How to improve at numerical reasoning tests: percentages, ratios, tables and mental arithmetic

1. Start with the question, not the calculation

Numerical reasoning tests commonly include questions based on tables, charts or short business-style scenarios. Some use multiple-choice answers; others may require a numerical response. Timing, calculator access and navigation rules vary, so check the instructions and any official sample material for the assessment you are taking. Do not assume that a practice site's format matches it.

Before calculating, identify three things: what the question asks for, which figures you need and the unit your answer should use. For example, “How much did sales increase?” asks for an amount, while “By what percentage did sales increase?” asks for a change relative to the starting figure.

Use a simple sequence: read, select, estimate, calculate, check. An estimate gives you a rough destination before you begin. If a quantity rises from about 200 to about 250, an answer near 25% is plausible; 2.5% or 250% should prompt another look. Estimate to catch scale errors, not to avoid necessary precision.

2. Master percentages by naming the base

A percentage is a fraction out of 100. To find 15% of £240, split it into 10% and 5%: £24 + £12 = £36. Useful anchors include 50% = one half, 25% = one quarter, 20% = one fifth and 12.5% = one eighth. These relationships make many calculations shorter.

For percentage change, use: (new value − original value) ÷ original value × 100. If orders rise from 160 to 200, the increase is 40, so the percentage increase is 40 ÷ 160 × 100 = 25%. The denominator is the original value, not the new one. Write “original” beside it if you often mix them up.

Reverse percentages need division. If an item costs £84 after a 30% discount, £84 represents 70% of its original price. The original price is therefore £84 ÷ 0.70 = £120. Adding 30% to £84 would not undo the discount because it uses a different base.

Also distinguish percentage points from percentage change. A rate rising from 20% to 25% increases by 5 percentage points, but its relative increase is 5 ÷ 20 × 100 = 25%. For successive changes, use multipliers: a 20% rise followed by a 20% fall gives 1.20 × 0.80 = 0.96, leaving the final value 4% below the starting value.

3. Treat ratios as parts, then attach quantities

A ratio describes relative amounts. If two teams share £560 in the ratio 3:4, there are seven parts altogether. One part is £560 ÷ 7 = £80, so the shares are £240 and £320. Check both conditions: the shares total £560, and £240:£320 simplifies to 3:4.

Notice whether a question gives a total or one component. If red and blue counters are in the ratio 2:5 and there are 35 blue counters, five parts equal 35. One part is seven, so there are 14 red counters and 49 counters altogether. Dividing 35 by seven would incorrectly treat the blue counters as the total.

For rate comparisons, convert to a common unit. A pack of six items costing £4.50 costs £0.75 per item; a pack of ten costing £7 costs £0.70 per item. The larger pack has the lower unit price. Keep labels such as “£ per item” visible: reversing a division produces a different rate, even if the arithmetic itself is correct.

4. Read tables selectively and compare like with like

When a table looks busy, read the question first, then locate the relevant row and column. Check headings, dates, units and footnotes before extracting numbers. A heading such as “Revenue (£000)” means that an entry of 250 represents £250,000, not £250. Avoid copying the whole table into your working.

Consider this small table, written as rows. Columns: region | enquiries | bookings. North: 240 | 60. South: 180 | 45. West: 300 | 90. Suppose the question asks which region has the highest booking rate. The required calculation is bookings divided by enquiries, not a comparison of booking totals alone.

North's rate is 60 ÷ 240 = 25%; South's is 45 ÷ 180 = 25%; West's is 90 ÷ 300 = 30%. West therefore has the highest rate. Notice that North and South have different booking totals but identical rates. Counts and proportions answer different questions.

For the overall booking rate, combine the underlying counts: total bookings are 60 + 45 + 90 = 195, and total enquiries are 240 + 180 + 300 = 720. The overall rate is 195 ÷ 720 × 100, approximately 27.1%. Simply averaging the three regional percentages gives approximately 26.7%, which is not the overall rate because the regions have different enquiry totals.

5. Make mental arithmetic smaller, not faster

Good mental arithmetic often means replacing one awkward calculation with several easy ones. Use partitioning: 18 × 24 = (20 × 24) − (2 × 24) = 480 − 48 = 432. Use compensation for addition: 398 + 267 = 400 + 267 − 2 = 665. Choose a method that reduces what you need to hold in mind.

Simplify fractions before converting them. For 48 ÷ 160, divide both numbers by 16 to get 3 ÷ 10 = 0.3, or 30%. For 25% of 68, divide 68 by four to get 17. Learning a few fraction–percentage equivalents is more useful than attempting every calculation through long division.

Keep an eye on magnitude. Since 19 × 31 is close to 20 × 30 = 600, an exact answer of 589 makes sense. With decimals, check whether the operation should make the number larger or smaller: 48 ÷ 0.5 = 96 because there are 96 halves in 48.

DailyQuest.ai's Rapid Balance drill offers mental arithmetic practice and is a natural choice for practising these operations. Keep written checks for any calculations you find difficult. If your target assessment permits a calculator, practise using that too: enter one calculation at a time and check the result against an estimate. Mental shortcuts should support accuracy, not become another source of mistakes.

6. Practise deliberately, then add time pressure

Begin with untimed questions on one topic. Explain each setup in a sentence: “I am dividing the increase by the original amount” or “I am finding the value of one ratio part.” Once you can reliably choose the correct operation, mix topics and introduce short timed sets. Record accuracy as well as completion time.

Keep an error log with four categories: misread question, wrong setup, arithmetic slip and unit or rounding error. Write the correction as an action, such as “underline the original value” or “check whether figures are in thousands”. Revisit missed questions later without looking at your previous working.

A practical 20-minute session could include five minutes of Rapid Balance, ten minutes of percentage, ratio or table questions, and five minutes reviewing errors. Number Sequences offers separate practice in spotting numerical relationships, but it is not a substitute for interpreting data tables. Prioritise exercises that resemble the skills you actually need.

DailyQuest.ai provides free practice drills. It is not a validated or official test, and it is not an IQ test; its result summaries are rule-based. Use those summaries as practice feedback, not as proof of assessment readiness. For format-specific preparation, return to the assessment provider's own instructions and sample questions.