Numerical Reasoning
What is being tested
Numerical reasoning checks speed and accuracy with percentages, ratios, averages, rates, and data interpretation. Most questions are short but time-pressured, so method choice matters as much as arithmetic.
Concepts to master
- Percentages: increase/decrease, percentage change, and reverse percentages (finding the original value after a change).
- Ratios and proportions: scaling recipes, dividing quantities, mixing problems.
- Averages: mean, and the effect of adding or removing a value.
- Rates: speed = distance/time; work rates add when people work together.
- Data interpretation: reading tables and charts accurately, watching units (minutes vs. hours, metres vs. kilometres).
Traps
Unit mismatches are the most common error. Reverse-percentage questions catch people who apply the change to the wrong base. Averages of averages are usually wrong unless group sizes are equal. Distractors often use the right numbers with the wrong operation, so estimate first and check the answer's rough size.
Rule of thumb
Write the formula before calculating, convert all units to one system, and sanity-check the result against a rough estimate.
Worked example
A recruit runs 3 km in 15 minutes. What is the average speed in km/h? Convert 15 minutes to 0.25 hours, then speed = 3 / 0.25 = 12 km/h. A common wrong answer, 0.2 km/h, comes from dividing distance by minutes instead of hours - the unit check catches it.
Worked example (percentages)
A time improves from 40 s to 32 s. The change is 8 s, and 8/40 = 20%, so the time fell by 20%. Do not divide by 32; the original value is the base.