbs b. 40.0 lbs c. 53.8 lbs d. 59.8 lbs e. 60.0 lbs
b
Simplify: -|3²-10|+|-(3)²-2| a. 9 b. 10 c. 11 d. 12 e. 13
b
Vanessa is bringing cakes for a birthday party. If each cake serves 8 people and there will be 48 guest, how many cakes should she buy? a. 3 b. 4 c. 6 d. 9 e. 12
C
(1/5) x [(1/4)+(5/8)-(3/2)] = a. -1/8 b. 1/8 c. 5/8 d. 7/8 e. -2/5
a
A company interviewed 21 applicants for a managerial position. All of them had relevant experience. Seven of the applicants had held management position in the last 5-10 years, while five more had held management positions over 10 years ago. How many of the applicants had been managers in the past five years? a. 9 b. 12 c. 15 d. 20 e. none
a
A latop is on sale for $825. it originally cost $1250. By what percentage has it been marked down? a. 34% b. 37% c. 52% d. 63% e. 66%
a
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 sandwiches and four cookies d. three sandwiches and no cookies e. three sandwiches and two cookies
a
A truck is moving at a speed of 30 miles per hour. Given that there are 5,280 feet in one mile, which expression accurately represents the truck's speed in feet per minute? a. (30 x 5280)/60 b. (60 x 5280)/30 c. (30 x 60)/5280 d. 30/(60 x 5280) e. 30/(60 x 5280)
a
Basic cable television service, which includes 16 channels, cost $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
a
Erika took a poll and discovered that students at her school preferred apple pie to cheery pie at a ratio of 4:5. If 200 student preferred apple pie, how many preferred cherry? a. 250 b. 300 c. 325 d. 375 e. 500
a
In the sequence below, each term is found by multiplying the previous two terms and subtracting four. What is the next term in the the sequence? 4, 6, 20, 116 a. 2316 b. 2320 c. 2324 d. 2784 e. 2788
a
One third (1/3) of students in John's history class are seniors and 2/3 are juniors. There are 28 students, 4/7 are female. How many are male? a. 21 b. 4 c. 5 d. 16 e. 12
e
Sarah will spend 3/4 of her workday writing a report. If she is at work for 9_(1/2) hours, how many whole hours will she spend on the report? a. 1 b. 9 c. 6 d. 8 e. 7
e
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
b
Maria collects $150 for office party supplies. If she spends $5 on drinks, $50 on food, $25 on decorations, and $2 each on 15 party favors, how much money will she have left? a. $46 b. $40 c. $36 d. $30 e. none
b
Rent - 48%; Food - 24%; Savings - 14%; Other 14% According to this budget, how much does an individual who makes $2400 a month spend on food and rent? a. $1152 b. $1728 c. $238 d. $728 e. $2000
b
If a driver average 70 miles per hour and drives 10 hours per day, how many days will it take to drive 1400 miles? a. less than one b. one full day c. more than one day d. less than two days e. two full days
e
If a, b, and c are different positive integers, and 2^a x 2^b x 2^c = 64, then 2^a + 2^b +2^c = a. 2 b. 4 c. 6 d. 10 e. 14
e
If seven apples and six bananas cost $3.65 and one banana cost 20 cents, how much does one apple cost? a. 10 cents b. 15 cents c. 20 cents d. 25 cents e. 35 cents
e
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
e
Leanne earns $10 per hour at her part-time job. She earns $15 per hour if she works holidays. During the week of X-mas, Leanne works four hours on Tuesday, six hours on Wednesday, and four hours on Thursday. If X-mas falls on Thursday, how much will Leanne earn that week? a. $140 b. $160 c. $180 d. $180 e. $210
b
Annette sells handmade necklaces. She earns $30 for each necklace. The cost of materials is $20 per week. Which of the following expressions represents Annette's' profit after x weeks if she makes y number of necklaces? a. 30y-20x b. 20y-30x c. 30y-20 d. 20y-30 e. 30y-20
a
Maria has 40 math problems to complete for homework. It takes her 5 minutes to complete each problem. She plans to complete her homework over the weekend. If she does two hours of work on Saturday, how much time will it take her to finish her homework on Sunday? a. 1 hour 20 minutes b. 1 hour 30 minutes c. 1 hour 40 minutes d. 1 hour 50 minutes e. 2 hours 10 minutes
a
Nate is planning a garden with rectangular raised beds measuring 5ft long by 2ft wide. He will line both sides of his driveway with flower beds. If his driveway is 35 ft long by 12 ft wide, how many raised beds will he need to build? a. 14 b. 10.5 c. 7.5 d. 7 e. 5
a
Rent - 48%; Food - 24%; Savings - 14%; Other 14% If this budget is kept over an individual's lifetime and that individual average $4000 a month income over his lifetime, what percentage of total earnings will be saved? a. 14% b. 28% c. 4% d. 0.14% e. 0.28%
a
Simplify: 2_5/8 + 6/7 - 3_4/7 a. -5/56 b. 1_51/56 c. -1_5/7 d. 1_5/7 e. -1_51/56
a
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
a
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.% b. 9.0% c. 15% d. 30% e. 40%
a
You are considering a short-term job that pays $10.75/hr. for a 40-hour work week and 1.5 times the base pay for any overtime. How much would you earn in a month if you work 48 hours a week? a. $2,2236.00 b. $2064.00 c. $774.00 d. $559.00 e. $516.00
a
how many quarts are in 15 gallons? a. 60 qt. b. 40 qt. c. 4 qt. d. 12 qt. e. 80 qt.
a
solve 1/5 x (1/5 + 6 x 5) a. 6_1/25 b. 6_1/5 c. 1_1/5 d. 1_1/25 e. 1/25
a
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
b
If 2x-y = 18, what is the value of (4^x)/(2^y)? a. 2² b. 2¹⁸ c. 4² d. 5² e. 18²
b
If a broken water line is leaking 3 quarts of water every minute, how many gallons of water will be lost in day? a. 360 b. 1,080 c. 5,000 d. 36,000 e. 108,000
b
If a car travels 324 miles in 6 hours, how many miles will it travel in 8 hours? a. 385 b. 432 c. 439 d. 486 e. 601
b
A bakery sells baguettes, bagels, and croissants at a ratio of 15:10:5. If the bakery sells 20 bagels, how many total baked goods does it sell? a. 80 b. 60 c. 40 d. 20 e. 4
b
A company wants to determine how many employees capitalize on casual Fridays and wear blue jeans or other casual clothes to work on Fridays. Administrators surveyed the number of junior staff wearing casual clothes to work on the last Friday of March. Out of the 650 junior staff, 48% were dressed casually. How many junior staff were wearing more formal clothes that day? a. 312 b. 338 c. 360 d. 384 e. none of the above
b
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
b
A truck is carrying apples and oranges at a ratio of 4:3. If there are 1,020 apples on the truck, how many total pieces of fruit are there? a. 3,060 b. 1,785 c. 765 d. 340 e. 225
b
Basic cable television service, which includes 16 channels, cost $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 the basic cable service? a. 25% b. 33% c. 50% d. 75% e. 85%
d
Carl took a survey to determine which sports are played by the student in his class. 25% of the students in his class play on only basket ball and 50% play only baseball. The remaining 25% do not play any sports. If there are 28 students in Carl's class, how many students play either basketball or baseball? a. 7 b. 14 c. 18 d. 21 e. 25
d
Convert 8 meters to feet and round to the nearest foot. a. 2 ft b. 3 ft c. 25 ft d. 26 ft e. 27 ft
d
Damian used 2/3 cups of sugar to make pancakes and 1_(2/3) cups sugar to make muffins. If he started with 5 cups of sugar, how much sugar will be left over? a. 1/3 b. 1_(1/3) c. 2_(1/3) d. 2_(2/3) e. 3_(1/3)
d
Entrees-43, Desserts-36, Appetizer-13, salads-8, soups-5 What is the average number of recipes in each of the cookbook? a. 10 b. 13 c. 15 d. 21 e. 36
d
Fifteen percent (15%) is the standard rate for tipping waitpersons in U.S. restaurants. If the bill for a meal totals $18.53, how much should the tip be. a. $18.50 b. $2.78 c. $1.85 d. $2.77 e. $27.80
d
Find the next number in the sequence: 3, 9, 27, 81 a. 84 b. 90 c. 162 d. 243 e. 324
d
Find the solution set for the following equation: x-6 = √x-6) a. 6 b. 7 c. -6,7 d. 6,7 e. √6
d
If three sandwiches and two small salads cost $26.50 and each sandwich cost $6.50, how much does a small salad cost? a. $0 b. $1.50 c. $3.00 d. $3.50 e. $6.50
d
If x is a negative number and y is a positive number, what is the absolute value of x plus the absolute value of y? a. |-x+y| b. -(x+y) c. |-x-y| d. x+y e. zero
d
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
d
Jerry has a house painting business. He charges $40 to paint bathrooms, $55 to paint bedrooms, $70 to paint kitchens, and $80 to paint living rooms. If he paints a house with two bathrooms, three bedroom, a kitchen, and a living room, how much will he earn? a. $300 b. $380 c. $385 d. $395 e. $410
d
Leslie earns $12 per hour as a babysitter. The family she works for also pays her an additional $5 per day for picking up their child from school. If Leslie works for three hours a day, Monday through Friday, how much will she earn each week. a. $180 b. $185 c. $200 d. $205 e. $225
d
Rock - 45.5%; Country - 27.5%; Rap - 15%; Jazz - 7.5%; Classical - 4.5% If 400 total songs were downloaded, how many downloads were country music? a. 11 b. 28 c. 55 d. 110 e. 270
d
Samantha's softball team played 18 games during their last season. They won 12 of their games. What percentage of their games did they lose? a. 12% b. 16% c. 18% d. 33.3% e. 66.6%
d
The average temperature in Cincinnati last month was 34° F. The temperature fluctuated from 7° below that average and 7° above it. Which equation represents the high and low temperature, t, in Cincinnati for the month? a. |t+7| = 34 b. |t+34| = 7 c. |t-7| = 34 d. |34-t|= 7 e. |t-43| = 7
d
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 adult, one 15 year old, and one 10 year old at 7:00 P.M. on a Sunday night? a. $17.00 b. $19.50 c. $25.00 d. $27.50 e. $37.50
d
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 afternoon at 1:00 P.M. e. none of the above
d
The population of centerville has increased from 350,000 to 500,000 people in the last ten year. on average, the population increases by how many people each year? a. 1,000 b. 10,000 c. 12,500 d. 15,000 e. 150,000
d
What is 2/5 as a decimal? a. .2 b. .3 c. .35 d. 4 e. .45
d
What is the probability of drawing either an ace or a king from a deck of cards? a. 0.13% b. 7.69% c. 13% d. 15.38% e. 25%
d
convert 2 feet to inches a. 12 inches b. 16 inches c. 18 inches d. 24 inches e. 36 inches
d
A woman is jogging at a rate of 2 meters per second. Given that there are 0.305 meters in one foot, what is the woman's speed in feet per minute, rounded to the nearest whole number? a. 93 b. 152 c. 153 d. 305 e. 393
e
An engineering student is building a model of a cone-shaped building at a scale of 3:450. If the building has a volume of 2700π, what is the volume of the model? a. π b. 4π c. 5.5π d. 16π e. 18π
e
Entrees-43, Desserts-36, Appetizer-13, salads-8, soups-5 What is the ratio of soup recipes to salads recipes expressed as a percentage? a. 10% b. 16% c. 36% d. 38% e. 63%
e
