Numerical Reasoning Test Practice

What the real test usually looks like

Numerical reasoning tests come from many publishers, so the exact format depends on the one your employer uses. Most versions share these features:

• Data first, then questions. You get a table, bar chart, line graph, pie chart or short business scenario, usually with several questions about the same data.
• Short and tightly timed. SHL lists its Verify Interactive Numerical Reasoning test as up to 10 questions in 18 minutes (SHL factsheet). Its separate Numerical Calculation test, aimed at entry-level jobs, is listed as up to 12 questions in 10 minutes (SHL factsheet).
• Often adaptive. Both of those SHL tests use computer adaptive technology, so the next question depends on how you did on the last one, and two candidates rarely see the same set.
• Taken online, often on any device. SHL says its interactive tests are designed for unsupervised use and can run on any device, including phones. In the interactive version you may build a chart or fill in a spreadsheet instead of only picking an option.
• Workplace data. SHL describes the content as budgets and costs, trends and margins, for roles in finance, IT, professional services, production and sales. TalentLens offers a Numerical Data Interpretation Test that assesses the ability "to interpret and manipulate numerical data in the workplace" (TalentLens), and Saville Assessment describes its numerical reasoning measure as interpreting figures (Saville Assessment).

What the employer sees. Usually a report with your result compared against a reference group, not a list of your answers. Whether you see your own result depends on the employer.

Calculator rules vary. Some tests allow your own calculator, some show one on screen, and some allow none. Your invitation or the instruction screen will tell you, so check before you start.

The math itself stops at high school level: percentages, ratios, averages, rates and conversions. The difficulty comes from finding the right numbers quickly, and from wrong options designed around common slips.

Question types with worked examples

These are the question types that come up again and again, each with the method and the trap that the wrong options are built on.

1. Percentage change. Revenue rose from $240,000 to $276,000. What was the percentage increase? The change is $36,000. Divide by the starting value: 36,000 / 240,000 = 0.15, so 15%. Trap: dividing by the new value (36,000 / 276,000 = about 13%), which is always one of the options.

2. Reverse percentage. After a 12% discount, a contract costs $8,800. What was the original price? The discounted price is 88% of the original, so divide: 8,800 / 0.88 = $10,000. Trap: adding 12% back on ($9,856). A percentage of the new figure is not the same as a percentage of the old one. Our percentage questions guide has more of these.

3. Successive changes. A price rises 10%, then falls 10%. Is it back where it started? No: 1.10 x 0.90 = 0.99, so it ends 1% lower. Trap: assuming the two changes cancel out.

4. Ratios from a table. A team of 48 is split between engineers and analysts in the ratio 5 : 3. How many more engineers than analysts are there? 8 parts make 48, so one part is 6. Engineers are 30, analysts 18, and the difference is 12. Trap: answering with one of the group sizes instead of the difference. See the ratio questions guide for sharing, scaling and combining ratios.

5. Weighted average. Store A has 30 staff with an average tenure of 6 years. Store B has 10 staff averaging 2 years. What is the average across both stores? Total years: 30 x 6 + 10 x 2 = 200, over 40 staff, so 5 years. Trap: averaging the two averages (4 years), which ignores that Store A is three times bigger.

6. Rates and time. Machine X fills 1,200 bottles an hour and Machine Y fills 800. Working together, how long do they take to fill 5,000 bottles? Combined they fill 2,000 an hour, so 5,000 / 2,000 = 2.5 hours. Trap: averaging the two times instead of adding the rates. The speed, distance and time guide covers the same method for journeys.

7. Currency and units. A table is headed "$ thousands" and shows a cost of 4.5, and a supplier invoice is for 4,600 euros at 1 dollar = 0.92 euros. The cost is $4,500, and the invoice is 4,600 / 0.92 = $5,000. Trap: multiplying by the rate (giving $4,232) or forgetting the "thousands" in the heading.

How to prepare

1. Find out which test you are taking. The invitation often names the publisher. A 10 question adaptive test and a 12 question calculation test need different pacing.
2. Know your pace before test day. SHL's interactive numerical test allows 18 minutes for up to 10 questions, about 1 minute 48 seconds each; its calculation test allows 10 minutes for up to 12, about 50 seconds each (SHL, SHL). Divide the minutes on your own invitation by the number of questions, and practice to that number.
3. Read the question before the data. Then hunt for only the two or three numbers you need. Tables often hold far more data than any one question uses.
4. Estimate first. A rough answer in your head ("a bit over 10%") lets you rule out options that are off by a factor of ten, and catches calculator typos.
5. Drill the five core calculations until you do not have to think about the method: percentage change, reverse percentage, ratio sharing, weighted average and unit conversion.
6. Keep full numbers until the end. Round only the final answer. Rounding at step one of a two-step question is how you land on the option next to the right one.
7. Use the calculator you will have. If the test has an on-screen calculator, practice with one; if you can use your own, use a basic model you know well.
8. Practice on the device you will use. Charts and tables are harder to read on a phone, so if you plan to take the test on one, practice on one.

How scoring usually works

Raw score. The number of questions you got right. On its own it says little, because tests differ in length and difficulty.

Percentile. Most publishers compare your result with a norm group, a large set of people who took the same test, such as graduates or managers. A 70th percentile means you scored as well as or better than 70% of that group. The employer chooses the norm group, so the same performance can give a different percentile on different applications.

Adaptive scoring. On adaptive tests, like SHL's interactive numerical test, the questions get harder or easier as you go, so the score reflects which questions you answered as well as how many. SHL says the adaptive design gives "a more precise score".

There is no universal pass mark. Each employer sets its own target for each role, and many look at your result alongside the rest of your application.

Our practice score is the number of our own questions you got right, with a breakdown by question type so you know which calculation to work on. It is not a score from any real test and does not predict a percentile.

Common mistakes on numerical reasoning tests

• Dividing by the wrong number. Percentage change uses the starting value. Share of a total uses the total. Say "out of what?" before you divide.
• Mixing up percent and percentage points. An interest rate going from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate.
• Reading the wrong row, column or year. Tables put similar figures side by side on purpose. Put a finger (or the cursor) on the row you need.
• Ignoring the chart axis. A bar chart whose axis starts at 80 makes small differences look huge. Read the numbers, not the bar heights.
• Missing the units. "$ thousands", "millions", percentages versus counts. Many wrong options are the right number in the wrong unit.
• Spending three minutes on one question. If a question is eating your time, choose your best estimate and move on. One question is rarely worth more than another.

A one-week numerical reasoning study plan

• Day 1: Take the free sample above without the timer. Note every question you got wrong and why: method, misreading or arithmetic.
• Day 2: Work through the percentage questions guide, especially percentage change and reverse percentages.
• Day 3: Do the ratio questions guide, then redo the sample's ratio questions from memory.
• Day 4: Rates and time, with the speed, distance and time guide. Practice reading two-step tables with a timer.
• Day 5: Take a full timed mock at the real pace. With the 30-Day Pass you get full mocks for this test, each with explanations.
• Day 6: Review your mock by question type, drill your weakest type, then take a second mock.
• Day 7: Light review only. Set up your device, calculator and quiet room, and get a good night's sleep.

Test day checklist

• A charged laptop or tablet, or the device the invitation asks for, with a stable internet connection.
• A basic calculator if your own is allowed, plus scratch paper and a pen for intermediate results.
• A quiet room where you will not be interrupted for at least 30 minutes.
• Notifications off, other tabs closed.
• Read every instruction screen: it tells you the time limit, the number of questions and whether you can go back.
• Glance at the timer at the halfway point, not after every question.