Numerical Reasoning
Numerical Reasoning checks that you can handle the arithmetic that appears in custodial work: rosters and pay, staffing ratios, incident rates, centre capacity and percentage changes. A calculator is usually unnecessary, but accuracy under time pressure is not, and most marks are lost to misread questions rather than hard maths.
Core skills
- Percentages: part ÷ whole × 100. Percentage change = (new − old) ÷ old × 100. A 20% increase then a 20% decrease does not return to the original figure.
- Percentage points vs per cent: a rise from 8% to 10% is 2 percentage points but a 25% increase.
- Ratios: scale both sides; find the value of one part by dividing the total by the number of parts.
- Averages: mean = total ÷ count. To find a missing value, work backwards from the required total.
- Rates and time: incidents per 100 inmates; hours × rate; distance ÷ speed.
- Unit discipline: convert everything to the same unit (minutes, hours, cents) before calculating, and round only at the end.
Worked example
An officer's ordinary week is 38 hours at $36.50 per hour. She works four 10-hour shifts, and the two hours beyond 38 are paid at time-and-a-half. What is her gross pay for the week?
Step 1 - ordinary hours: 38. Ordinary pay: 38 × $36.50 = $1,387.00. Step 2 - overtime hours: 40 − 38 = 2. Step 3 - overtime rate: $36.50 × 1.5 = $54.75. Step 4 - overtime pay: 2 × $54.75 = $109.50. Step 5 - total: $1,387.00 + $109.50 = $1,496.50.
Notice the trap: paying all 40 hours at time-and-a-half. Only the hours beyond 38 attract the loading.
Traps
- Mixing percentages and percentage points.
- Calculating a percentage of the wrong base (e.g., of the new figure instead of the original).
- Forgetting that 'time-and-a-half' applies only to the excess hours.
- Rounding mid-calculation and drifting away from the answer options.
- Using 60 minutes correctly in one step and 100 in another.