Numerical Reasoning Test Practice: 20 Questions in 20 Minutes

It is a reading test wearing a maths test's clothes

Candidates prepare for numerical reasoning by brushing up arithmetic. That is preparing for the wrong half. The arithmetic in these papers is deliberately easy — percentages, ratios, averages, unit conversion, nothing beyond what a calculator handles in one line. Almost every employer allows a calculator, which tells you plainly that computation is not what is being measured.

What is being measured is whether you can pull the correct number out of a cluttered table under time pressure, and whether you know which number the question actually asked for. Mark a batch of wrong answers and you will find the same pattern: the method was right, the figure that went into it was not. Wrong row, wrong year, wrong units, or the total when the question wanted one segment of it.

This changes how you should practise. Doing more arithmetic drills will not move your score. Slowing down for eight seconds before you compute — to point at the exact cell you are about to use and say what it represents — will. That habit is the whole subject.

Percentage change: the base decides the answer

Percentage change is the most-tested idea on these papers and the most-failed. The formula is trivial: (new − old) ÷ old. The trap is entirely in which number plays the role of 'old'.

Revenue goes from 250 to 300. The increase is 50, and 50 ÷ 250 = 20 percent. Now read it backwards: revenue falls from 300 to 250. The decrease is the same 50, but now 50 ÷ 300 = 16.7 percent. The same gap, two different percentages, because the base changed. A rise of 20 percent followed by a fall of 20 percent does not return you to where you started — 100 becomes 120 becomes 96.

Before dividing, say out loud which figure is the starting point. If the question says 'increase from', the base is the first figure. If it says 'compared with last year', the base is last year. If it asks what percentage A is of B, the base is B — the word 'of' points at the denominator every time.

• Increase from 40 to 52: 12 ÷ 40 = 30 percent.

• Decrease from 52 to 40: 12 ÷ 52 = 23.1 percent.

• 40 as a percentage of 52: 40 ÷ 52 = 76.9 percent.

• 52 as a percentage of 40: 52 ÷ 40 = 130 percent.

Four different answers from two numbers. When your result is close to an option but not exact, you almost certainly used the wrong one of these four.

Percentage points are not percent

A market share moves from 5 percent to 7 percent. Has it risen by 2 percent or by 40 percent? Both statements are true and they mean different things. It rose by 2 percentage points, which is the arithmetic difference, and by 40 percent, which is the relative change (2 ÷ 5).

Test writers use this deliberately because the distractor list will contain both numbers. Read the question's exact wording: 'by how many percentage points' wants the subtraction; 'by what percentage' wants the division. When the wording is just 'by how much', check the options — if both 2 and 40 appear, the answer is whichever matches the unit the options are written in.

The same distinction hides inside interest rates, unemployment figures, margins and conversion rates, which is exactly the material these papers draw on. Any time you see two percentages being compared, pause and decide whether the question wants their difference or their ratio.

Where table questions actually leak marks

Table and chart questions carry the most marks and take the most time. The leaks are predictable, and they are all in the reading, not the sums.

• Units in the header. 'Revenue (£m)' means the 42 in the cell is 42 million. Mixing a thousands column with a millions column produces an answer that is off by exactly 1,000 — if your result is a clean factor of ten or a thousand away from every option, this is why.

• The footnote. Small print under a table routinely excludes a region, restates a period, or says the figures are provisional. Footnotes exist in these papers because they change the answer.

• 'Of which' rows. A row labelled 'of which: exports' is a subset of the row above, not an addition to it. Adding it to the total double-counts.

• Axes that do not start at zero. A bar that looks twice as tall may represent a 6 percent difference. Read values off the axis; never judge by the height of a bar.

• Two y-axes. Combination charts put one series on the left scale and another on the right. Check which series belongs to which axis before reading any value.

• Period labels. 'Q3' and 'the three months to September' may be the same thing or may not be, depending on the fiscal year the table declares.

A working habit that costs three seconds and repays often: after you locate a figure, name it to yourself — 'that is 42 million, exports only, 2025'. If the question wanted total revenue for 2024, the mismatch surfaces before you have spent a minute computing with it.

Ratios: always ask 'per what'

Ratio questions look simpler than table questions and produce a similar number of errors, because a ratio is meaningless until you know what it is a ratio of.

Staff are split between two offices in the ratio 3 : 5, and there are 240 staff in total. The parts are 3 + 5 = 8, so each part is 240 ÷ 8 = 30, giving 90 and 150. The common error is dividing 240 by 3 or by 5 — treating one side of the ratio as though it were the number of parts. Sum the parts first, always.

Scaling questions work the same way. If 3 machines produce 450 units in 6 hours, find the rate per machine per hour before changing anything: 450 ÷ 3 ÷ 6 = 25. Now any variation is one multiplication away — 5 machines for 4 hours is 25 × 5 × 4 = 500. Candidates who try to scale the original figure directly get lost as soon as two quantities change at once.

For currency and unit conversion, write the rate as a fraction with the unit you want on top. Converting 300 euros at 1.15 dollars per euro: you want dollars, so 300 × 1.15 = 345. If you find yourself unsure whether to multiply or divide, the sanity check is whether the answer should be bigger or smaller than what you started with.

When not to calculate

Full precision is often wasted effort. Look at the spacing of the options before you compute. If they are 12 percent, 18 percent, 24 percent and 31 percent, an estimate to the nearest few percent identifies the answer without a single keystroke. If they are 18.2, 18.4, 18.6 and 18.8, you need the exact figure and should not estimate.

Useful approximations under time pressure: 10 percent is a decimal shift, 5 percent is half of that, 25 percent is a quarter, and 'roughly a third' handles anything near 33 percent. To compare two fractions quickly, cross-multiply rather than converting both to decimals.

This is also the recovery move when a question is running long. If you are 50 seconds in and still setting up, estimate, pick the closest option, flag it, and move on. On a paper with no negative marking, an estimate you can justify is worth far more than a perfect answer you never reach.

What the calculator changes, and what it does not

Most employer numerical tests allow a calculator, and this paper assumes one. Knowing that should change your strategy in two ways. First, do not burn time on mental arithmetic gymnastics — type it. Second, and less obvious, a calculator makes wrong-figure errors more dangerous, not less, because it returns a confident, precise, entirely wrong number that often sits close enough to a distractor to look right.

The defence is order of operations in the human sense: identify the figures, state what they represent, then compute. Never start typing while you are still deciding which row to use.

If a test you are sitting does not allow a calculator, the arithmetic will be visibly friendlier — round numbers, simple fractions, answers that come out whole. That itself is a signal: if you find yourself doing long division by hand on a no-calculator paper, you have probably set up the wrong calculation.

Pacing 20 minutes and reading your report

Twenty questions in twenty minutes is a minute each, but the questions are not equal. Ratio and conversion one-liners take 30 to 40 seconds; a table question with a footnote can take 90. Bank time on the short ones deliberately so the long ones do not force a rush.

Two clock rules: never exceed 100 seconds on any single question, and never leave one blank — there is no negative marking here or on most employer papers. Flag anything you estimated and revisit it only if time remains.

The report splits your accuracy four ways: percentages, ratios, data interpretation, and rates and conversion. Read it as a diagnosis rather than a score. A low percentages figure almost always means the base problem from the second section above, not weak arithmetic. A low data-interpretation figure means the reading habits in the fourth section. If all four are level but the total is low, the issue is time, and the fix is the estimation habit rather than more practice papers. Sign in before you start and your score is saved with a history for this paper alone, so a re-sit next week is measured against this one rather than against memory.