Arithmetic Reasoning Practice Test

Practice test questions — Arithmetic Reasoning

1. A pizza is cut into 12 equal slices. If 4 people share the pizza equally, how many slices does each person get?

   • 2 slices
   • 3 slices ✓
   • 4 slices
   • 6 slices

   This is a basic division problem: 12 slices ÷ 4 people = 3 slices per person. Word problems on the ASVAB require translating the situation into a math operation. Look for keywords: 'share equally' or 'divided equally' indicates division; 'total' or 'altogether' indicates addition; 'how much more' or…

2. A truck driver drove 240 miles in 4 hours. What was the average speed?

   • 40 miles per hour
   • 50 miles per hour
   • 60 miles per hour ✓
   • 70 miles per hour

   Average speed = total distance ÷ total time = 240 miles ÷ 4 hours = 60 miles per hour. This is the basic rate formula: rate × time = distance, which rearranges to rate = distance ÷ time. The same formula handles many ASVAB problems: speed, work rate, flow rate, production rate. Three-variable proble…

3. What is 3/4 + 1/3?

   • 4/7
   • 4/12
   • 13/12 ✓
   • 1/12

   To add fractions with different denominators, find the common denominator. Least common multiple of 4 and 3 is 12. Convert: 3/4 = 9/12 (multiply by 3/3), 1/3 = 4/12 (multiply by 4/4). Add: 9/12 + 4/12 = 13/12. The answer is 13/12 or 1 1/12 as a mixed number. Common mistakes: adding numerators and de…

4. What is 15% of 80?

   • 8
   • 12 ✓
   • 15
   • 20

   Percent of a number = (percent ÷ 100) × number. 15% of 80 = 0.15 × 80 = 12. Three methods to solve percent problems: (1) Convert percent to decimal and multiply: 15% = 0.15; 0.15 × 80 = 12. (2) Use the fraction equivalent: 15% = 15/100; (15/100) × 80 = 1200/100 = 12. (3) Set up proportion: 15/100 = …

5. If a shirt that originally costs $50 is on sale for 20% off, what is the sale price?

   • $30
   • $40 ✓
   • $45
   • $48

   Two ways to solve: (1) Calculate the discount, then subtract: 20% of $50 = 0.20 × $50 = $10 discount; $50 - $10 = $40 sale price. (2) Calculate the percent remaining and multiply: 100% - 20% = 80% remaining; 80% of $50 = 0.80 × $50 = $40 sale price. Method 2 is often faster on the ASVAB. Be careful …

6. If 5 pounds of apples cost $4, how much would 15 pounds of apples cost?

   • $8
   • $10
   • $12 ✓
   • $14

   Set up a proportion: 5 pounds / $4 = 15 pounds / x. Cross-multiply: 5x = 60. Divide: x = $12. Alternative thinking: 15 pounds is 3 times 5 pounds, so the cost is also 3 times: 3 × $4 = $12. Either method works. Proportions are central to many ASVAB problems: cooking (recipe scaling), maps (distance …

7. The ratio of cats to dogs at a shelter is 3:5. If there are 24 cats, how many dogs are there?

   • 15
   • 20
   • 30
   • 40 ✓

   Set up the ratio as a proportion. Cats/dogs = 3/5 = 24/x. Cross-multiply: 3x = 120. Solve: x = 40 dogs. Alternative: cats are 3 'parts', and there are 24 actual cats; so each 'part' = 24/3 = 8. Dogs are 5 parts; 5 × 8 = 40 dogs. Total animals would be 24 + 40 = 64, with 3:5 ratio confirmed (24:40 re…

8. How much simple interest does $1,000 earn at 5% annual interest over 3 years?

   • $50
   • $100
   • $150 ✓
   • $300

   Simple interest formula: I = P × r × t, where P is principal, r is rate (as decimal), t is time (in years). I = 1000 × 0.05 × 3 = $150. The simple interest formula is straightforward: just multiply principal × rate × time. Watch units: rate must be in the same time unit as time (annual rate with yea…

9. What is the average of these test scores: 70, 75, 80, 85, 90?

   • 75
   • 78
   • 80 ✓
   • 85

   Average (mean) = sum of values ÷ number of values. Sum: 70 + 75 + 80 + 85 + 90 = 400. Count: 5 values. Average: 400 ÷ 5 = 80. Three types of averages: Mean — what most people call 'average', the sum divided by count. Median — the middle value when sorted (or mean of two middle values if even count);…

10. A student's first three test scores are 80, 75, and 90. What score must the student earn on the fourth test to average exactly 85?

    • 85
    • 90
    • 95 ✓
    • 100

    To average 85 over four tests, the total of all four scores must be 4 × 85 = 340. Current total: 80 + 75 + 90 = 245. Required fourth score: 340 - 245 = 95. Verification: (80 + 75 + 90 + 95) ÷ 4 = 340/4 = 85 ✓. This 'find the missing value to achieve an average' problem appears regularly on the ASVAB…

11. What is the area of a rectangle that is 8 feet long and 5 feet wide?

    • 13 square feet
    • 26 square feet
    • 40 square feet ✓
    • 45 square feet

    Area of a rectangle = length × width = 8 × 5 = 40 square feet. Common geometry formulas tested on ASVAB: Rectangle area = L × W; Square area = side²; Triangle area = (1/2) × base × height; Circle area = π × radius² (use π ≈ 3.14 or 22/7). Rectangle perimeter = 2L + 2W; Square perimeter = 4 × side; C…

12. A rectangular swimming pool is 20 feet long, 10 feet wide, and 5 feet deep. What is its volume?

    • 100 cubic feet
    • 500 cubic feet
    • 1,000 cubic feet ✓
    • 1,500 cubic feet

    Volume of a rectangular prism (or box) = length × width × height = 20 × 10 × 5 = 1,000 cubic feet. Volume formulas commonly tested: Rectangular prism = L × W × H; Cube = side³; Cylinder = π × r² × h; Sphere = (4/3) × π × r³. Volume units: cubic feet (cu ft or ft³), cubic meters, gallons (1 cu ft ≈ 7…

13. Sergeant Johnson has 24 soldiers in her platoon. She wants to divide them into squads of equal size. If she creates 4 squads, how many soldiers are in each squad?

    • 4
    • 6 ✓
    • 8
    • 12

    Division problem: 24 soldiers ÷ 4 squads = 6 soldiers per squad. Verification: 6 × 4 = 24 ✓. Military-themed word problems are common on the ASVAB. Key skill: translating context to operation. 'Divide equally' or 'split into equal groups' is division. Variations might ask: How many squads of 8 can s…

14. Convert 0.375 to a fraction in lowest terms.

    • 3/4
    • 3/8 ✓
    • 5/8
    • 7/8

    0.375 = 375/1000. Simplify by dividing both by greatest common factor. 375 ÷ 125 = 3; 1000 ÷ 125 = 8. So 0.375 = 3/8. Common decimal-fraction equivalents to memorize: 0.5 = 1/2; 0.25 = 1/4; 0.75 = 3/4; 0.125 = 1/8; 0.375 = 3/8; 0.625 = 5/8; 0.875 = 7/8; 0.333... = 1/3; 0.666... = 2/3; 0.1 = 1/10; 0.…

15. A car travels 200 miles using 8 gallons of gas. At this rate, how many miles can the car travel on 12 gallons?

    • 240 miles
    • 280 miles
    • 300 miles ✓
    • 320 miles

    Method 1 (proportion): 200 miles / 8 gallons = x miles / 12 gallons; cross-multiply: 8x = 2400; x = 300 miles. Method 2 (unit rate): 200 miles ÷ 8 gallons = 25 miles per gallon; 25 × 12 = 300 miles. Both methods give the same answer. Fuel efficiency problems are common on the ASVAB and in real milit…

16. A jacket is marked up 40% from its cost. If the cost is $30, what is the selling price?

    • $36
    • $40
    • $42 ✓
    • $50

    Markup is added to cost to determine selling price. Markup = 40% of $30 = 0.40 × $30 = $12. Selling price = cost + markup = $30 + $12 = $42. Alternative: selling price = cost × (1 + markup percentage as decimal) = $30 × 1.40 = $42. The second method is faster — multiplying by 1.40 is one step. Disti…

17. A soldier carries 45 pounds of gear. If the gear is reduced by 1/3, what is the new weight?

    • 15 pounds
    • 20 pounds
    • 25 pounds
    • 30 pounds ✓

    Method 1 (subtract the reduction): 1/3 of 45 = 15 pounds reduction; 45 - 15 = 30 pounds new weight. Method 2 (multiply by the fraction remaining): if 1/3 is removed, 2/3 remains; 2/3 × 45 = 30 pounds. Both give the same answer. Fractional reduction is similar to percent reduction. Useful shortcuts: …

18. A truck driver drove 320 miles in 4 hours, then 360 miles in 6 hours. What was the average speed over the entire trip?

    • 60 mph
    • 65 mph
    • 68 mph ✓
    • 70 mph

    Average speed over entire trip = total distance / total time. Total distance: 320 + 360 = 680 miles. Total time: 4 + 6 = 10 hours. Average speed: 680/10 = 68 mph. Important: this is NOT the average of the two individual speeds! Speed 1: 320/4 = 80 mph; Speed 2: 360/6 = 60 mph. Simple average of spee…

19. What is 2.5 × 0.4?

    • 0.1
    • 1.0 ✓
    • 10.0
    • 100.0

    Multiply as if integers: 25 × 4 = 100. Then count decimal places in the original numbers: 2.5 has 1 decimal place; 0.4 has 1 decimal place. Total decimal places: 2. Place the decimal in the answer: 1.00 or 1.0. So 2.5 × 0.4 = 1.0. Quick check: 2.5 is between 2 and 3; 0.4 is less than half. So the an…

20. A circular fountain has a diameter of 14 feet. What is its circumference? (Use π ≈ 22/7)

    • 22 feet
    • 44 feet ✓
    • 154 feet
    • 616 feet

    Circumference = π × diameter. Using π ≈ 22/7: C = (22/7) × 14 = 22 × 2 = 44 feet. Alternative: C = 2 × π × radius; radius = diameter/2 = 7; C = 2 × (22/7) × 7 = 2 × 22 = 44 feet. Both forms of the formula give the same answer. When diameter is a multiple of 7, using π = 22/7 makes the arithmetic cle…

21. If 3 workers can complete a job in 8 hours, how many hours will it take 4 workers to complete the same job? (Assume all workers work at the same rate.)

    • 6 hours ✓
    • 8 hours
    • 10 hours
    • 12 hours

    This is an inverse proportion problem — more workers means less time, not more. Total work = workers × time = 3 × 8 = 24 worker-hours. With 4 workers: time = 24/4 = 6 hours. The product 'workers × time' stays constant; more workers reduces time proportionally. Direct proportion (more of one means mo…

22. A bank account earns 4% annual simple interest. After 2 years, the account has $1,080. What was the original deposit?

    • $1,000 ✓
    • $1,020
    • $1,040
    • $1,060

    Let P = original principal. Simple interest formula: A = P(1 + rt), where A is the final amount, r is the rate, t is the time. $1,080 = P(1 + 0.04 × 2) = P(1.08). Solve: P = $1,080/1.08 = $1,000. Verification: interest = $1,000 × 0.04 × 2 = $80; total = $1,000 + $80 = $1,080 ✓. This 'reverse' intere…

23. A military supply truck carries 250 cases of rations. Each case contains 24 individual meals. How many meals total are in the truck?

    • 274 meals
    • 1,200 meals
    • 6,000 meals ✓
    • 10,000 meals

    Multiplication problem: 250 × 24 = 6,000 meals. Calculation strategies: (1) Standard multiplication: 250 × 24 = 250 × 20 + 250 × 4 = 5,000 + 1,000 = 6,000. (2) Doubling: 250 × 24 = 500 × 12 = 1000 × 6 = 6,000 (doubling one factor and halving the other gives the same product). (3) Mental math: 250 × …

24. If the average of 5 numbers is 30, what is the sum of the 5 numbers?

    • 6
    • 35
    • 150 ✓
    • 300

    Sum = average × count = 30 × 5 = 150. This is the basic rearrangement of the average formula: average = sum/count, therefore sum = average × count. This relationship is the key to many average problems. Variations: (1) 'Average of 4 numbers is 25; if one number is removed and the new average is 23, …

25. A rectangular room measures 12 feet by 15 feet. Carpet costs $4 per square foot. How much will it cost to carpet the entire room?

    • $54
    • $180
    • $540
    • $720 ✓

    Multi-step problem: first find the area, then multiply by the unit cost. Area = 12 × 15 = 180 square feet. Cost = 180 × $4 = $720. Common mistake: computing the perimeter (2 × 12 + 2 × 15 = 54 feet) instead of the area — but carpet covers the floor area, not just the perimeter. The perimeter would b…

26. A truck travels 420 miles using 28 gallons of diesel. What is the fuel economy in miles per gallon?

    • 12 mpg
    • 15 mpg ✓
    • 18 mpg
    • 21 mpg

    420 ÷ 28 = 15 miles per gallon. Division word problem: divide total miles by total gallons to find miles per gallon.

27. A recipe calls for 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed for 8 cups of sugar?

    • 10
    • 11
    • 12 ✓
    • 14

    Set up the proportion: 3/2 = x/8. Cross-multiply: 2x = 24, so x = 12 cups of flour.

28. A rectangular room is 15 feet long and 12 feet wide. How many square feet of carpet are needed to cover the floor?

    • 27 sq ft
    • 54 sq ft
    • 108 sq ft
    • 180 sq ft ✓

    Area = length × width = 15 × 12 = 180 square feet.

29. What is 15% of 240?

    • 24
    • 30
    • 36 ✓
    • 40

    15% of 240 = 0.15 × 240 = 36. Convert percent to decimal (÷100) then multiply.

30. A soldier earns $2,400 per month. After deductions of $360 for taxes and $120 for insurance, what is the take-home pay?

    • $1,800
    • $1,920 ✓
    • $2,040
    • $2,160

    Total deductions = $360 + $120 = $480. Take-home = $2,400 - $480 = $1,920.

31. If 5 workers can complete a job in 8 days, how many days would 10 workers take to complete the same job?

    • 2
    • 4 ✓
    • 6
    • 16

    Inverse proportion: 5 workers × 8 days = 10 workers × d days. d = 40 ÷ 10 = 4 days.

32. A jacket costs $80. It is on sale for 25% off. What is the sale price?

    • $20
    • $55
    • $60 ✓
    • $65

    25% of $80 = $20 discount. Sale price = $80 - $20 = $60.

33. A soldier scored 72, 85, 91, and 80 on four tests. What is the average (mean) score?

    • 81
    • 82 ✓
    • 83
    • 84

    Sum = 72 + 85 + 91 + 80 = 328. Mean = 328 ÷ 4 = 82.

34. A circular target has a radius of 7 inches. What is its area? (Use π ≈ 3.14)

    • 43.96 sq in
    • 87.92 sq in
    • 153.86 sq in ✓
    • 219.8 sq in

    Area = π r² = 3.14 × 7² = 3.14 × 49 ≈ 153.86 square inches.

35. A soldier uses 3/8 of a fuel can. The can held 16 gallons. How many gallons were used?

    • 4
    • 5
    • 6 ✓
    • 8

    3/8 × 16 = 48/8 = 6 gallons.

36. A convoy of 6 trucks each carries 4.5 tons of supplies. What is the total cargo weight?

    • 24 tons
    • 25 tons
    • 27 tons ✓
    • 30 tons

    6 × 4.5 = 27 tons total cargo weight.

37. On a map, 1 inch represents 50 miles. Two cities are 3.5 inches apart on the map. How far apart are they in actual miles?

    • 150 miles
    • 175 miles ✓
    • 200 miles
    • 225 miles

    3.5 × 50 = 175 miles. Scale proportion: inches × miles-per-inch = actual miles.

38. A unit ran 5 miles, 6 miles, 7 miles, 4 miles, and 8 miles over five days. What was the median daily distance?

    • 5 miles
    • 6 miles ✓
    • 7 miles
    • 8 miles

    Arrange in order: 4, 5, 6, 7, 8. The median (middle value) is 6 miles.

39. An item costs $1,200. With 6% sales tax, what is the total price?

    • $1,272 ✓
    • $1,268
    • $1,206
    • $1,260

    Tax = 6% × $1,200 = $72. Total = $1,200 + $72 = $1,272.

40. A rectangular container is 4 feet long, 3 feet wide, and 2 feet deep. What is its volume in cubic feet?

    • 9
    • 18
    • 24 ✓
    • 36

    Volume = length × width × height = 4 × 3 × 2 = 24 cubic feet.

41. A car travels 240 miles on 8 gallons of gas. How many miles per gallon does it get?

    • 28 mpg
    • 30 mpg ✓
    • 32 mpg
    • 26 mpg

    MILES PER GALLON = total miles ÷ gallons used = 240 ÷ 8 = 30 mpg. ASVAB Arithmetic Reasoning tests rate/word problems. 'Per gallon' signals division (miles divided by gallons). Set it up as a unit rate: 240 miles / 8 gallons = 30 miles/gallon. Strategy: identify what's being asked (a rate, 'per' som…

42. A shirt originally costs $40 and is on sale for 25% off. What is the sale price?

    • $10
    • $30 ✓
    • $35
    • $32

    SALE PRICE = original − discount. The discount is 25% of $40 = 0.25 × 40 = $10. Sale price = $40 − $10 = $30. ASVAB Arithmetic Reasoning tests percentage problems. SHORTCUT: 25% off means you pay 75% (100% − 25%): 0.75 × $40 = $30. Either method gives $30. Strategy: convert the percentage to a decim…

43. A recipe uses 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how many cups of sugar do you need?

    • 4 cups
    • 6 cups ✓
    • 5 cups
    • 8 cups

    Set up a PROPORTION: flour/sugar = 3/2 = 9/x. Cross-multiply: 3x = 2 × 9 = 18, so x = 6 cups of sugar. ASVAB Arithmetic Reasoning tests ratios/proportions. SHORTCUT: 9 cups of flour is 3 times the original 3 cups (9 ÷ 3 = 3), so multiply the sugar by 3 too: 2 × 3 = 6 cups. Strategy: keep the ratio c…

44. If 5 workers can build a wall in 12 days, how long would it take 10 workers (working at the same rate)?

    • 24 days
    • 6 days ✓
    • 10 days
    • 8 days

    This is an INVERSE proportion — more workers means LESS time. Total work = 5 workers × 12 days = 60 worker-days. With 10 workers: 60 ÷ 10 = 6 days. ASVAB Arithmetic Reasoning tests work-rate problems. KEY INSIGHT: doubling the workers (5 to 10) halves the time (12 to 6 days). Strategy: for inverse r…

45. A store buys an item for $60 and sells it for $75. What is the percent markup?

    • 15%
    • 25% ✓
    • 20%
    • 30%

    PERCENT MARKUP = (increase ÷ original cost) × 100. The increase is $75 − $60 = $15. Markup = (15 ÷ 60) × 100 = 0.25 × 100 = 25%. ASVAB Arithmetic Reasoning tests percent change. Strategy: percent increase/markup is always based on the ORIGINAL (cost) amount, not the new price. Find the difference ($…

46. Three people split a restaurant bill of $90 equally, then add a $18 tip split equally. How much does each person pay in total?

    • $30
    • $36 ✓
    • $34
    • $38

    Total to split = bill + tip = $90 + $18 = $108. Split among 3 people: $108 ÷ 3 = $36 each. ASVAB Arithmetic Reasoning tests multi-step word problems. ALTERNATE: split each part separately — bill: $90 ÷ 3 = $30; tip: $18 ÷ 3 = $6; total per person: $30 + $6 = $36. Both methods give $36. Strategy: for…

47. A tank is 3/4 full. After 12 gallons are removed, it is 1/2 full. What is the total capacity of the tank?

    • 36 gallons
    • 48 gallons ✓
    • 24 gallons
    • 60 gallons

    The 12 gallons removed represents the difference between 3/4 and 1/2 of the tank: 3/4 − 1/2 = 3/4 − 2/4 = 1/4. So 1/4 of the tank = 12 gallons. Total capacity = 12 × 4 = 48 gallons. ASVAB Arithmetic Reasoning tests fraction word problems. Strategy: find what fraction of the whole the known amount re…

48. A train leaves at 2:00 PM traveling at 60 mph. How far has it traveled by 5:30 PM?

    • 180 miles
    • 210 miles ✓
    • 195 miles
    • 240 miles

    DISTANCE = rate × time. Time elapsed from 2:00 PM to 5:30 PM = 3.5 hours. Distance = 60 mph × 3.5 hours = 210 miles. ASVAB Arithmetic Reasoning tests distance-rate-time problems (d = r × t). Strategy: carefully calculate the time (3 hours 30 minutes = 3.5 hours, NOT 3.3), then multiply by the rate. …

49. A jacket is marked down 20%, then an additional 10% is taken off the sale price. If the original price was $100, what is the final price?

    • $70
    • $72 ✓
    • $68
    • $75

    Successive discounts must be applied ONE AT A TIME (not added together). First discount: 20% off $100 → pay 80% → 0.80 × $100 = $80. Second discount: 10% off $80 → pay 90% → 0.90 × $80 = $72. ASVAB Arithmetic Reasoning tests successive percentages. COMMON ERROR: adding 20% + 10% = 30% off ($70) is W…

50. If a 15% tip on a meal is $9, what was the cost of the meal?

    • $45
    • $60 ✓
    • $54
    • $72

    If 15% of the meal = $9, then the meal cost = $9 ÷ 0.15 = $60. ASVAB Arithmetic Reasoning tests working backward from a percentage. Set up: 0.15 × (meal) = $9, so meal = 9 ÷ 0.15 = $60. Strategy: when given the result of a percentage and asked for the original, DIVIDE by the decimal form of the perc…

51. A soldier must pack 156 rations into boxes that each hold 12 rations. How many full boxes can be packed, and how many rations are left over?

    • 12 boxes, 0 left over
    • 13 boxes, 0 left over ✓
    • 13 boxes, 5 left over
    • 11 boxes, 4 left over

    This is a division word problem. Divide 156 by 12: 12 × 13 = 156 exactly, so 156 ÷ 12 = 13 with no remainder. That means 13 full boxes can be packed with 0 rations left over. The key skill in arithmetic reasoning is translating words into the correct operation — 'pack into boxes that each hold' sign…

52. A recipe calls for 3/4 cup of flour. If you want to make 2/3 of the recipe, how much flour do you need?

    • 1/2 cup ✓
    • 5/12 cup
    • 1 1/3 cups
    • 7/12 cup

    To find a fraction of a fraction, multiply them: 3/4 × 2/3 = (3 × 2)/(4 × 3) = 6/12 = 1/2 cup. The word 'of' between fractions means multiply. Multiply the numerators (3 × 2 = 6) and the denominators (4 × 3 = 12), then reduce 6/12 to 1/2. A useful shortcut is to cancel before multiplying: the 3 in t…

53. A map uses a scale where 1 inch represents 25 miles. If two cities are 4.5 inches apart on the map, how far apart are they in reality?

    • 100 miles
    • 112.5 miles ✓
    • 125 miles
    • 29.5 miles

    Set up a proportion using the scale: 1 inch / 25 miles = 4.5 inches / x miles. Cross-multiply: 1 × x = 25 × 4.5, so x = 112.5 miles. Scale and proportion problems are solved by writing the known ratio equal to the unknown ratio and cross-multiplying. Here each inch is 25 miles, so 4.5 inches is simp…

54. A jacket originally priced at $80 is discounted 25%. What is the sale price?

    • $55
    • $60 ✓
    • $65
    • $20

    A 25% discount means you subtract 25% of the price. First find the discount: 25% of $80 = 0.25 × 80 = $20. Then subtract from the original: $80 − $20 = $60. A faster method is to recognize that after a 25% discount you pay 75% of the original: 0.75 × $80 = $60. Discount problems test whether you can…

55. How much simple interest is earned on $1,500 invested at 4% annual interest for 3 years?

    • $60
    • $180 ✓
    • $1,680
    • $200

    Simple interest uses the formula I = P × r × t, where P is the principal, r is the annual rate as a decimal, and t is the time in years. Here I = $1,500 × 0.04 × 3 = $60 × 3 = $180. The interest earned is $180. Note the question asks only for the interest, not the total balance — the total would be …

56. A rectangular room is 12 feet long and 9 feet wide. How many square feet of carpet are needed to cover the floor?

    • 21 square feet
    • 42 square feet
    • 108 square feet ✓
    • 120 square feet

    The area of a rectangle is length × width. Here area = 12 ft × 9 ft = 108 square feet. Carpeting a floor is an area problem, so you multiply the two dimensions. Be careful not to confuse area with perimeter: the perimeter (distance around) would be 2 × (12 + 9) = 42 feet, which is offered as a distr…

57. A student scored 82, 90, and 95 on three tests. What score must the student earn on a fourth test to have an average of 90?

    • 88
    • 90
    • 93 ✓
    • 95

    To average 90 over four tests, the total of all four scores must be 4 × 90 = 360. The three known scores add to 82 + 90 + 95 = 267. The needed fourth score is 360 − 267 = 93. Average problems where you must find a missing value are solved by working from the required total: multiply the desired aver…

58. If 3 workers can complete a job in 8 hours, how long would it take 4 workers, assuming they all work at the same rate?

    • 6 hours ✓
    • 8 hours
    • 10.7 hours
    • 12 hours

    This is an inverse proportion: more workers means less time. The total work is 3 workers × 8 hours = 24 worker-hours. With 4 workers, time = 24 worker-hours ÷ 4 workers = 6 hours. In inverse-proportion (work-rate) problems, the product of workers and time stays constant for the same job. Compute the…

59. A car travels 165 miles using 5.5 gallons of gas. What is the car's fuel efficiency in miles per gallon?

    • 25 mpg
    • 30 mpg ✓
    • 33 mpg
    • 27.5 mpg

    Miles per gallon is total miles divided by gallons used: 165 ÷ 5.5 = 30 mpg. Rate problems like this are solved by dividing the quantity (miles) by the unit you want it per (gallons). To divide by 5.5, you can multiply both numbers by 2 to clear the decimal: 330 ÷ 11 = 30. The car gets 30 miles per …

60. Convert the fraction 7/8 to a decimal.

    • 0.78
    • 0.875 ✓
    • 0.87
    • 0.7

    To convert a fraction to a decimal, divide the numerator by the denominator: 7 ÷ 8 = 0.875. You can do this by long division, or by recognizing common conversions (1/8 = 0.125, so 7/8 = 7 × 0.125 = 0.875). Fraction-to-decimal conversions appear in arithmetic reasoning when comparing values or comput…

61. A circular garden has a radius of 7 feet. Using π ≈ 22/7, what is its area?

    • 44 square feet
    • 154 square feet ✓
    • 22 square feet
    • 308 square feet

    The area of a circle is π × r². Here r = 7, so r² = 49, and area = (22/7) × 49 = 22 × 7 = 154 square feet. Using 22/7 for π is convenient when the radius is a multiple of 7 because the 7 cancels neatly. Don't confuse area (πr²) with circumference (2πr); the circumference here would be 2 × (22/7) × 7…

62. A store marks up an item that costs $40 by 30%. What is the selling price?

    • $12
    • $52 ✓
    • $70
    • $48

    A markup is added to the cost. First find the markup: 30% of $40 = 0.30 × 40 = $12. Then add it to the cost: $40 + $12 = $52. Equivalently, a 30% markup means selling at 130% of cost: 1.30 × $40 = $52. Markup problems are the mirror image of discount problems — you add the percentage instead of subt…

63. The average of five numbers is 20. If four of the numbers are 18, 22, 25, and 15, what is the fifth number?

    • 20 ✓
    • 18
    • 20.5
    • 100

    If the average of five numbers is 20, their total is 5 × 20 = 100. The four known numbers add to 18 + 22 + 25 + 15 = 80. The fifth number is 100 − 80 = 20. The method for a missing value in an average is always the same: multiply the average by the count to get the required total, then subtract the …

64. A photograph that is 4 inches by 6 inches is enlarged so the shorter side becomes 10 inches. What is the new length of the longer side, keeping the same proportions?

    • 12 inches
    • 15 inches ✓
    • 16 inches
    • 14 inches

    Keeping the same proportions means the ratio of sides stays constant. Original ratio is 4:6. Set up a proportion with the new short side: 4/6 = 10/x. Cross-multiply: 4x = 60, so x = 15 inches. Proportional scaling problems are solved by matching corresponding sides in a ratio and cross-multiplying. …

65. A worker earns $18 per hour and works 7.5 hours. After $24 is withheld for taxes, what is the take-home pay?

    • $135.00
    • $111.00 ✓
    • $159.00
    • $108.00

    First compute gross pay: $18 × 7.5 hours = $135. Then subtract the withholding: $135 − $24 = $111 take-home pay. Multi-step word problems require doing the operations in the right order: earnings first (rate × hours), then deductions. To multiply $18 by 7.5, note 18 × 7 = 126 and 18 × 0.5 = 9, so 12…