25 numerical reasoning practice questions with worked answers
Below are 25 free numerical reasoning questions with step-by-step worked answers. They are grouped by question family so you can drill the patterns that repeat on real tests: percentages, ratios, weighted averages, rates, and multi-step chart interpretation. Read the numerical reasoning guide first if you need the method, or move to the formula sheetif the maths is the bottleneck.
- Use this page as a timed drill, not a reading exercise.
- Work one section at a time so the pattern becomes recognisable.
- Mark the failed step: reading, setup, arithmetic, rounding or time pressure.
- Redo only the weakest family instead of repeating all 25 questions.
For the full method behind these questions, read the numerical hub first. Read the numerical guide
What to focus on first
| Focus area | Why it matters | Best drill |
|---|---|---|
| Percentages | Tests whether you choose the correct base. | Write old/new before dividing. |
| Ratios | Tests parts, totals and scaling. | Convert to total parts first. |
| Weighted averages | Tests whether you weight by volume. | Multiply before averaging. |
| Rates | Tests per-unit thinking. | Write the denominator explicitly. |
| Charts | Tests reading plus arithmetic. | Find the row, period and unit before calculating. |
Common traps
- Reading the solution too early. Struggle time is where the pattern forms.
- Repeating the whole page. Drill the section that caused the mistakes.
- Scoring without diagnosis. A 17/25 means little unless you know which family cost you marks.
How to practise from here
Set a 30-minute timer and attempt all 25 questions without checking answers. Then spend 20 minutes reviewing only the wrong answers and tagging the failed step.
Percentages (Questions 1–5)
15% of £80 = 10% (£8) + 5% (£4) = £12. Sale price = £80 − £12 = £68.
Increase = £0.6m. % = 0.6 / 2.4 = 0.25 = 25%.
£56 = 80% of original. Original = 56 / 0.80 = £70.
£336,000 = 112% of original. Original = 336,000 / 1.12 = £300,000.
8% of £575k = £46k. Q3 = £575k − £46k = £529k.
Ratios (Questions 6–10)
1 part = 450 / 3 = 150. Sugar = 150g.
Total parts = 6. Developers = (5/6) × 24 = 20.
Total parts = 10. B = (3/10) × £40,000 = £12,000.
If concentrate = 1 part = 2L, then water = 4 parts = 8 litres.
Total parts = 5. Women = (2/5) × 45 = 18.
Weighted averages (Questions 11–15)
(200×10 + 300×15) / (200+300) = (2000+4500) / 500 = £13.
(0.2×80) + (0.3×70) + (0.5×90) = 16 + 21 + 45 = 82.
(8×45 + 12×55) / 20 = (360+660) / 20 = £51k.
(0.4×65) + (0.6×80) = 26 + 48 = 74%.
(1000×5 + 500×8) / 1500 = (5000+4000) / 1500 = £6.
Rates (Questions 16–20)
18 / (3×6) = 18/18 = 1 task per worker per hour.
Rate = 240/8 = 30/hour. In 5 hours = 150 widgets.
2.5 × 14 × 30 = 1050p = £10.50.
Rate = 30 miles/gallon. 10 × 30 = 300 miles.
Rate = 1200 / (4×3) = 100 records per person-day. 2000 / (5×100) = 4 days.
Multi-step chart questions (Questions 21–25)
Quarterly sales by region (£k)
120 + 95 = £215k.
(145 − 120) / 120 = 25/120 = 20.8%.
Total Q2 = 145 + 110 = 255. South share = 110/255 = 43.1%.
Growth rate = 20.8%. Q3 = 145 × 1.208 = £175.2k.
Shortfall = £120k − £110k = £10k (missed by 8.3%).
If your real invite names a provider, switch from generic practice into the exact format: SHL numerical reasoning, AON numerical reasoning, or Korn Ferry Talent Q numerical.
Source notes
These practice questions are forge originals, but the format choices are cross-checked against provider candidate materials such as SHL’s official practice tests and SHL’s cognitive assessment overview.
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