Arithmetic and Mathematical Reasoning
What is tested
The math section is practical: percentages, ratios and proportions, averages, fractions and decimals, unit conversions, rate problems, and multi-step word problems drawn from everyday and agency settings - payroll, distance, staffing, budgets, and supply inventories.
Core tools
- Percent: part = percent × whole. Percent increase = (new − old) ÷ old.
- Averages: average = sum ÷ count. If you know the average and the count, multiply to recover the sum.
- Proportions: set two ratios equal and cross-multiply; keep units aligned in the same position.
- Rate: distance = rate × time. Convert minutes to hours before multiplying.
- Order of operations: parentheses, exponents, multiply/divide left to right, add/subtract left to right.
Traps
- Wrong base: a discount applies to the original price, not the already-reduced price; a percent increase and an equal percent decrease do not cancel.
- Mixed units: minutes with hours, inches with feet, ounces with pounds.
- Stopping one step early when the question asks for a total rather than a difference.
- Rounding too soon - carry decimals through and round at the end.
- Averages: adding a new value without increasing the count.
Worked example
A patrol car travels 84 miles in 1 hour 45 minutes. What is its average speed in miles per hour? Convert: 1 hour 45 minutes = 1.75 hours. Then divide: 84 ÷ 1.75 = 48 mph. Check by multiplying back: 48 × 1.75 = 84. ✔ The trap is treating 1:45 as 1.45 hours, which yields about 58 mph - a wrong answer that will appear among the choices. Always convert time to the unit the answer requires before you divide.