Numerical reasoning reflects mathematical ability, including general calculation skills and the ability to process and understand numbers. The ability to solve mathematical problems often indicates a person’s capacity to draw correct conclusions.

Auditors, physicists, and statisticians work with numbers professionally and are skilled at drawing conclusions based on numerical information. However, calculation skills are generally needed in almost every profession and in daily activities, such as shopping. For this reason, numerical reasoning is highly valued, and it is useful to maintain your calculation skills and familiarity with numbers.

In aptitude tests, numerical reasoning is measured through a variety of tasks, including:

• Graphs
• Tables
• Word problems
• Number series
• Pattern or figure tasks

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Graphs

In graph interpretation tasks, you must be able to read the information presented and calculate an answer based on it. Common types of graphs include bar charts, line graphs, scatter plots, and pie charts. Understanding the units and scales of the X and Y axes is essential. Reading the chart alone is usually not enough; the information must be processed using calculations as needed.

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Tables

Large sets of numbers are usually organized in tables, making it easy to find the necessary information quickly. When interpreting tables, pay attention to the title and the units provided.

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Word Problems

Word problems can be quite challenging because they often combine reading comprehension with calculation skills. These tasks test how a person filters information, so they may contain extraneous data. Solving word problems typically requires forming an equation and solving it.

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Number Series

This is a classic task type, and it is helpful to learn common repeating patterns. A number series is a sequence of numbers that continues according to a certain rule. The rules usually involve basic arithmetic, such as addition, subtraction, multiplication, or division. Multiple rules can also apply, e.g., alternating addition and subtraction. This type of task is common, especially in paper-and-pencil aptitude tests.

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Pattern / Figure Tasks

Figure tasks are often based on a number series, which is extended into visual patterns or sequences. n this case, figure or pattern tasks also require spatial awareness and spatial reasoning skills. These tasks usually demand creativity, so finding the solution often involves bold experimentation.

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Examples

Graphs

Question: How many percent more wheels were produced for product A than the total wheels for products B and C in 2018?

Answer: 40 percent

Explanation: In 2018, 105,000 wheels of product A were produced. Products B and C were produced in total 60,000 + 15,000 = 75,000 wheels.

The production ratio of A to B and C combined is: = A / (B + C) = 105000 kpl / 75000 kpl = 1,4. This means that the production of A is 1.4 times the combined total of B and C. In percentage terms, this is: 100 * 1,4 = 140 %. Therefore, product A was produced 40% more than the combined total of B and C (140% − 100% = 40%).

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Word Problem

Kristiina buys 100 iron rods for €2,250 and sells them the same day to Pirjo for €2,500, giving her a 2-year credit. The annual interest rate is 5 percent. How much profit does Kristiina actually make?

Answer options:
A = 5% B = 0% C = 20% D = 10% E = 7.5%

Answer: B

Explanation: Kristiina gave Pirjo a loan at 0% interest. If Kristiina had deposited the same amount she lent to Pirjo, she would have earned 5% interest annually. When calculating Kristiina’s actual sales profit, the lost interest income must be taken into account.

Vuosi	Sum	5 percent growth	Lost interest income
1 vuosi	2500 €	2500 € * 1,05 = 2625 €	2625 € - 2500 € = 125 €
2 vuosi	2500 € + 125 € = 2625 €	2625 € * 1,05 = 2756,25 €	2756,25 € - 2625 € = 131,25 €

Yhteensä menetettyjä korkotuloja on 125 € + 131,25 € = 256,25 €. Kristiinan myyntivoitto = myyntihinta – ostohinta = 2500 € – 2250 € = 250 €. Kristiinan todellinen myyntivoitto = myyntivoitto – menetetyt korkotulot = 256,25 € – 250 € = -6,25 €. Kristiinan todellinen myyntivoitto on siis 0 %.

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Number Series

Question: What is the next number in the series?

3  13  22  30  37  43  ?

Answer: 48

Explanation: The differences between consecutive numbers are as follows:

13 – 3 = 10

22 – 13 = 9

30 – 22 = 8

37 – 30 = 7

43 – 37 = 6.

From this, we can immediately see that the numbers are increased in order by 10, 9, 8, 7, 6. The missing number is obtained by adding: 43 + 5 = 48.

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Figure tasks

Which numbers should replace the question marks?

Answer: 32 in the square and 9 in the circle.

Explanation: The number inside the square is obtained by adding the numbers in the circles. The number for the middle square is calculated as follows: 12 + 4 + 1 + 15 = 32.

The number for the circle is obtained by subtracting the known numbers from the sum in the square: 30 − 9 − 2 − 10 = 9.

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Exercises

Age	Jan	Feb	Mar	Apr	May	Jun
under 24	4 %	5 %	6 %	12 %	11 %	12 %
25...34	17 %	19 %	17 %	19 %	18 %	18 %
35...34	35 %	37 %	38 %	35 %	37 %	36 %
45...54	27 %	24 %	25 %	22 %	22 %	24 %
over 54	17 %	15 %	14 %	12 %	12 %	10 %

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