Numerical Reasoning
What is tested
Numerical reasoning in the prison officer recruit process checks whether you can handle the everyday arithmetic of a prison environment: staff rosters, prisoner counts, overtime, incident statistics and simple budgets. You need confidence with percentages, ratios and proportion, averages (mean, median), unit conversion (hours to minutes, euro and cent), and multi-step word problems. Most questions are set in plain text rather than charts, so the skill is translating a paragraph into a calculation.
Traps to watch
- Percentage change direction. A 20% rise then a 20% fall does not return to the original number. Apply each change to the new base.
- Mixing units. Convert minutes to hours, or cent to euro, before calculating.
- Averages of averages. You cannot average two group means unless the groups are the same size.
- Distractor numbers. Some figures in the stem are irrelevant; identify what is actually asked.
- Rounding too early. Keep full precision until the final step.
Rule of thumb
Estimate first, then calculate, then check the answer is plausible and in the right units. If the question asks "per officer" or "per hour", divide; if it asks "in total", multiply.
Worked example
A landing holds 84 prisoners. Officers work a 12-hour shift and the ratio is one officer to 21 prisoners. How many officers are needed, and what is the total officer-hours for a 24-hour period? 84 ÷ 21 = 4 officers per shift. Two shifts cover 24 hours, so 4 × 2 = 8 shifts of officers, giving 8 × 12 = 96 officer-hours. Watch the trap: the answer is not 4 × 24; you must convert to the unit asked.