OTEE - Officer Trainee Entrance Mathematical Aptitude Questions and Answers 1 — Questions and Answers
Question 1: A patrol car, traveling at 90 km/h, is pursuing a suspect's vehicle which is 500 meters ahead and moving at a constant speed of 75 km/h. How long will it take for the patrol car to catch up to the suspect's vehicle?
- 90 seconds
- 120 seconds (Correct answer)
- 150 seconds
- 180 seconds
Correct answer: 120 seconds
First, convert all units to be consistent (meters and seconds). The patrol car's speed is 90 km/h = 25 m/s. The suspect's speed is 75 km/h = 20.83 m/s. The relative speed of the patrol car to the suspect is the difference between their speeds: 25 m/s - 20.83 m/s = 4.17 m/s. The distance to be covered is 500 meters. Time = Distance / Speed, so Time = 500 meters / 4.17 m/s ≈ 120 seconds.
Question 2: Three officers can process a crime scene in 10 hours. If two more officers, who work at the same rate, are assigned to the task, how many hours will it take for the team of five officers to process the same crime scene?
- 6 hours (Correct answer)
- 4 hours
- 8 hours
- 5 hours
Correct answer: 6 hours
The total work required can be measured in 'officer-hours'. For three officers over 10 hours, the total work is 3 officers * 10 hours = 30 officer-hours. With five officers working at the same rate, the time required is Total Work / Number of Officers = 30 officer-hours / 5 officers = 6 hours.
Question 3: The average weight of four seized packages is 25 kg. A fifth package is added, and the new average weight of the five packages is 27 kg. What is the weight of the fifth package?
- 30 kg
- 29 kg
- 38 kg
- 35 kg (Correct answer)
Correct answer: 35 kg
The total weight of the first four packages is 4 * 25 kg = 100 kg. The total weight of the five packages is 5 * 27 kg = 135 kg. The weight of the fifth package is the difference between these two totals: 135 kg - 100 kg = 35 kg.
Question 4: An intelligence unit is comprised of 8 analysts and 5 field agents. A special task force of 3 members must be formed. What is the probability that the task force will consist of exactly 2 analysts and 1 field agent?
- 70/143 (Correct answer)
- 28/143
- 70/286
- 140/286
Correct answer: 70/143
First, find the total number of ways to choose 3 members from the 13 people (8+5), which is 13C3 = (13*12*11)/(3*2*1) = 286. Next, find the number of ways to choose 2 analysts from 8, which is 8C2 = (8*7)/(2*1) = 28. Then, find the number of ways to choose 1 field agent from 5, which is 5C1 = 5. The number of favorable outcomes is 28 * 5 = 140. The probability is the number of favorable outcomes divided by the total number of outcomes: 140/286, which simplifies to 70/143.
Question 5: A rectangular storage room is 15 meters long and 10 meters wide. The department plans to increase the floor area by 44% by increasing both the length and the width by the same percentage. By what percentage will the length and width be increased?
- 15%
- 22%
- 20% (Correct answer)
- 44%
Correct answer: 20%
Let 'x' be the percentage increase (as a decimal). The new length will be 15(1+x) and the new width will be 10(1+x). The original area is 15 * 10 = 150 sq meters. A 44% increase in area means the new area is 150 * 1.44 = 216 sq meters. So, 15(1+x) * 10(1+x) = 216. This simplifies to 150(1+x)^2 = 216. (1+x)^2 = 216/150 = 1.44. Taking the square root, 1+x = 1.2. Therefore, x = 0.2, which is a 20% increase.
Question 6: A supply clerk is mixing a disinfectant solution. He needs to create a 20-liter batch that is 15% concentrate. He has two stock solutions available: one is 10% concentrate and the other is 30% concentrate. How many liters of the 10% solution must he use?
- 5 liters
- 10 liters
- 15 liters (Correct answer)
- 12 liters
Correct answer: 15 liters
Let x be the amount of the 10% solution and y be the amount of the 30% solution. We have two equations: 1) x + y = 20 (total volume). 2) 0.10x + 0.30y = 20 * 0.15 = 3 (total amount of concentrate). From eq 1, y = 20 - x. Substitute this into eq 2: 0.10x + 0.30(20 - x) = 3. This becomes 0.10x + 6 - 0.30x = 3. Simplifying, -0.20x = -3, so x = 15. He must use 15 liters of the 10% solution.
OTEE - Officer Trainee Entrance Mathematical Aptitude Questions and Answers 1
A patrol car, traveling at 90 km/h, is pursuing a suspect's vehicle which is 500 meters ahead and moving at a constant speed of 75 km/h.
How long will it take for the patrol car to catch up to the suspect's vehicle?