AFOQT - Air Force Officer Qualifying Arithmetic Reasoning Word Problems 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?

Accepted Answer

3 hours and 9 minutes

Answer

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?

Accepted Answer

16.8 aircraft

Answer

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?

Accepted Answer

24 days

Answer

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?

Accepted Answer

$1,062.50

Answer

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?

Accepted Answer

2.4 hours

Answer

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.

AFOQT Practice Test

AFOQT Practice Test

AFOQT - Air Force Officer Qualifying Arithmetic Reasoning Word Problems Questions and Answers