Numerical Reasoning and Data Interpretation Flashcards

Three adjacent policing regions are evaluated against the provincial benchmark of 4.0 property crimes per 1,000 residents per quarter. Region A has 340,000 residents and recorded 1,326 property crimes. Region B has 215,000 residents and recorded 952 property crimes. Region C has 180,000 residents and recorded 774 property crimes. How many of the three regions exceed the provincial benchmark?

Answer: Two regions

Each region's rate must be calculated per 1,000 residents: Region A = (1,326 ÷ 340,000) × 1,000 = 3.9 — below benchmark. Region B = (952 ÷ 215,000) × 1,000 = 4.43 — exceeds. Region C = (774 ÷ 180,000) × 1,000 = 4.3 — exceeds. Only two regions exceed the benchmark. Region A is a deliberate trap: it has the highest absolute crime count but the lowest rate once population is accounted for.

A division's overtime budget was $2,400,000 in 2023. A 12% reduction was applied for 2024, followed by a 15% increase for 2025. What is the net percentage change in the budget from 2023 to 2025?

Answer: +1.2%

After the 12% cut: $2,400,000 × 0.88 = $2,112,000. After the 15% increase: $2,112,000 × 1.15 = $2,428,800. Net change = ($2,428,800 − $2,400,000) ÷ $2,400,000 × 100 = +1.2%. The most common error is adding the percentages directly (−12 + 15 = +3%), which ignores that the 15% increase is applied to the already-reduced base, not the original amount.

A division's annual case clearance data is shown below: Robbery: 240 cases, 168 cleared Assault: 580 cases, 435 cleared Fraud: 190 cases, 76 cleared Theft: 340 cases, 187 cleared What is the overall clearance rate across all crime types combined?

Answer: 64.1%

The overall rate requires combining totals, not averaging individual rates. Total cases = 240 + 580 + 190 + 340 = 1,350. Total cleared = 168 + 435 + 76 + 187 = 866. Overall clearance = 866 ÷ 1,350 = 64.1%. The answer of 60.0% is a trap: it is the simple (unweighted) average of the four individual rates (70% + 75% + 40% + 55%) ÷ 4, which incorrectly treats each crime category as equally sized.

A regional crime index uses 2020 as its base year (index = 100). In 2025 the index stands at 125, and the division recorded 3,750 incidents that year. How many incidents were recorded in the base year 2020?

Answer: 3,000

An index of 125 in 2025 means incident volume is 125% of the 2020 level, i.e., 2020 × 1.25 = 3,750. Solving for 2020: 3,750 ÷ 1.25 = 3,000 incidents. A common error is multiplying 3,750 × 1.25 = 4,688, which reverses the direction — that would give the 2025 count if 2020 were the unknown higher value. The index tells you how much higher the current year is relative to base, so you must divide by the index factor to recover the base.

In 2024, a division handled 3,600 calls for service with 20 patrol officers, yielding an average of 15 calls per officer per month. For 2025, five officers will be reassigned to a specialized unit, and call volume is projected to rise by 25%. What will be the new average number of calls per officer per month?

Answer: 25.0

2025 call volume = 3,600 × 1.25 = 4,500 calls. Remaining officers = 20 − 5 = 15. Monthly calls per officer = 4,500 ÷ (15 officers × 12 months) = 4,500 ÷ 180 = 25.0. The trap answer of 18.75 results from applying only the 25% volume increase to the existing rate (15 × 1.25) without accounting for the officer reduction. Both changes must be applied simultaneously.

A headquarters review sets two simultaneous performance targets: an arrest rate of at least 28% of incidents, and a case closure rate above 70%. Using the table below, which division(s) meet BOTH targets? North: 1,240 incidents, 316 arrests, 892 cases closed South: 876 incidents, 198 arrests, 614 cases closed East: 1,560 incidents, 442 arrests, 1,105 cases closed West: 1,088 incidents, 289 arrests, 762 cases closed

Answer: East Division only

Arrest rates: North = 316/1,240 = 25.5% (fails); South = 198/876 = 22.6% (fails); East = 442/1,560 = 28.3% (passes); West = 289/1,088 = 26.6% (fails). Of these, only East needs its closure rate checked: 1,105/1,560 = 70.8% — passes. East is the only division satisfying both criteria. West's closure rate (762/1,088 = 70.0%) meets exactly 70% but does not exceed it, and West already fails the arrest threshold. North's closure rate (71.9%) passes, but its arrest rate does not.