A typical numerical reasoning test question gives you a table or chart of business data and asks you to find one figure from it: a percentage change, an average, a ratio, a share of a total or a converted amount. The maths is school level. The skill being tested is picking the right figures, using the right method and watching the units, all against the clock.
Below are eight example questions built around one data table, each worked through step by step with the trap the wrong answers are designed to catch. When you have read them, try the same question types in a free numerical reasoning test.
The data for the example questions
Most questions in a real test share a single table or chart, so these do too. Read the headings before the numbers: the figures are in thousands of pounds.
Quarterly sales by region (£000s)
| Region | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| North | 240 | 264 | 300 | 285 |
| South | 180 | 171 | 198 | 225 |
| East | 150 | 165 | 150 | 180 |
| West | 210 | 231 | 252 | 240 |
Example 1: percentage change
Question. By what percentage did North’s sales increase from Q1 to Q2?
A) 9.1% B) 10% C) 11% D) 24%
- Find the change: 264 − 240 = 24.
- Divide by the original figure, which is the earlier one: 24 ÷ 240 = 0.1.
- Multiply by 100: 10%.
Answer: B. Option A is what you get if you divide by the new figure (24 ÷ 264 = 9.1%), and option D is the raw change mistaken for a percentage. Our guide to calculating percentage increase covers this method in more depth.
Example 2: the mean
Question. What were South’s average quarterly sales over the year?
A) £193.50 B) £19,350 C) £193,500 D) £774,000
- Add the four quarters: 180 + 171 + 198 + 225 = 774.
- Divide by the number of quarters: 774 ÷ 4 = 193.5.
- Apply the units. The table is in £000s, so 193.5 means £193,500.
Answer: C. Option A ignores the units heading entirely, and option D is the annual total rather than the average. When a question says “average” without naming a type, it means the mean.
Example 3: the median
Question. What was the median of North’s quarterly sales?
- Put the four figures in order: 240, 264, 285, 300.
- With an even number of values there is no single middle value, so take the two middle ones: 264 and 285.
- Find their mean: (264 + 285) ÷ 2 = 549 ÷ 2 = 274.5.
Answer: £274,500. For comparison, the mean of North’s figures is 1,089 ÷ 4 = 272.25, or £272,250. Questions sometimes offer both, so check which average is being asked for.
Example 4: a ratio
Question. What is the ratio of North’s Q4 sales to South’s Q4 sales, in its simplest form?
- Write the ratio in the order the question gives: 285:225.
- Find the highest common factor. Both numbers divide by 5 and by 3, so the highest common factor is 15.
- Divide both parts: 285 ÷ 15 = 19 and 225 ÷ 15 = 15.
Answer: 19:15. Reversing the order to 15:19 is the usual wrong option. For more on this, see our guide to calculating a ratio.
Example 5: share of a total
Question. What percentage of total Q4 sales came from the North region? Give your answer to one decimal place.
- Add all four regions for Q4: 285 + 225 + 180 + 240 = 930.
- Divide North’s figure by the total: 285 ÷ 930 = 0.3065 (to four decimal places).
- Multiply by 100 and round: 30.6%.
Answer: 30.6%. The trap here is using a total from the wrong column or row, so write down which numbers you are adding before you add them.
Example 6: reverse percentage
Question. West’s Q3 sales were 20% higher than in Q3 of the previous year. What were West’s sales in Q3 of the previous year?
A) £201,600 B) £210,000 C) £232,000 D) £302,400
- After a 20% rise, this year’s figure is 120% of last year’s, so the multiplier is 1.2.
- Divide this year’s figure by the multiplier: 252 ÷ 1.2 = 210.
- Apply the units: £210,000.
Answer: B. Option A is what you get by taking 20% off this year’s figure (252 × 0.8 = 201.6). That fails because the 20% was calculated on last year’s smaller figure. Check by working forwards: 210 × 1.2 = 252. There is more practice in our guide to reverse percentages.
Example 7: currency conversion
Question. East’s Q4 sales are to be reported to a European parent company. The exchange rate is £1 = €1.16. What were East’s Q4 sales in euros?
- Convert the units first: 180 in £000s is £180,000.
- You are going from pounds to euros, and each pound buys €1.16, so multiply: 180,000 × 1.16 = 208,800.
Answer: €208,800.
Going the other way, you divide. A Q1 figure of €58,000 would be 58,000 ÷ 1.16 = £50,000. A quick check catches the wrong direction: at this rate, the euro figure should always be the bigger number.
Example 8: combining two averages
Question. Team A has 5 sales staff who average 22.6 client calls a day. Team B has 10 staff who average 24.5 calls a day. What is the average for all 15 staff combined, to one decimal place?
- Turn each average back into a total. Team A: 5 × 22.6 = 113 calls. Team B: 10 × 24.5 = 245 calls.
- Add the totals: 113 + 245 = 358 calls.
- Divide by the total number of staff: 358 ÷ 15 = 23.87, which is 23.9 to one decimal place.
Answer: 23.9 calls. Averaging the two averages gives (22.6 + 24.5) ÷ 2 = 23.55, which is wrong because the teams are different sizes. The larger team has to count for more.
Formulas these examples use
| Calculation | Formula |
|---|---|
| Percentage change | (new − original) ÷ original × 100 |
| Reverse percentage | final value ÷ multiplier, such as ÷ 1.2 after a 20% rise or ÷ 0.8 after a 20% fall |
| Share of a total | part ÷ total × 100 |
| Mean | total of the values ÷ number of values |
| Median | middle value once the values are in order, or the mean of the middle two |
| Ratio share | part ÷ sum of the ratio parts × amount being shared |
| Currency | multiply by the rate to go from the first currency to the second, divide to go back |
How to approach the real thing
- Read the question before the data. Then you know which row and column you are looking for, and you can ignore the rest.
- Check the units in every heading. “£000s”, “millions” and “%” change what the answer looks like, and a wrong unit is almost always one of the options.
- Estimate first. If you expect an answer of roughly 10%, an option of 24% is ruled out before you calculate.
- Use the answer options. Widely spaced options often mean an estimate is enough. Close options mean you need to be careful with rounding.
- Write the working down. A figure you have written cannot be misremembered halfway through a calculation.
For a closer look at reading tables and charts, see our guide to data interpretation. Then put the methods above to work under time pressure with a timed numerical reasoning practice test.