Mathematics and Quantitative Reasoning
What this domain tests
Mathematics and Quantitative Reasoning measures practical arithmetic: percentages, ratios and proportions, averages, unit conversion, distance/rate/time, basic algebra, and interpretation of tables or word problems in a law-enforcement context. Calculators are usually not allowed, so estimation and order of operations matter.
Core rules
- Translate words into an equation before calculating. '15% of 240' is 0.15 × 240.
- Distinguish percent change from percent of: change = (new − old) ÷ old; 'of' means multiply.
- Keep units consistent. Convert minutes to hours before using rate × time.
- Use the average formula: total ÷ count. If you know the average and count, multiply to recover the total.
- Follow order of operations: parentheses, exponents, multiply/divide left to right, add/subtract left to right.
- Estimate first to catch a misplaced decimal.
Worked example
A patrol car travels 45 miles in 40 minutes. At the same rate, how far will it travel in 1 hour 20 minutes? Reasoning: Convert 40 minutes to 2/3 hour. Rate = 45 ÷ (2/3) = 45 × 3/2 = 67.5 mph. 1 hour 20 minutes = 4/3 hour. Distance = 67.5 × 4/3 = 90 miles. A faster route: 40 minutes is half of 80 minutes, so 80 minutes doubles the 45 miles to 90 miles. The second method is safer under time pressure.
Traps that cost marks
- Using 40 minutes as 0.40 hour.
- Reporting a percent increase as the new value.
- Rounding too early, then choosing an answer close to but not equal to the exact result.
- Reversing the ratio in a proportion.
- Forgetting that 'average' can hide very different totals.