Numerical reasoning practice test

This numerical reasoning practice test has 12 questions and a 12-minute clock, with no timer on each question. It covers percentages, ratios, rates, averages, growth and break-even, which many graduate and professional numerical tests ask for. When you finish you get a worked explanation for every question and a list of the skills you missed.

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Try three numerical reasoning questions, with worked answers

Each example is a short workplace problem of a kind the 12-question diagnostic also asks, written for Testonome practice. Work it out on paper first: Check your answer then shows the full solution. There is no clock and no score, and the questions and answers are free to use, with no sign-up.

Percentage change
A delivery team recorded 250 orders in March and 320 orders in April. By what percentage did the number of orders change?
Check your answer
1. Take the difference first: 320 - 250 = 70 orders.
2. Divide by March, the month the change started from: 70 ÷ 250 = 0.28.
3. Read that as a percentage: 0.28 × 100 = 28 percent, a rise.
Answer: 28 percent.
Check first
Dividing 320 by 250 gives 1.28, which makes April 128 percent of March. That says how big April is next to March, not how far the orders moved. The rise is the difference, 320 - 250, divided by 250, which comes to 28 percent.
Learn and practise percentage change
Ratio sharing
A bonus pool of 4,800 euros is shared between the early and late shifts in the ratio 5 : 3. How much does the late shift receive?
Check your answer
1. Count the parts before splitting anything: 5 + 3 = 8 parts.
2. One part is worth 4,800 ÷ 8 = 600 euros.
3. The late shift holds three of those parts: 600 × 3 = 1,800 euros.
Answer: 1,800 euros.
Check first
Dividing 4,800 by 3 would treat the late shift's 3 parts as the whole pool. The pool is split into 8 equal parts, and the 3 says how many of them the late shift takes.
Reading the ratio from the wrong end gives 3,000 euros, which is the early shift's five parts. The late shift takes the smaller share, so anything above half of the 4,800 pool is the wrong shift.
Learn and practise ratio sharing
Weighted average
60 customers rated a service a mean of 9 out of 10, and a separate group of 140 customers rated it a mean of 6.5. What is the mean rating across both groups together?
Check your answer
1. Weight each mean by the group behind it: 60 × 9 = 540 rating points.
2. Then the larger group: 140 × 6.5 = 910 points.
3. Add the two totals: 540 + 910 = 1,450 points from 200 customers.
4. Divide by the people, not by the number of groups: 1,450 ÷ 200 = 7.25.
Answer: 7.25 points out of 10.
Check first
Averaging the two means gives 7.75, which is right only when both groups are the same size. Here the 140 customers who rated it 6.5 outnumber the 60 who rated it 9, so the combined mean sits nearer the lower rating.
Learn and practise weighted average

The 12 questions measure 12 skills

Percentage changeWork out how much a figure rose or fell, as a percentage of where it started.Learn and practise percentage change
Share of a totalExpress one part as a percentage of the whole it belongs to.Start the share of a total drill
Reverse percentageRecover the figure a stated percentage change was applied to.Learn and practise reverse percentage
Ratio sharingSplit a total in a given ratio, or read one share back to the whole.Learn and practise ratio sharing
Proportional scalingCarry a rate from one quantity to another in direct proportion.Learn and practise proportional scaling
Rate conversionCarry a rate across a change of time unit without losing the conversion factor.Start the rate conversion drill
Unit priceReduce two offers to a price per unit so they can be compared.Start the unit price drill
Currency conversionConvert an amount at a stated rate and apply a charge in the right direction.Learn and practise currency conversion
Nested proportionApply a percentage to the group a first percentage picked out, not to the whole.Start the nested proportion drill
Weighted averageCombine group means using the sizes of the groups behind them.Learn and practise weighted average
Compound growthApply a percentage repeatedly to a base that moves with each period.Learn and practise compound growth
Break-evenCover a fixed cost from the margin each unit earns, not from its price.Start the break-even drill

The formula behind each skill, with one worked example, is on one page: Numerical reasoning test formulas, with examples

How to choose which of these to practise next, from one practice attempt you have reviewed: Numerical reasoning test tips: make practice count

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Numerical reasoning practice test

Try three numerical reasoning questions, with worked answers

Percentage change

Ratio sharing

Weighted average

The 12 questions measure 12 skills

Preparing for a test an employer named