Arithmetic Reasoning
2.7. 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 worked 48 hours a week? A. $2236.00 B. $2064.00 C. $774.00 D. $559.00 E. $516.00
A. $2236.00
3.9. 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*5280)/60 B. (60*5280)/30 C. (30*60)/5280 D. 30/(60*5280) E. 30/(60*5280
A. (30*5280)/60
3.5. (1/5) * ((1/4)+(5/8)-(3/2)) = A. -(1/8) B. (1/8) C. (5/8) D. (7/8) E. -(2/5)
A. -(1/8)
3.17. 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. -(5/56)
2.19. 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 35ft long by 12ft wide, how many raised beds will he need to build? A. 14 B. 10.5 C. 7.5 D. 7 E. 5
A. 14
2.13. (See Graph) If this budget is kept over an individual's lifetime and that individual averages $4000 a month income over his/her lifetime, what percentage of total earnings will be saved? A. 14% B. 28% C. 4% D. .14% E. .28%
A. 14%
3.22. Solve: (1/5)((1/5)+6*5) A. 6(1/25) B. 6(1/5) C. 1(1/5) D. 1(1/25) E. 1/25
A. 6(1/25)
2.16. How many quarts are in 15 gallons? A. 60 qt. B. 40 qt. C. 4 qt. D. 12 qt. E. 80 qt.
A. 60 qt.
2.3. The smallest angle of a non-right triangle is 5º and the largest is 100º. If the longest side of the triangle is 20", what is the value of the third angle? A. 75 ° B. .75° C. 1.77" D. .80° E. 7.5°
A. 75 °
2.24. A company interviewed 21 applicants for a managerial position. All of them had relevant experience. Seven of the applicants had held a 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. 9
2.11. (See Graph) 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. $1728
2.1. 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
B. $2.78
2.10. 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. $40
2.6. If a broken water line is leaking 3 quarts of water every minute, how many gallons of water will be lost in one day? A. 360 B. 1,080 C. 5,000 D. 36,000 E. 108,000
B. 1,080
2.22. 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. 255
B. 1,785
3.8. Simplify: -|3^2 - 10| + |-(3)^2 - 2| A. 9 B. 10 C. 11 D. 12 E. 13
B. 10
3.2. If 2𝑥 − 𝑦 = 18, what is the value of (4^x)/(2^y)? A. 2^2 B. 2^18 C. 4^2 D. 5^2 E. 18^2
B. 2^18
3.20. A company wants to determine how many of its 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 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. 338
3.7. 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 does the Labrador weigh? A. 35.4 lbs. B. 40.0 lbs. C. 53.8 lbs. D. 59.8 lbs. E. 60.0 lbs.
B. 40.0 lbs.
2.23. 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. 60
3.24. (See Chart) What is the annual growth rate of the investment, given annual compounding? A. 5% B. 8% C. 10% D. 16% E. none of the above
B. 8%
2.12. (See Graph) According to this budget, how much money will an individual who makes $2000 a month save in one year? A. $30 B. $300 C. $3360 D. $36,000 E. nothing
C. $3360
3.16. Which of the following represents 3/5 ? A. 5/6 B. .50 C. .60 D. 5% E. 6%
C. .60
2.20. 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. .13% B. .10% C. 13% D. 15% E. 23%
C. 13%
3.18. 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 total 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. 15
2.5. 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. .48% B. 83% C. 18% D. 26% E. 28%
C. 18%
3.4. A bakery sells muffins in boxes of 4 and cupcakes in boxes of 6. The baker determines that he sold 140 cupcakes and muffins—a total of 30 boxes in one day. How many boxes of muffins did he sell? A. 10 B. 15 C. 20 D. 25 E. 30
C. 20
3.1. 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. 3/2, 9/4, 27/8, 81/16, 243/32
2.25. 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 bag 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. 8/10
3.14. (See Graph) 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 change by the same amount. E. There is no change in values.
C. Median
2.18. 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. $3.50
3.25. If the investment continues to grow at the same rate, what will the account balance be in year five? A. $4,353.56 B. $50,388.48 C. $54,419.56 D. $58,773.13 E. $63,474.99
D. $58,773.13
2.8. The population of Centerville has increased from 350,000 to 500,000 people in the last ten years. On average, the population increases by how many people each year? A. 1000 B. 10,000 C. 12,500 D. 15,000 E. 150,000
D. 15,000
3.21. What is the probability of drawing either an ace or a king from a deck of cards? A. .13% B. 7.69% C. 13% D. 15.38% E. 25%
D. 15.38%
3.13. (See Graph) What is the average number of recipes in each chapter of the cookbook? A. 10 B. 13 C. 15 D. 21 E. 36
D. 21
2.17. 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. 26 ft.
2.2. 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. 30
3.10. 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. 900
3.11. 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. {6,7}
3.6. The average temperature in Cincinnati last month was 34° F. The temperature fluctuated from 7 degrees below that average to 7 degrees 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 - 34| = 7
D. |34 - t| = 7
3.23. 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 | + 1 D. 𝑥 + 𝑦 E. zero
D. 𝑥 + 𝑦
1.12. 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) 1 hour 20 minutes
1.23. In the sequence below, each term is found by multiplying the previous two terms and subtracting four. What is the next term in the sequence? {4, 6, 20, 116...} a) 2316 b) 2320 c) 2324 d) 2784 e) 2788
a) 2316
1.17. Erika took a poll and discovered that students at her school preferred apple pie to cherry pie at a ratio of 4:5. If 200 students preferred apple pie, how many preferred cherry pie? a) 250 b) 300 c) 325 d) 375 e) 500
a) 250
1.15. 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) 30y - 20x
1.4. A laptop is on sale for $825. It originally cost $1,250. By what percentage has it been marked down? a) 34% b) 37% c) 52% d) 63% e) 66%
a) 34%
4.13. Juan plans to spend 25% of is workday writing a report. If he is at work for 9 hours, how many hours will he spend writing the report? a. 2.25 b. 2.50 c. 2.75 d. 3.25 e. 4.00
a. 2.25
4.20. A high school football team played 12 games in a season. If they won 75 percent of their games, how many games did they lose? a. 3 b. 4 c. 6 d. 9 e. 10
a. 3
4.10 Allison used 2(1/2) cups of flower to make a cake, and (3/4) of a cup of flour to make a pie. If she started with 4 cups of flour, how many cups of flour does she have left? a. 3/4 b. 1 c. 5/4 d. 5/2 e. 13/4
a. 3/4
4.9. Lynn has 4 test scores in science class. Each test is worth 100 points, and Lynn has an 85% average. If Lynn scored 100% on each of the first 3 tests, what did she score on her 4th test? a. 40% b. 55% c. 60% d. 85% e. 100%
a. 40%
4.15. Justin has a summer lawn care business and earns $40 for each lawn he mows. He also pays $35 per week in business expenses. Which if the following expressions represents Justin's profit after x weeks if he mows m number of lawns. a. 40m - 35x b. 40m + 35x c. 35x(40+ m) d. 35(40m +x) e. 40x(35 +m)
a. 40m - 35x
4.4. The average speed of cars on a highway (s) is inversely proportional to the number of cars on the road (n). If a car drives at 65 mph when there are 250 cars on the road, how fast will a car drive when there are 325 cars on the road? a. 50 mph b. 55 mph c. 60 mph d. 85 mph e. 87 mph
a. 50 mph
4.12. Valerie receives a base salary of $740 a week for working 40 hours. For every extra hour she works, she is paid at a rate of $27.75 per hour. If Valerie works t hours in a week, which of the following equations represents the amount of money, A, she will receive? a. A= 740 + 27.75(t - 40) b. A= 740 + 27.75(40 - t) c. A= 740 - 27.75(40 - t) d. A= 27.75t- 740 e. A= 27.75t + 740
a. A= 740 + 27.75(t - 40
1.13. Leanne earns $10 per hour at her part-time job. She earns $15 per hour if she works on holidays. During the week of Christmas, Leanne works four hours on Tuesday, six hours on Wednesday, and four hours on Thursday. If Christmas falls on Thursday, how much will Leanne earn that week? a) $140 b) $160 c) $180 d) $190 e) $210
b) $160
1.3. Solve the proportion for x: (5x-8)/3 = (x+4)/2 ' a) 3 b) 4 c) 5 d) 6 e) 7
b) 4
1.22. 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) 432
1.8. 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) 5 hours
4.11. Alex cleans houses and charges $25 per bedroom, $35 per bathroom, and $40 per kitchen. If he cleans a house with 4 bedrooms 2 bathrooms, and 1 kitchen, how much will h be paid? a. $205 b. $210 c. $215 d. $230 e. $245
b. $210
4.5. If three burgers and two orders of fries cost $26.50 and a burger costs $6.50, how much does one order of fries cost? a. $1.75 b. $3.50 c. $6.75 d. $7.00 e $10.00
b. $3.50
4.6. A worker was paid $15,036 for 7 months of work. If he received the same amount for each month, how much was he paid for the first 2 months? a. $2,148 b. $4,296 c. $5,137 d. $6,444 e. $8,592
b. $4,296
4.24. In the sequence below, each term is found by finding the difference between the previous two numbers and multiplying the result by -3. What is the 6th term of the sequence? {3, 0, -9, -36, ... } a. -81 b. -135 c. 45 d. 81 e. 135
b. -135
4.25. If the length of a rectangle is increased by 40% and its width is decreased by 40%, what is the effect on the rectangle's area? a. The area is the same. b. It increases by 16%. c. It increases by 20%. d. It decreases by 16%. e. It decreases by 20%.
b. It increases by 16%.
1.18. 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) $19
1.5. If |x - 5| = 35, what are the possible values for x? a) 20, 30 b) -25, 30 c) -30, 40 d) 30, 45 e) 45, 50
c) -30, 40
1.16. Vanessa is bringing cakes for a birthday party. If each cake serves 8 people and there will be 48 guests, how many cakes should she buy? a) 3 b) 4 c) 6 d) 9 e) 12
c) 6
1.6. A card is drawn from a standard deck. What is the probability that the card is either red or a king? a) 2/13th b) 4/13th c) 7/13th d) 8/13th e) 10/13th
c) 7/13th
1.1. 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% of the second test, and 80% on the third test, which of the following is closest to his average score? a) 71 b) 72 c) 78 d) 82 e) 83
c) 78
4.19. Maria paid $24.65 for her meal at a restaurant. If that price included a tax of 8.25 percent, what was the price of the meal before tax? a. $22.61 b. $22.68 c. $22.77 d. $22.82 e. $22.93
c. $22.77
4.8. The population of a town was 7,250 in 2014 and 7,375 in 2015. What as the percent increase from 2014 to 2015 to the nearest tenth of a percent? a. 1.5% b. 1.6% c. 1.7% d. 1.8% e. 2.0%
c. 1.7%
4.17. If a plane travels 2775 miles in 3 hours, how far will it travel in 5 hours? a. 1655 miles b. 3475 miles c. 4625 miles d. 5,550 miles e. 13,875 miles
c. 4625 miles
4.16. Micah has invited 23 friends to his house and is having pizza for dinner. If each pizza feeds 4 people, how many pizzas should he order? a. 4 b. 5 c. 6 d. 7 e. 8
c. 6
4.18. In the fall, 425 students pass the math benchmark. In the spring, 680 students pass the same benchmark. What is the percentage increase in passing scores from fall to spring. a. 37.5% b. 55% c. 60% d. 62.5% e. 80%
c. 60%
4.1. A high school cross country team sent 25% of its runners to a regional competition. Of these, 10% won medals. If 2 runners earned medals, how many members does the cross country team have? a. 8 b. 10 c. 80 d. 125 e. 1250
c. 80
1.14. 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 bedrooms, a kitchen, and a living room, how much will he earn? a) $300 b) $380 c) $385 d) $395 e) $410
d) $395
1.2. What is 2/5ths expressed as a decimal? a) .2 b) .3 c) .35 d) .4 e) .45
d) .4
1.11. Damian used 2/3rd cup of sugar to make pancakes and 1 and 2/3rd cups of sugar to make muffins. If he started with 5 cups of sugar, how much sugar will be left over? a) 1/3rd b) 1 1/3rd c) 2 1/3rd d) 2 2/3rd e) 3 1/3rd
d) 2 2/3rd
1.25. Leslie earns $12 hour as a babysitter. The family she works for also pays her an additional $5 per day for picking their child up 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) 205
1.24. Carl took a survey to determine which sports are played by the students in his class. 25% of the students in his class play only basketball 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) 21
1.7. Convert 2 feet to inches. a) 12 inches b) 16 inches c) 18 inches d) 24 inches e) 36 inches
d) 24 inches
1.20. Find the next number in the sequence: 3, 9, 27, 81... a) 84 b) 90 c) 162 d) 243 e) 324
d) 243
1.21. 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) 33.3%
4.21 Aprille has $50 to buy the items on her shopping list. Assuming there is no sales tax, about how much change will Aprille receive after buying all the items on her list. Aprille's List Hammer - $13.24 Screwdriver - $11.99 Nails - $4.27 Wrench - $5.60 a. $12 b. $13 c. $14 d. $15 e. $16
d. $15
4.7 The probability of drawing a blue marble from a bag of marbles is (1/20) and the probability of drawing a red marble from the same bag is (7/20) What is the probability of drawing a blue marble or a red marble? a. (1/10) b. (3/10) c. (7/10) d. (2/5) e. (1/2)
d. (2/5)
4.14 if triangle ABD is approximately triangle DEF and the similarity ratio is 3:4, what is the measure of DE if AB =12? a. 6 b. 9 c. 12 d. 16 e. 96
d. 16
4.3. If a person reads 40 pages in 45 minutes, approximately how many minutes will it take her to read 265 pages? a. 202 b. 236 c. 265 d. 298 e. 300
d. 298
1.19. The probability of drawing a white marble from a bag of marbles is ¼. The probability of drawing a black marble from the same bag is also ¼. 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) 1/2
1.9. If seven apples and six bananas cost $3.65 and one banana costs 20 cents, how much does one apple cost? a) 10 cents b) 15 cents c) 20 cents d) 25 cents e) 35 cents
e) 35 cents
1.10. 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) 6.5%
4.23. A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore both blue and white. What is the number of applicants who wore neither blue nor white? a. 1 b. 6 c. 8 d. 12 e. 13
e. 13
4.2. Convert 55 meter to feet (round to the nearest tenth of a foot) a. 16.8ft b. 21.7ft c. 139.7ft d. 165.0ft e. 180.4ft
e. 180.4ft
4.22. A fruit stand sells apples, bananas, and oranges at a ration of 3:2:1. If the fruit stand sells 20 bananas, how many total pieces of fruit does the fruit stand sell? a. 10 b. 30 c. 40 d. 50 e. 60
e. 60
2.4. 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. 11:33
2.14. One-third (1/3) of the students in John's history class are seniors and 2/3rd are juniors. There are 28 students, and 4/7th are female. How many are male? A. 21 B. 4 C. 5 D. 16 E. 12
E. 12
3.3 If a, b, and c are different positive integers, and 2^a × 2^b × 2^c = 64, then 2^a + 2^b + 2^c = ____. A. 2 B. 4 C. 6 D. 10 E. 14
E. 14
3.15. 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. 18π
2.9. 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 minutes and 0 seconds B. 4 minutes and 4 seconds C. 3 minutes and 4 seconds D. 3 minutes and 54 seconds E. 3 minutes and 56 seconds
E. 3 minutes and 56 seconds
3.19. A woman is jogging at a rate of 2 meters per second. Given that there are .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. 393
3.12 (See Graph) What is the ratio of soup recipes to salad recipes, expressed as a percentage? A. 10% B. 16% C. 36% D. 38% E. 63%
E. 63%
2.15. Sarah will spend 3/4ths of her workday writing a report. If she is at work for 9½ hours, how many whole hours will she spend on the report? A. 1 B. 9 C. 6 D. 8 E. 7
E. 7
2.21. If a driver averages 70 miles per hour and drives 10 hours per day, how many days will it take to drive 1400 miles? A. less than one day B. one full day C. more than one day D. less than two days E. two full days
E. two full days
