Numerical Reasoning Tests

What does a numerical reasoning test actually measure?

A numerical reasoning test measures whether you can draw correct conclusions from data quickly, not whether you can do arithmetic. The maths rarely goes beyond percentages, ratios and simple arithmetic that you covered by age sixteen. What makes it difficult is that you are given more information than you need, less time than feels comfortable, and answer options designed to match the mistakes people commonly make.

Employers use it because the skill transfers. Someone who can read a table under pressure and spot which figure matters is doing the same thing an analyst does with a sales report or a manager does with a budget. It is a test of judgement applied to numbers.

In practice you will be asked to work with tables and charts covering revenue, headcount, production, market share or costs. You will calculate percentage change, work out ratios, convert between units and currencies, and compare rates. Almost every question is multiple choice with four or five options.

How do you solve percentage questions under time pressure?

Fix the base before you calculate anything. Almost every wrong answer in a percentage question comes from dividing by the wrong number, not from bad arithmetic.

Percentage change always uses the starting value as its base. If revenue goes from £240,000 to £276,000, the change is £36,000 and the calculation is 36,000 divided by 240,000, which is 15%. Divide by the finishing value instead and you get 13%, which will be sitting there as an answer option because the examiner expects that error.

Three habits save time:

1. Say the base out loud before you divide. “Percentage of what?” If you cannot answer that in a word, you are about to pick the wrong denominator.
2. Work in 10% and 1% chunks. 10% of 1,240 is 124, so 1% is 12.4, so 35% is 372 plus 62, which is 434. This is usually faster than reaching for a calculator and far less error prone.
3. Never add percentages across two stages. A 15% rise followed by an 8% fall is not a 7% rise. Multiply: 1.15 × 0.92 = 1.058, so it is a 5.8% rise. The tempting “7%” will be on the list of options.

When a question asks for the largest percentage change across several rows, the biggest absolute movement is very often not the answer, because it comes off the biggest base. Check each one against its own starting figure.

How do you read a data table quickly without missing the trap?

Read the question before you read the table. Most candidates lose time absorbing data they never use, because a typical stimulus contains three to five times more information than any single question needs.

A reliable order of operations:

1. Read the question stem first and note exactly which figure it wants.
2. Read the column headers and the units. This is where the trap usually lives. A column headed “pence per kWh” against answer options in pounds is not an accident, and neither is a table labelled “£000s”.
3. Find only the cells you need. Put a finger or a cursor on them.
4. Check whether a Total row is a total or a category. Using a total as a denominator when the question asked about one department is one of the most common errors there is.

Watch for questions that span two tables, or a table plus a line of text underneath it. The text often carries the piece that makes the calculation possible, such as an exchange rate or a fee, and it is easy to skip.

If a chart is shown alongside a table, use the chart to see the shape and the table to get the numbers. Charts are for direction and comparison. They are not precise enough to answer from, and the answer options are usually close enough together to punish anyone who tries.

How do you handle ratio questions?

Convert the ratio into parts, then find the value of one part. That single habit solves the large majority of ratio questions in a graduate test.

If 4,900 parcels are split between three depots in the ratio 3:4:7, add the parts: 3 + 4 + 7 = 14. One part is 4,900 ÷ 14 = 350. The largest depot takes 7 parts, so 7 × 350 = 2,450. Check by adding: 1,050 + 1,400 + 2,450 = 4,900.

The two errors to avoid:

• Stopping at one part. 350 will be one of the options.
• Answering for the wrong share. Read whether the question wants the largest, the smallest, or the difference between two of them.

Ratio questions also appear disguised, as “for every”, “per” or “out of”. A question saying three machines produce 7,200 units in four hours is a rate question that behaves like a ratio: reduce it to one machine for one hour, then scale back up.

How do you avoid unit and currency conversion errors?

Convert first, calculate second, and write the unit next to every number you write down. Conversion errors are the most avoidable marks lost in the whole test, and they are almost always caused by carrying two units at once.

Common traps:

• Pence and pounds. A tariff quoted in pence per kWh against options in pounds. Divide by 100 before you do anything else.
• Time written as a decimal. Two hours twenty minutes is 140 minutes. It is not 2.2 hours. Writing “2.20” and treating it as decimal gives 132 minutes, and that wrong figure will be an option.
• Thousands separators in table headers. A column headed “£000s” means a cell reading 240 is £240,000.
• Multiplying when you should divide. If the rate is quoted as units per £1, you divide the foreign amount by the rate to get pounds. Multiplying gives a number that is wrong by the square of the rate, and it is offered as an option because so many people do it.

When a fee or commission is involved, read carefully whether it applies before or after conversion, and whether it is added or deducted. Both readings will usually appear in the answer options.

How are numerical reasoning tests scored?

Most employers score you against other candidates, not against a fixed pass mark. Your raw score is converted into a percentile: being told you scored in the 70th percentile means you did better than 70% of the comparison group.

This matters for how you prepare. A raw score of 14 out of 20 tells you very little on its own, because everything depends on who else applied and what threshold that employer sets. Competitive graduate schemes commonly sift at around the 70th to 80th percentile, and some investment banks and consultancies go higher.

Two practical consequences:

• Speed is worth as much as accuracy. Most tests are designed so that very few candidates finish. Leaving questions unanswered costs you percentile position against people who attempted them.
• Guessing usually pays. Negative marking is rare in graduate numerical tests. If you are running out of time, eliminate what you can and pick. Check the instructions, because the rare exception matters.

Which employers and test publishers use numerical reasoning tests?

Numerical reasoning tests are standard across graduate recruitment in finance, consulting, engineering, law, accountancy and the civil service. If a role involves interpreting data, expect one.

Most employers do not write their own. They license from a small number of test publishers, and the format varies noticeably between them, which is why practising the right style matters more than practising more:

• SHL produce some of the most widely used tests in graduate recruitment, typically data interpretation from tables and charts under tight timing.
• Cubiks, Talent Q and Kenexa each use their own timing and question conventions, including adaptive formats where difficulty adjusts as you go.
• Employer-specific tests are common at large recruiters, often built on a publisher’s engine with the employer’s own branding and thresholds.

Find out which publisher your employer uses before you prepare seriously. It is often stated in the invitation email, and it changes what good practice looks like.

What is the best way to prepare?

Practise under the real time limit from the beginning. Working through questions untimed builds accuracy but not the thing the test actually measures, and most candidates discover the timing problem too late.

A preparation sequence that works:

1. Take one full test untimed first, reading every worked solution. The test on this page is designed for exactly that. The aim is to understand the question types, not to score well.
2. Then take tests under the clock. Around one minute per question is the usual pressure. Expect your score to fall at first.
3. Review the questions you got wrong, and equally the ones you guessed right. A lucky guess is a gap you have not found yet.
4. Practise the formats your employer actually uses, once you know the publisher.

Do not spend your time on mental arithmetic drills. The bottleneck is almost never the calculation. It is reading the question correctly, choosing the right base, and not being led into the prepared mistake.

Can you use a calculator?

Usually yes, and it matters less than people expect. Most graduate numerical reasoning tests permit a basic calculator, and many online tests provide one on screen.

The reason it matters less than expected is that reaching for a calculator costs seconds, and the arithmetic is rarely the hard part. Candidates who estimate first are consistently faster: if you can see the answer is roughly a quarter, you can often eliminate three options before calculating anything.

Check the instructions in your invitation email. Where a calculator is not permitted, the arithmetic will have been written to stay manageable by hand, which is itself a clue about the intended method.