Arithmetic, Data Interpretation, and Reasoning
Arithmetic, Data Interpretation, and Reasoning checks practical math used in corrections: counts, percentages, ratios, averages, staffing, overtime, and reading tables without being misled.
Core rules
- Identify the base for every percentage. A rise from 40 to 46 is 6/40 = 15%, not 6/46.
- Percent change = (new minus old) divided by old, times 100.
- Average = total divided by number of items; do not average already-averaged numbers unless the groups are equal size.
- Keep units attached and convert before calculating.
- In tables, read the title, column headings, and totals first; check whether figures are counts, rates, or percentages.
- Round only at the end unless the question states otherwise.
Worked example
An officer earns $24.50 per hour. Overtime is 1.5 times the regular rate for hours over 40. She works 46 hours in a week. What is her gross pay? Reasoning: Regular pay = 40 times $24.50 = $980.00. Overtime hours = 6. Overtime rate = $24.50 times 1.5 = $36.75. Overtime pay = 6 times $36.75 = $220.50. Gross = $980.00 + $220.50 = $1,200.50. A common wrong answer applies $36.75 to all 46 hours, which inflates pay and misreads 'hours over 40.'
Traps
Using the new value as the base; confusing percentage points with percent; reversing a ratio; ignoring a 'per day' versus 'per shift' unit; misreading a row as a column; rounding $36.75 to $37 before multiplying.