Question bank
Free Numerical Reasoning Questions with Answers
Free numerical reasoning questions and answers in the real test format — each with answer options, a full worked solution, and the specific mistake behind every wrong answer. The full bank holds 1125+ questions; these are the open ones.
Whether your test is called a numerical reasoning, numerical ability, numerical aptitude or numeracy test, these examples cover the same ground — the names differ by publisher, the data interpretation doesn’t.
Percentages
Drill this topicBy what percentage did Carraway plc's Revenue change from 2023 to 2024?easyBy what percentage did Caldera One's Revenue change from 2023 to 2024?easyA fund is worth £219m. Class A is 10.8% of it; within Class A, item B is 13.1%. What is the value of B?very hardWhat percentage of the £370,000 total is the Print channel?easyWhat percentage of the £380,000 total is the Digital channel?easyWhat is 30% of 1,680?easyWhat is 25% of 520?easyAfter a 12% increase, a price is £196.00. What was the original price?mediumAfter a 15% increase, a price is £132.25. What was the original price?mediumA £380 item rises 20%, then a further 10% on the new price. What is the final price?mediumA price including 20% VAT is £192.00. What is the price excluding VAT?mediumA £105 item is reduced 15%, then a further 25% off the new price. What is the final price?mediumA £176 item is reduced 10%, then a further 10% off the new price. What is the final price?mediumAfter a 20% rise and then a 10% fall, a price is £205.20. What was the original price?very hard
Ratios & Proportion
Drill this topicRegion A: £3.9m over 15 stores. Region B: £2.0m over 9 stores. What were the higher region's sales per store?mediumRegion A: £3.9m over 6 stores. Region B: £2.5m over 14 stores. What were the higher region's sales per store?medium£1140 is shared in the ratio 2:5. How much is the larger share?easy£660 is shared in the ratio 2:5. How much is the larger share?easy£1,520 is shared in the ratio 1:2:5. What is the largest share?medium£1,160 is shared in the ratio 3:4:1. What is the largest share?medium5 litres at £4/L are mixed with 7 litres at £10/L. What is the price per litre of the mixture?hardSolve for x: 4/7 = 12/xeasySolve for x: 2/5 = 6/xeasyA debt:equity position moves from 30:40 to 36:44. What is the percentage change in the ratio?very hard
Tables & Data Lookup
Drill this topicHow many units did the Highland warehouse ship in Q4?very easyHow many units did the Norwich warehouse ship in Q4?very easyDivision A earned £550m and Division B £190m. How much more did A earn?easyDivision A earned £590m and Division B £350m. How much more did A earn?easyWhat was total revenue across the three years?easyWhat was total revenue across the three years?easyIn which year was gross profit (revenue − costs) the largest?hardNo total is given. What percentage of the combined total is Alpha?mediumNo total is given. What percentage of the combined total is Delta?mediumA train departs at 09:00 and the journey takes 1h 08m. When does it arrive?mediumUnits are in the first exhibit and unit price in the second. What was the revenue for North?hard
Charts & Graphs
Drill this topicUsing the chart, how much CO2 from a 3.6-mile car journey then a 15.0-mile train journey?hardFrom the chart, what is the value for Feb?easyFrom the chart, what is the value for May?easyA pie-chart slice has an angle of 90°. The whole chart represents 209. What value does the slice represent?mediumA pie-chart slice has an angle of 90°. The whole chart represents 471. What value does the slice represent?mediumBy how much did Series A exceed Series B in 2024?mediumUsing price and volume, what percentage of total revenue does product D represent?very hard
Averages & Spread
Drill this topicWhat was the fund's overall return, weighted by holding size?hardFind the median of: 58, 33, 55, 26, 53, 45, 52.easyFind the median of: 53, 52, 55, 26, 25, 32, 57.easyTwo groups are combined. What is the mean of the combined group?mediumTwo groups are combined. What is the mean of the combined group?mediumThe mean of 5 numbers is 58. 4 of them are 30, 60, 63, 62. What is the missing number?mediumBy what percentage did the portfolio's weighted-average return change from period 1 to period 2?very hard
Number Series & Patterns
Drill this topicMoney & Finance
Drill this topic£3,500 at 3% simple interest for 2 years. How much interest is earned?easy£6,000 at 4% compound interest for 3 years. What is it worth? (nearest £)mediumA product sells for £40, variable cost £15, fixed costs £7,000. Units to break even?mediumRevenue grew from £250m to £488m over 3 years. What was the CAGR?very hardWith the base year value 500 set to an index of 100, what is the index for a year with value 700?mediumA sequence grows by a fixed amount: 100, 120, 140, 160. What is the value 2 steps after the last term shown?mediumAn item costs £186 and sells for £223. What is the profit margin (profit as a percentage of the selling price)…mediumA trader buys stock at £15/unit, then sells 41 units at £19 and 36 units at £25. What is the total profit?very hard
Rates, Speed & Conversions
Drill this topicA council's budget is £24m and the population is 137,000. What is the spend per person?medium£1 = €1.25. How many euros for £550?easy£1 = €1.25. How many euros for £450?easyA line produced 1,040 units over 10 hours. What is the output per hour?easyA line produced 1,140 units over 10 hours. What is the output per hour?easyHow many minutes are there from 09:25 to 11:34?mediumTravelling at 40 mph for 5 hours, how far do you travel?easyTravelling at 60 mph for 3 hours, how far do you travel?easyOffice A earns $52,000; office B earns €40,000. With £1 = $1.25 and £1 = €1.15, how much more (in £) does one …very hard
Probability & Statistics
Drill this topicOne commuter is chosen at random. What is the probability they take the Train?easyOf 88 people, 53 like tea, 43 like coffee, 14 like both. How many like neither?mediumA raffle ticket pays the prizes shown with the stated probabilities. What is the expected value of one ticket?hardThe probability of an event is 3/8. What is the probability it does NOT happen?easy
Algebra
Drill this topicSolve for x: 3x + 14 = 29easyIf y = 2x² − 2x + 4, what is y when x = 5?mediumUsing v = u + a·t, make a the subject and find a when v = 28, u = 8, t = 5.mediumSolve the pair: 2x + 3y = 26 and x − y = -2. What is x?mediumFor what value of n does 4n + 8 equal 1n + 29?mediumA number is multiplied by 2, then 3 is added, giving 13. What is the number?easy
Speed & Mental Maths
Drill this topicData Sufficiency / Statement Evaluation
Drill this topicUsing the table, is this True, False, or Cannot say?
Statement: More than half of Packing's staff are aged und…mediumUsing the table, is this True, False, or Cannot say?
Statement: More than half of QA's staff are aged under 30…mediumUsing the table, is this True, False, or Cannot say?
Statement: More than half of Bristol's staff are part-tim…mediumUsing the table, is this True, False, or Cannot say?
Statement: More than half of QA's staff are women.medium
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Common questions
Are these numerical reasoning practice questions free?
Yes. Every question listed here is free, in the real test format, with a full worked solution and the specific mistake behind each wrong option.
How are the questions verified?
Each question is generated programmatically and its correct answer is computed from its own data, never hand-keyed. Every wrong option maps to a named mistake, and each item passes automated quality gates before it is published.
Do the questions come with worked solutions?
Yes — every question has a step-by-step worked solution generated from the same data used to compute the answer, plus the named mistake behind each wrong option.
Are these the real SHL or CCAT questions?
No. They are original practice questions in the same formats the real tests use. We replicate published formats, timing and calculator policy — not the actual questions, which are confidential to each publisher.