Numerical reasoning test practice
Numerical reasoning questions give a short scenario, a small table or a chart, and ask for one figure: a percentage change, a ratio share, a rate or a conversion. Each has four or five options and only one is correct. You are usually allowed a calculator, so the difficulty lies in choosing the right operation, not in the arithmetic.
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Time pressure
The time per question is short compared with the reading involved, so most candidates finish only if they avoid dead ends. A question that is not yielding after a reasonable attempt is better flagged and left than allowed to consume the time of the next three.
Heuristics that transfer
- Chain successive percentage changes by multiplying growth factors, never by adding the percentages.
- Write the units beside every number before you combine them; most wrong options are correct arithmetic on the wrong quantity.
- Estimate first. A rough answer within ten per cent usually eliminates two options before any exact calculation.
- For ratios, convert to parts of a whole first (4:3:2 is nine parts) and then scale.
- Check what the question asks against a base: a percentage of the original, of the selling price, or of the total.
Three worked examples
Try each question before opening the answer.
Example 1
A charity's £45,000 fundraising total is split between three programmes in the ratio 4:3:2. How much does the smallest programme receive?
Show the answer and worked method
Correct answer: £10,000
The principle
Dividing a total in a given ratio requires scaling each share by the total number of parts.
Steps
- Total parts = 4 + 3 + 2 = 9.
- Value of one part = 45,000 / 9 = 5,000.
- Smallest share = 2 parts × 5,000 = £10,000.
Heuristic to carry forward
Always find the value of a single part first (total ÷ total parts), then multiply by the number of parts for the share you need.
Why each other answer is wrong
- £15,000
- Gives the middle programme's share (3 parts × 5,000) instead of the smallest.
- £5,000
- Treats the value of a single part (5,000) as the answer, forgetting to multiply by the smallest programme's 2 parts.
- £20,000
- Gives the largest programme's share (4 parts × 5,000) instead of the smallest.
Example 2
Eight workers can complete a job in 12 days. Working at the same individual rate, how many days would 6 workers take to complete the same job?
Show the answer and worked method
Correct answer: 16 days
The principle
Work rate problems are governed by the person-days invariant: total effort (workers × days) is constant.
Steps
- Total effort required = 8 workers × 12 days = 96 person-days.
- With 6 workers, days needed = 96 / 6 = 16 days.
Heuristic to carry forward
Fewer workers means the job takes longer: fix the total person-days first, then divide by the new number of workers, not multiply.
Why each other answer is wrong
- 12 days
- Repeats the original number of days, overlooking that fewer workers must take longer to finish the same job.
- 9 days
- Multiplies the original days by the ratio of new to original workers (12 × 6/8 = 9), applying a direct rather than inverse proportion.
- 10 days
- Subtracts the change in workers directly from the original days (12 - 2), treating the relationship as linear rather than inverse.
Example 3
A student's module scores are 70, 80 and 60, weighted at 30%, 50% and 20% of the final grade respectively. What is the weighted average grade?
Show the answer and worked method
Correct answer: 73
The principle
A weighted average multiplies each value by its own weight before summing, rather than treating all values equally.
Steps
- Weighted contribution: (0.30 × 70) + (0.50 × 80) + (0.20 × 60).
- = 21 + 40 + 12 = 73.
Heuristic to carry forward
Multiply each score by its own weight and sum the results; only use a simple mean when all items genuinely carry equal weight.
Why each other answer is wrong
- 70
- Computes the simple (unweighted) mean of the three scores: (70 + 80 + 60) / 3 = 70.
- 75
- Averages only the two highest-weighted scores (70 and 80), ignoring the 60 entirely: (70 + 80) / 2 = 75.
- 72
- Swaps the 30% and 20% weights, applying 20% to the 70-score module and 30% to the 60-score module: (0.20×70) + (0.50×80) + (0.30×60) = 72.
Every question in the bank has a verified answer key and a worked solution.
Keep going
Related guides: Successive percentage changes, Average speed is not the average of two speeds, or all worked examples.
Other test types: Verbal reasoning, Logical reasoning, Abstract reasoning. For timed shape matching, try Shapefinder.