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AFQT practice questions

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Question 1Arithmetic Reasoning (AR)

Evaluate 12 + 3 × (8 − 5).

  1. 21 Correct answer.
  2. 36
  3. 15
  4. 45

Explanation

Use order of operations: evaluate the parentheses first, so 8 − 5 = 3. Then multiply 3 × 3 = 9 and add 12 + 9 = 21.

Question 2Arithmetic Reasoning (AR)

What is 20% of 150?

  1. 35
  2. 30 Correct answer.
  3. 25
  4. 45

Explanation

Convert 20% to 0.20 and multiply by 150: 0.20 × 150 = 30. A percent of a number is found by multiplying the decimal form by the number.

Question 3Arithmetic Reasoning (AR)

A rope is 6 feet long. How many inches long is the rope?

  1. 84 inches
  2. 66 inches
  3. 60 inches
  4. 72 inches Correct answer.

Explanation

There are 12 inches in 1 foot, so multiply 6 by 12. The rope is 6 × 12 = 72 inches long.

Question 4Arithmetic Reasoning (AR)

A student scored 80, 85, 90, and 95 on four tests. What is the average score?

  1. 85
  2. 87.5 Correct answer.
  3. 86.5
  4. 90

Explanation

Add the scores: 80 + 85 + 90 + 95 = 350. Divide the sum by 4 to get the average: 350 ÷ 4 = 87.5.

Question 5Arithmetic Reasoning (AR)

What is 1/4 + 3/8?

  1. 7/8
  2. 5/8 Correct answer.
  3. 1/2
  4. 3/4

Explanation

Rewrite 1/4 as 2/8 so the fractions have a common denominator. Then 2/8 + 3/8 = 5/8.

Question 6Arithmetic Reasoning (AR)

A recipe uses 2 cups of flour for every 3 cups of milk. If 8 cups of flour are used, how many cups of milk are needed?

  1. 12 cups Correct answer.
  2. 14 cups
  3. 10 cups
  4. 16 cups

Explanation

The flour amount is multiplied by 4, since 2 × 4 = 8. Multiply the milk amount by the same factor: 3 × 4 = 12 cups.

Question 7Arithmetic Reasoning (AR)

A rectangle has a length of 9 meters and a width of 5 meters. What is its perimeter?

  1. 28 meters Correct answer.
  2. 14 meters
  3. 18 meters
  4. 45 meters

Explanation

The perimeter of a rectangle is 2 × (length + width). Here, 2 × (9 + 5) = 2 × 14 = 28 meters.

Question 8Arithmetic Reasoning (AR)

A shopper pays for a $12.75 item with a $20 bill. How much change should the shopper receive?

  1. $7.75
  2. $7.00
  3. $6.25
  4. $7.25 Correct answer.

Explanation

Subtract the item price from the amount paid: $20.00 − $12.75 = $7.25. The change is $7.25.

Question 9Arithmetic Reasoning (AR)

A jacket regularly priced at $80 is reduced by 25%. What is the sale price?

  1. $55
  2. $60 Correct answer.
  3. $20
  4. $65

Explanation

A 25% discount means the shopper pays 75% of the original price. Multiply $80 by 0.75 to get $60.

Question 10Arithmetic Reasoning (AR)

On a map, 1 inch represents 40 miles. How many miles does 3.5 inches represent?

  1. 160 miles
  2. 120 miles
  3. 180 miles
  4. 140 miles Correct answer.

Explanation

Multiply the map distance by the scale: 3.5 × 40 = 140. So 3.5 inches represents 140 miles.

Question 11Arithmetic Reasoning (AR)

The average of five numbers is 18. Four of the numbers are 15, 17, 20, and 18. What is the fifth number?

  1. 18
  2. 19
  3. 20 Correct answer.
  4. 22

Explanation

The five numbers must total 5 × 18 = 90. The four known numbers total 15 + 17 + 20 + 18 = 70, so the fifth number is 90 − 70 = 20.

Question 12Arithmetic Reasoning (AR)

A machine makes 120 parts in 8 minutes. At the same rate, how many parts does it make in 15 minutes?

  1. 210 parts
  2. 180 parts
  3. 225 parts Correct answer.
  4. 200 parts

Explanation

Find the unit rate: 120 ÷ 8 = 15 parts per minute. Multiply by 15 minutes: 15 × 15 = 225 parts.

Question 13Arithmetic Reasoning (AR)

What is the simple interest on $500 at an annual rate of 4% for 3 years?

  1. $60 Correct answer.
  2. $75
  3. $20
  4. $120

Explanation

Use the simple interest formula I = P × r × t. Here, $500 × 0.04 × 3 = $60.

Question 14Arithmetic Reasoning (AR)

A student answered 45 of 60 questions correctly. What percent of the questions did the student answer correctly?

  1. 70%
  2. 75% Correct answer.
  3. 80%
  4. 85%

Explanation

Divide the number correct by the total: 45 ÷ 60 = 0.75. Convert 0.75 to a percent by multiplying by 100 to get 75%.

Question 15Arithmetic Reasoning (AR)

A triangle has a base of 12 centimeters and a height of 7 centimeters. What is its area?

  1. 42 square centimeters Correct answer.
  2. 21 square centimeters
  3. 56 square centimeters
  4. 84 square centimeters

Explanation

The area of a triangle is 1/2 × base × height. Here, 1/2 × 12 × 7 = 42 square centimeters.

Question 16Arithmetic Reasoning (AR)

A 24-ounce box of cereal costs $4.80. What is the cost per ounce?

  1. $0.18
  2. $0.15
  3. $0.20 Correct answer.
  4. $0.24

Explanation

Divide the total cost by the number of ounces: $4.80 ÷ 24 = $0.20 per ounce. The unit price is 20 cents per ounce.

Question 17Arithmetic Reasoning (AR)

A car travels 195 miles in 3 hours. What is its average speed in miles per hour?

  1. 60 mph
  2. 75 mph
  3. 70 mph
  4. 65 mph Correct answer.

Explanation

Average speed equals total distance divided by total time. Divide 195 by 3 to get 65 miles per hour.

Question 18Arithmetic Reasoning (AR)

A recipe uses 3/4 cup of sugar to make 12 cookies. How much sugar is needed to make 20 cookies at the same rate?

  1. 1.75 cups
  2. 1.25 cups Correct answer.
  3. 1.50 cups
  4. 1.00 cups

Explanation

Set up the proportion (3/4)/12 = x/20. Cross-multiply to get 12x = 15, so x = 1.25 cups.

Question 19Arithmetic Reasoning (AR)

The sum of three consecutive integers is 72. What is the largest of the three integers?

  1. 24
  2. 26
  3. 25 Correct answer.
  4. 23

Explanation

Let the integers be x, x + 1, and x + 2. Their sum is 3x + 3 = 72, so 3x = 69 and x = 23. The largest is 23 + 2 = 25.

Question 20Arithmetic Reasoning (AR)

A $40 item is subject to a 6% sales tax. What is the total cost including tax?

  1. $42.40 Correct answer.
  2. $40.60
  3. $41.20
  4. $42.00

Explanation

The sales tax is 6% of $40, or 0.06 × $40 = $2.40. Add the tax to the price: $40.00 + $2.40 = $42.40.

Question 21Arithmetic Reasoning (AR)

A price is increased by 20% and then decreased by 20%. What is the net change from the original price?

  1. No change
  2. 20% decrease
  3. 4% increase
  4. 4% decrease Correct answer.

Explanation

Multiplying by 1.20 and then by 0.80 gives 1.20 × 0.80 = 0.96. The final price is 96% of the original, which is a 4% decrease.

Question 22Arithmetic Reasoning (AR)

A 40-liter solution is 15% acid. How many liters of water must be added to make the solution 10% acid?

  1. 25 liters
  2. 15 liters
  3. 30 liters
  4. 20 liters Correct answer.

Explanation

The solution contains 0.15 × 40 = 6 liters of acid. To make 6 liters be 10% of the total, the total must be 6 ÷ 0.10 = 60 liters. Add 60 − 40 = 20 liters of water.

Question 23Arithmetic Reasoning (AR)

A driver travels 60 miles at 30 miles per hour and returns along the same route at 60 miles per hour. What is the average speed for the entire round trip?

  1. 45 mph
  2. 50 mph
  3. 40 mph Correct answer.
  4. 35 mph

Explanation

The trip out takes 60 ÷ 30 = 2 hours, and the return takes 60 ÷ 60 = 1 hour. The total distance is 120 miles and total time is 3 hours, so average speed is 120 ÷ 3 = 40 mph.

Question 24Arithmetic Reasoning (AR)

Pipe A can fill a tank in 6 hours, and Pipe B can fill the same tank in 12 hours. Working together, how long will they take to fill the tank?

  1. 5 hours
  2. 4 hours Correct answer.
  3. 3 hours
  4. 6 hours

Explanation

In one hour, Pipe A fills 1/6 of the tank and Pipe B fills 1/12. Together they fill 1/6 + 1/12 = 3/12 = 1/4 of the tank per hour, so they need 4 hours.

Question 25Arithmetic Reasoning (AR)

An item costs a store $80. The store marks the price up by 40%, then offers a 25% discount on the marked price. What is the final selling price?

  1. $84 Correct answer.
  2. $88
  3. $80
  4. $92

Explanation

A 40% markup makes the marked price $80 × 1.40 = $112. A 25% discount means the customer pays 75% of that price, so $112 × 0.75 = $84.

Question 26Arithmetic Reasoning (AR)

What is the value of 5 + 3 × (8 − 2)?

  1. 20
  2. 48
  3. 33
  4. 23 Correct answer.

Explanation

Evaluate the parentheses first: 8 − 2 = 6. Multiplication comes before addition, so 3 × 6 = 18, and then 5 + 18 = 23.

Question 27Arithmetic Reasoning (AR)

A carpenter has a board 7/8 inch thick and sands off 1/3 inch. What is the remaining thickness?

  1. 13/24 in
  2. 5/8 in
  3. 3/4 in
  4. 6/5 in Correct answer.

Explanation

Subtract the fractions using a common denominator of 24: 7/8 = 21/24 and 1/3 = 8/24. Then 21/24 − 8/24 = 13/24 inch.

Question 28Arithmetic Reasoning (AR)

A rope is 14 feet long. How many 8-inch pieces can be cut from it, with no rope left over?

  1. 21 Correct answer.
  2. 20
  3. 24
  4. 18

Explanation

Convert 14 feet to inches: 14 × 12 = 168 inches. Then divide by 8 inches per piece: 168 ÷ 8 = 21 pieces.

Question 29Arithmetic Reasoning (AR)

What is the median of the numbers 7, 3, 9, 15, and 11?

  1. 15
  2. 7
  3. 11
  4. 9 Correct answer.

Explanation

Arrange the numbers in order: 3, 7, 9, 11, 15. With five values, the median is the middle value, which is 9.

Question 30Arithmetic Reasoning (AR)

If 5 pounds of potatoes cost $6.25, what is the cost of 8 pounds at the same rate?

  1. $8.75
  2. $9.60
  3. $10.00 Correct answer.
  4. $12.50

Explanation

Find the unit price by dividing $6.25 by 5 pounds, which gives $1.25 per pound. Then multiply $1.25 by 8 pounds to get $10.00.

Question 31Arithmetic Reasoning (AR)

A school has 310 students. Each bus can carry 48 students. What is the least number of buses needed to transport all students?

  1. 5
  2. 7 Correct answer.
  3. 6
  4. 8

Explanation

Divide 310 by 48: 48 × 6 = 288, which leaves 22 students still needing transport. Since 6 buses are not enough, 7 buses are required.

Question 32Arithmetic Reasoning (AR)

A movie starts at 7:45 p.m. and runs for 2 hours 25 minutes. At what time does it end?

  1. 10:00 p.m.
  2. 10:25 p.m.
  3. 10:10 p.m. Correct answer.
  4. 9:10 p.m.

Explanation

Add 2 hours to 7:45 p.m. to get 9:45 p.m. Then add 25 minutes, giving 10:10 p.m.

Question 33Arithmetic Reasoning (AR)

A town's population increased from 1,200 to 1,500. What was the percent increase?

  1. 25% Correct answer.
  2. 15%
  3. 30%
  4. 20%

Explanation

The increase is 1,500 − 1,200 = 300 people. Divide the increase by the original population: 300 ÷ 1,200 = 0.25, which is 25%.

Question 34Arithmetic Reasoning (AR)

An amount of $84 is divided between two people in the ratio 3:4. What is the larger share?

  1. $42
  2. $48 Correct answer.
  3. $56
  4. $36

Explanation

The ratio has 3 + 4 = 7 equal parts. Each part is $84 ÷ 7 = $12, so the larger share is 4 × $12 = $48.

Question 35Arithmetic Reasoning (AR)

A $250 item is discounted 15%. Then an additional 10% is taken off the reduced price. What is the final price?

  1. $191.25 Correct answer.
  2. $175.00
  3. $187.50
  4. $200.00

Explanation

After the 15% discount, the price is $250 × 0.85 = $212.50. The additional 10% discount gives $212.50 × 0.90 = $191.25.

Question 36Arithmetic Reasoning (AR)

Four workers can build a wall in 12 days. At the same rate, how many days will 6 workers take?

  1. 6
  2. 18
  3. 9
  4. 8 Correct answer.

Explanation

The job requires 4 × 12 = 48 worker-days. Dividing 48 worker-days by 6 workers gives 8 days.

Question 37Arithmetic Reasoning (AR)

A circular track has a radius of 35 meters. Using π ≈ 22/7, what is the circumference of the track?

  1. 220 m Correct answer.
  2. 770 m
  3. 440 m
  4. 110 m

Explanation

The circumference formula is C = 2πr. Substitute r = 35 and π ≈ 22/7: C = 2 × (22/7) × 35 = 220 meters.

Question 38Arithmetic Reasoning (AR)

45 is what percent of 180?

  1. 40%
  2. 30%
  3. 25% Correct answer.
  4. 20%

Explanation

Divide the part by the whole: 45 ÷ 180 = 0.25. Multiply by 100 to convert the decimal to 25%.

Question 39Arithmetic Reasoning (AR)

A train travels 84 miles in 1 hour 45 minutes. What is its average speed in miles per hour?

  1. 56
  2. 48 Correct answer.
  3. 42
  4. 52

Explanation

Convert 1 hour 45 minutes to hours: 45 minutes is 0.75 hour, so the time is 1.75 hours. Divide distance by time: 84 ÷ 1.75 = 48 miles per hour.

Question 40Arithmetic Reasoning (AR)

A salesperson earns a 4% commission on total sales. If the commission is $1,200, what were the total sales?

  1. $30,000 Correct answer.
  2. $24,000
  3. $4,800
  4. $48,000

Explanation

Let sales be S. Then 0.04S = $1,200. Dividing both sides by 0.04 gives S = $30,000.

Question 41Arithmetic Reasoning (AR)

The sum of three consecutive even integers is 90. What is the smallest of the three integers?

  1. 28 Correct answer.
  2. 26
  3. 30
  4. 32

Explanation

Let the integers be n, n + 2, and n + 4. Their sum is 3n + 6 = 90, so 3n = 84 and n = 28. The smallest integer is 28.

Question 42Arithmetic Reasoning (AR)

A jar contains 24 red marbles and 36 blue marbles. What percent of the marbles are red?

  1. 24%
  2. 36%
  3. 60%
  4. 40% Correct answer.

Explanation

The total number of marbles is 24 + 36 = 60. The red fraction is 24/60 = 0.40, which is 40%.

Question 43Arithmetic Reasoning (AR)

If 6 identical books weigh 4.5 pounds, how much do 10 such books weigh?

  1. 6.0 lb
  2. 8.0 lb
  3. 7.5 lb Correct answer.
  4. 9.0 lb

Explanation

One book weighs 4.5 ÷ 6 = 0.75 pound. Ten books weigh 10 × 0.75 = 7.5 pounds.

Question 44Arithmetic Reasoning (AR)

After a 20% discount, a jacket sells for $64. What was the original price?

  1. $76.80
  2. $84
  3. $72
  4. $80 Correct answer.

Explanation

A 20% discount means the sale price is 80% of the original price. Let the original price be x; then 0.80x = $64, so x = $64 ÷ 0.80 = $80.

Question 45Arithmetic Reasoning (AR)

A trapezoid has bases of 8 cm and 14 cm and a height of 6 cm. What is its area?

  1. 84 cm²
  2. 66 cm² Correct answer.
  3. 44 cm²
  4. 132 cm²

Explanation

The area of a trapezoid is A = (b₁ + b₂) ÷ 2 × h. Substituting gives (8 + 14) ÷ 2 × 6 = 11 × 6 = 66 square centimeters.

Question 46Arithmetic Reasoning (AR)

How many ounces of a 20% acid solution must be mixed with 8 ounces of a 50% acid solution to produce a 30% acid solution?

  1. 20 oz
  2. 24 oz
  3. 12 oz
  4. 16 oz Correct answer.

Explanation

Let x be the ounces of 20% solution. The acid equation is 0.20x + 0.50(8) = 0.30(x + 8). Solving gives 0.20x + 4 = 0.30x + 2.4, so 1.6 = 0.10x and x = 16 ounces.

Question 47Arithmetic Reasoning (AR)

Worker A can complete a job in 10 days, and Worker B can complete it in 15 days. They work together for 3 days, and then A leaves. How many more days does B need to finish the job alone?

  1. 9
  2. 5
  3. 7.5 Correct answer.
  4. 6

Explanation

Together they complete 1/10 + 1/15 = 1/6 of the job per day. In 3 days they finish 3 × 1/6 = 1/2 of the job, leaving 1/2. B completes 1/15 per day, so B needs (1/2) ÷ (1/15) = 7.5 more days.

Question 48Arithmetic Reasoning (AR)

A tank is 40% full. After 18 gallons of water are added, the tank is 70% full. What is the tank's full capacity in gallons?

  1. 60 Correct answer.
  2. 54
  3. 72
  4. 45

Explanation

The 18 gallons added increased the tank's fill level from 40% to 70%, a change of 30%. Thus 0.30C = 18, so C = 18 ÷ 0.30 = 60 gallons.

Question 49Arithmetic Reasoning (AR)

A savings account earns 5% interest compounded annually. If $2,000 is deposited and no money is withdrawn, how much interest is earned after 2 years?

  1. $210
  2. $205 Correct answer.
  3. $200
  4. $220

Explanation

After one year the balance is $2,000 × 1.05 = $2,100. After two years it is $2,100 × 1.05 = $2,205, so the interest earned is $2,205 − $2,000 = $205.

Question 50Arithmetic Reasoning (AR)

A car purchased for $20,000 loses 15% of its value each year. What is its value after 2 years?

  1. $17,000
  2. $14,000
  3. $15,300
  4. $14,450 Correct answer.

Explanation

Each year the car retains 85% of its value, so multiply by 0.85 twice. After one year the value is $20,000 × 0.85 = $17,000; after two years it is $17,000 × 0.85 = $14,450.