- The following page contains a
**10-question free SHL Numerical Reasoning practice test (Multiple-Choice version)**, a test developed by the screening tests provider SHL**.** - If you are about to take the
**SHL Interactive version**, check out the Free SHL Numerical Reasoning practice test (Interactive). - If you are not sure which version you have, check out our SHL Test Finding Guide.

This sample test will **get a sense of the difficulty, content, and structure** of the SHL Numerical Reasoning Test.

Based on the actual SHL Numerical Reasoning Test time constraints, the practice test should take approximately** 10 minutes** to complete.

For a timed version of this test, click here.

Good luck!

SHL Numerical Free Practice Sample Question #1

Lea had £2,400 in her bank account, she spent 1/6 of the money on rent, and from the remainder, she paid 2/5 for the credit card company. If Lea spent another £450 on a new coffee table, what fraction of the initial amount was left in her bank account?

29/240

7/48

1/4

5/16

11/15

Correct Answer

Incorrect Answer

The money left after paying the rent was:

(1 - 1/6) X 2400 = 5/6 X 2400 = $2,000

After paying for the credit card company she had left:

(1 - 2/5) x 2000 = 3/5 X 2000 = $1,200

The total amount left is 1200 - 450 = $750, and therefore the fraction that was left out of the original amount is 750/2400 = 75/240 = 25/80 = 5/16

SHL NumericalFree Practice Sample Question #2

What proportion of both sites' April and May traffic was for Cuisine.net?

29.7%

31.3%

34.2%

35.7%

38.1%

Correct Answer

Incorrect Answer

To calculate this, we add up the total page views of cuisine.net for April and May and divide this amount by the total hits of both sites for the same period.

Therefore, the calculation would be:

(35+45)/(35+45+70+60) = 80/210 = 38.1%

**The SHL Numerical Reasoning Test combines the ability to conduct quick and accurate calculations (a challenging task although a calculator is usually allowed), and, more importantly, the deduction and interpretation of numerical data from tables and graphs.**

SHL Numerical Free Practice Sample Question #3

What proportion of the unemployed graduates for 2020 studied in private universities?

0.45

0.54

0.2

0.17

0.3

Correct Answer

Incorrect Answer

To answer the question, you need to calculate the total number of unemployed graduates in 2020 (private + state universities), and from that amount, find the proportion of graduates from private universities.

The total number of unemployed graduates in 2020 = 125 + 150 = 275

The proportion of unemployed graduates who studied in private universities = 125 / 275 = 0.45

The answer is 0.45.

SHL Numerical Free Practice Sample Question #4

Which of these breweries has the highest ratio of operational costs to revenues?

Uxbridge, UK

Malmo, Sweden

Torino, Italy

Ottawa, Canada

Canberra, Australia

Correct Answer

Incorrect Answer

A ratio refers to the **relative sizes** of two or more values.

Therefore, the ratio is calculated in the following manner: **Operational Costs / Revenues**. Since both are provided in millions of Euros, and you need to find the ratio, you can omit the millions from the calculation.

Thus, you get: **Uxbridge, UK:** 3.6 / 25 = **0.144****Malmo, Sweden:** 0.3 / 3 = **0.1****Torino, Italy:** 2.8 / 14 = **0.2** **Ottawa, Canada:** 0.28 / 3 = **0.093****Canberra, Australia:** 0.3 / 8 = **0.037****0.037 < 0.093 < 0.1 < 0.144 < 0.2****Torino, Italy** has the highest operational costs to revenues ratio.** Solving tip**: For the ratio to be high, the operational costs should be relatively high, and the revenues relatively low. Malmo and Ottawa have the same revenues, but Malmo has higher costs. This means Malmo’s ratio is higher than that of Ottawa so we can eliminate Ottawa. Similarly, Malmo and Canberra have the same costs, but Canberra has higher revenues, so Canberra has a smaller ratio, and we can eliminate it, as well.

**Since the SHL Numerical Reasoning Test is mostly used by the finance industry, expect to see a lot of finance-related concepts. The SHL Numerical Reasoning Test Preparation Pack is specifically tailored to address that, covering all the common financial topics included in the test.**

SHL Numerical Free Practice Sample Question #5

A mobile company offers insurance that covers cases of theft and accidental water damage. According to their policy, the insurance pays 60% and 50%, respectively, with a £30 deductible. This means the client pays the first £30, after which the insurance pays 60% in the case of theft and 50% in the case of accidental water damage.

How much will a client pay if her cell phone worth £1,080 was accidentally dropped into a glass of water?

£475

£500

£525

£555

£630

Correct Answer

Incorrect Answer

The client will pay the first £30, which leaves another £1,050, of which her insurance covers 50%.

50% of £1,050 = (50/100) x 1,050 = (1/2) x 1,050 = £525

Thus, the client's total amount will pay: £30 + £525 = **£555**.

Please note that you can use the “10%” method in this question:

10% of £1,050 = £105

50% = 5 x 10% = 5 x 105 = £525

525 + 30 = **£555**

SHL Numerical Free Practice Sample Question #6

Next year the company plans to stop making the product that requires the most extended time to produce. Which product will the company probably cut?

Product A

Product B

Product C

Product D

Product E

Correct Answer

Incorrect Answer

In this question, we must find the time required to produce each product. Since the decision about defective products is made after production has been completed, we can assume all products of a specific type are produced simultaneously, defective or functional.

Here is an explanation of a "brute-force" calculation. **Note that you can solve this question without striking a single key on your calculator - this explanation is provided in the end.**

First, we calculate the total number of units produced per year.

For example,** Product A**: We know from the table that the number of market-worthy units is 6,347. Additionally, since the percentage of defective units from total production is 36%, we can infer that the 6,347 market-worthy units are 64% of the total production (100%-36%).

Therefore, the total number of units is:

6347/0.64 = 9917.19.

Then we calculate how many units of every product are manufactured per hour:

For example:

**Product A**: 9917.19/5462 = 1.816

*Note that using your calculator can calculate this process using one step (6347/0.64/5462).

Following the same logic:**Product B**: 2380/0.76 = 3131.58 => 3131.58/5736 = 0.546**Product C**: 2849/0.77 = 3700 => 3700/4270 = 0.867**Product D**: 5467/0.71 = 7700 => 7700/3055 = 2.52**Product E**: 3620/0.75 = 4826.67 => 4826.67/4380 = 1.102

Therefore, production will cease on product B.**However**, this question can be solved without any calculations by merely examining the table. Product B has the least amount of units made, both defective and functional while having the highest total work hours. Therefore, it will have the highest ratio of **Total work hours per year** to the **Number of market-worthy units** and be cut.

**Being able to spot shortcuts like the one mentioned in question 6 is going to prove extremely valuable in saving time and increasing your score on the SHL Numerical Reasoning Test. The SHL Numerical Reasoning Test Preparation Pack is loaded with solving tips and shortcuts specifically designed to address the common obstacles and tricks used in this test.**

SHL Numerical Free Practice Sample Question #7

Which product has the lowest defective units to total work hours ratio?

Product A

Product B

Product C

Product D

Product E

Correct Answer

Incorrect Answer

This question can be solved without any calculations, using the **estimation technique**.

The lower the numerator and the higher the denominator, the lower the ratio will be. In this case, the numerator is the **number** of defective units, and the denominator is the number of work hours.

Therefore, you need to look for a product with a **low** number of defective units and a **high** number of work hours.

Product B has the highest number of work hours. Now look for the number of defective units:

The data in the table shows the **percentage** of defective units, not the absolute figures. Product B has one of the two lowest percentages, but a low percentage does not necessarily mean a low absolute number. However, we do have the absolute figures for the market-worthy units.

The smallest number belongs to Product B. Therefore, we can estimate that Product B has the lowest total number of units. We may conclude that the low percentage of defective units also means a low absolute number.

The full calculation for Product B is as follows:

- % of defective units: 24%
- % of market-worthy units: 100%-24% = 76%
- Number of market-worthy units: 2,380

If 2,380 are 76% of the units, the total number of units is:

2,380/0.76 = 3,131.58

Defective units are 24% of the total:

3,131.58*0.24 = 751.58

Finally, the total work hours per year is 5,736. Therefore, the ratio of defective units per work hour is 751.58/5,736 = 0.131

The same can be done with other products. Eventually, you will see that Product B has the lowest number of defective units and the lowest ratio.

SHL Numerical Free Practice Sample Question #8

The yearly Maths exam was administered three times. Of 432 students, 160 students took the exam on Date 1 and gained an average score of 80. As seen below, the statistics of Date 1 were used as comparison measures to the other two dates.

What was the difference between the number of students who took the exam on Date 2 and Date 3?

70

92

102

112

122

Correct Answer

Incorrect Answer

The blue columns show that the number of students who took the exam on Date 2 is 120% of Date 1. To find the number of students on Date 1, use the following principle:

160 students took the exam on Date 1 = 100%.

Students that took the exam on Date 2 = 120% of Date 1 = 160x1.2 = 192.

Likewise:

Students that took the exam on Date 3 = 50% of Date 1 = 160x0.5 = 80.

The difference is (192-80) = 112.

Shortcut:

The absolute difference between the students who took the exam on Date 2 and Date 3 is 120-50 = 70% of the students who took the exam on Date 1.

70% of 160 = 160 x 0.7 = 112.

**The SHL Numerical Test requires proficiency in various aspects of basic math - percentages, ratios, fractions, etc. The SHL Numerical Reasoning Test Preparation Pack will both walk you through the basics of these aspects and will teach you how to use them effectively to solve SHL questions.**

SHL Numerical Free Practice Sample Question #9

A bag of 100 blue and purple marbles has three times as many blue marbles as purple marbles. If purple marbles are added to the bag until the number of purple marbles in the bag is double the original amount, what is the probability of taking out a blue marble and then choosing another blue marble?

111/310

37/62

3/5

203/301

9/25

Correct Answer

Incorrect Answer

Let X represent the number of purple marbles in the bag. If so, then there are 3X blue marbles in the bag. We can thus find the initial number of purple marbles in the bag using the following equation:

3X + X = 100

4X = 100

X = 25

If additional purple marbles are added to the bag to double the original number of purple marbles, then there are now 25 x 2 = 50 purple marbles, 3 x 25 = 75 blue marbles, and a total of 125 marbles in the bag.

The probability of choosing a blue marble in the first draw is ^{75}⁄_{125} = ^{3}⁄_{5}. Now that a blue marble has been selected, only 74 blue marbles remain in a bag of 124 marbles. Therefore, the probability of choosing another blue marble is ^{74}⁄_{124} = ^{37}⁄_{62}.

Therefore, the total probability of choosing one blue marble and then another blue marble is ^{3}⁄_{5} x ^{37}⁄_{62} = ^{111}⁄_{310}.

SHL Numerical Free Practice Sample Question #10

In 2018, 667,284 unemployed people in the Netherlands, whose population was 27.53% of England. With a fixed annual population increase of 0.639% (in England- not in the Netherlands), approximately how many unemployed people in England in 2020?

4,296,108

4,801,138

8,511,287

6,987,322

6,895,245

Correct Answer

Incorrect Answer

Occasionally, you will need to make some assumptions on the SHL Numerical Reasoning Test.

For instance, in this question, while unemployment rates are measured in proportion to the labor force and not the entire population, you must answer according to the data you are given.

That is why the "Cannot say" option does not appear.

- Netherlands population 2018: 667,284/0.04 = 16,682,100.
- England population 2018: 16,682,100/0.2753 = 60,596,077

Calculating a yearly increase of England's population would require multiplying by 1.00639, equivalent to 1+0.639%. Taking that action twice: multiplying by 1.006392

England population 2020: 60,596,077*1.006392 = 61,372,969

To find out the rate of unemployment in proportion to England's population in 2020, look for the purple line's location in 2020's column in the diagram. The rate of unemployment in 2020 in England is 7% or 0.07.

England unemployed 2020: 61,372,969*0.07 = 4,296,108

**The need to make correct assumptions and solve problems based on the data given is one of the main challenges of the SHL Numerical Reasoning Test. Preparing in advance is the only way to develop this mindset.**

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