AFOQT - Air Force Officer Qualifying Arithmetic Reasoning Word Problems Questions and Answers 1 — Questions and Answers
Question 1: A cargo plane flies 600 miles in 2.5 hours. On the return trip, it travels against a headwind, which reduces its speed by 50 mph. How long will the return trip take?
- 2 hours and 45 minutes
- 3 hours
- 3 hours and 9 minutes (Correct answer)
- 3 hours and 30 minutes
Correct answer: 3 hours and 9 minutes
First, calculate the plane's initial speed: Speed = Distance / Time. Speed = 600 miles / 2.5 hours = 240 mph. The return trip speed is reduced by the headwind: 240 mph - 50 mph = 190 mph. Now, calculate the time for the return trip: Time = Distance / Speed. Time = 600 miles / 190 mph ≈ 3.158 hours. To convert the decimal part to minutes, multiply by 60: 0.158 * 60 ≈ 9.5 minutes. The closest answer is 3 hours and 9 minutes.
Question 2: A maintenance team of 5 people can service 12 aircraft in an 8-hour shift. If 2 more people are added to the team, how many aircraft can they service in the same amount of time, assuming everyone works at the same rate?
- 15 aircraft
- 17 aircraft
- 16.8 aircraft (Correct answer)
- 18 aircraft
Correct answer: 16.8 aircraft
First, find the rate of work for one person. If 5 people service 12 aircraft, then one person services 12/5 = 2.4 aircraft in 8 hours. With 2 more people, the team has 7 members. Now, multiply the number of people by the individual rate: 7 people * 2.4 aircraft/person = 16.8 aircraft. Therefore, the team can service 16.8 aircraft in an 8-hour shift.
Question 3: A supply depot has enough rations to feed a group of 120 airmen for 30 days. If 30 more airmen join the group, how many days will the rations last?
- 24 days (Correct answer)
- 25 days
- 22 days
- 37.5 days
Correct answer: 24 days
This is an inverse proportion problem. First, calculate the total number of 'man-days' of rations: 120 airmen * 30 days = 3600 man-days. Now, with the new group size (120 + 30 = 150 airmen), divide the total man-days by the new number of airmen: 3600 man-days / 150 airmen = 24 days. The rations will last for 24 days.
Question 4: An aircraft part costs $1,250. Due to a new manufacturing process, the cost is reduced by 15%. What is the new cost of the part?
- $1,062.50 (Correct answer)
- $1,100.00
- $1,437.50
- $187.50
Correct answer: $1,062.50
First, calculate the discount amount: 15% of $1,250 is 0.15 * 1250 = $187.50. Then, subtract the discount from the original price: $1,250 - $187.50 = $1,062.50. Alternatively, you can calculate the remaining percentage: 100% - 15% = 85%. The new price is 85% of the original: 0.85 * $1,250 = $1,062.50.
Question 5: Two technicians are working on a jet engine. Technician A can complete the job alone in 6 hours. Technician B can complete the same job alone in 4 hours. If they work together, how long will it take them to complete the job?
- 5 hours
- 2.5 hours
- 2.4 hours (Correct answer)
- 3 hours
Correct answer: 2.4 hours
The formula for work rate problems is (1/Time_A) + (1/Time_B) = (1/Total_Time). So, (1/6) + (1/4) = 1/T. To add the fractions, find a common denominator, which is 12. (2/12) + (3/12) = 1/T. This simplifies to 5/12 = 1/T. To solve for T, take the reciprocal of both sides: T = 12/5 = 2.4 hours.
Question 6: A rectangular aircraft hangar has a length of 200 feet and a width of 150 feet. A smaller, square maintenance bay with a side length of 50 feet is located within the hangar. Which of the following represents the area of the hangar floor that is NOT occupied by the maintenance bay?
- 32,500 sq ft
- 30,000 sq ft
- 2,500 sq ft
- 27,500 sq ft (Correct answer)
Correct answer: 27,500 sq ft
First, calculate the total area of the hangar: Area = Length * Width = 200 ft * 150 ft = 30,000 sq ft. Next, calculate the area of the square maintenance bay: Area = Side * Side = 50 ft * 50 ft = 2,500 sq ft. Finally, subtract the area of the bay from the total area of the hangar: 30,000 sq ft - 2,500 sq ft = 27,500 sq ft.
AFOQT - Air Force Officer Qualifying Arithmetic Reasoning Word Problems Questions and Answers 1
A cargo plane flies 600 miles in 2.5 hours.
On the return trip, it travels against a headwind, which reduces its speed by 50 mph.
How long will the return trip take?