How to Solve SHL's Numerical Reasoning Practice Test (2024)

Since we have 4 persons for whom we should calculate, the best and shortest way to do this will be to create a general formula and to plug in the correct numbers for each person.

According to the data given in the top section, the formula should be:

(Miles_0-250) x 0.11 + (Miles_250-500) x 0.10 + (Miles₅₀₀₊) x 0.05

Intuitive Explanation for the Formula:

If the person has traveled more than 250 miles, then they have covered the entire first milestone (first 250 miles).

If they traveled more than 500 miles, it means they have also covered the second milestone (second 250 miles).

Everything that is left after the first 500 miles will be calculated in the third and last milestone (501 miles and above).

Let’s solve for each person to make it clearer.

Person A

For person A, the data given is:

• (Miles_0-250) = 250 miles (Person A traveled more than 250 miles).
• (Miles_250-500) = 250 miles (Person A traveled more than 500 miles).
• (Miles₅₀₀₊) = 505 – 500 = 5 miles

Plugging the numbers into the formula above, we gain:

250 x 0.11 + 250 x 0.10 + 5 x 0.05 = £52.75

That means that person A has calculated his or her expenses correctly.

Person B

For person B, the data given is:

• (Miles_0-250) = 250 miles (Person B traveled more than 250 miles).
• (Miles_250-500) = 330 – 250 = 80 miles (Person B traveled less than 500 miles).
• Since person B traveled less than 500 miles, (Miles₅₀₀₊) is 0 and will be ignored.

Plugging the numbers into the formula above, we gain:

250 x 0.11 + 80 x 0.10 + 5 x 0.05 = £35.50

That means that person B has calculated his or her expenses incorrectly.

Person C

Using the method above:

• (Miles_0-250) = 250 miles
• (Miles_250-500) = 250 miles
• (Miles₅₀₀₊) = 732 – 500 = 232 miles

Plugging the numbers into the formula above, we gain:

250 x 0.11 + 250 x 0.10 + 232 x 0.05 = £64.10

That means that person C has calculated his or her expenses incorrectly.

Person D

Using the method above:

• (Miles_0-250) = 250 miles
• (Miles_250-500) = 289 – 250 = 39 miles

Plugging the numbers into the formula above, we gain:

250 x 0.11 + 39 x 0.10 = £31.40

That means that person B has calculated his or her expenses correctly.

Tip: In such questions, it is recommended to take note of commonly used numbers, such as (250 x 0.11 = 27.5, 250 x 0.1 = 25), and not to calculate them again every time.

To calculate yearly interest, we use the following formula:

This formula is a special case of the general formula to calculate change, this way:

Intuitively, we’re basically asking “how much more money do I have by the end of the year compared with what I had in the beginning, relative to the sum I had).

A very simple example to clarify this:

If I deposited $100 at the beginning of the year and ended with $110, then:

Year 1:

Tip: If you feel confident taking shortcuts, you may save time by dividing the entire formula by 10,000 for a more convenient calculation:

Year 2:

Remember! You should always use last year’s sum (in this case, $10,125), and not the initial sum (in this case, $10,000).

Year 3:

Putting the data on a graph, we gain:

First, we notice that we are not given (nor are we requested to find) the actual budget of each department – only the percentages.

That means that we should calculate using the percentage data only.

To solve it in the best and fastest way, we will form 3 equations based on the data given for each department:

• Engineering - E + 2P = 76
• Product Delivery - P + F + 2M = 93
• Marketing - No Data
• Finance - 2F + 2P + 3M = 171

Where:

• E – Engineering budget
• P – Product Delivery budget
• F – Finance budget
• M – Marketing budget

Let’s rewrite the equations:

(1) E + 2P = 76 (%)

(2) P + F + 2M = 93 (%)

(3) 2F + 2P + 3M = 171 (%)

Now we have 4 equations in 4 variables to solve, where the last equation is, naturally:

(4) E + P + F + M = 100 (%)

(The entire company’s 100% budget is divided between the four departments).

Note: From now on, all numbers refer to percentages.

When approaching such a system of equations, the best thing to do is to take a moment and look at the equations, finding the combination to allow us to reduce the number of variables to 1.

Note that if we subtract Equation 3 from two times Equation 2, we are left only with variable M:

2 x (Equation 2) – (Equation 3) :

2 x (F + P + 2M) – (2F + 2P + 3M) =

2F + 2P + 4M – 2F – 2P – 3M = 2 x 93 – 171

So:

4M – 3M = 15

M = 15

Now, although we cannot find any other variable (E, F, or P) explicitly, we can explicitly express the combination F + P, and use equation 4 to find E:

From Equation 2:

P + F + 2M = 93

Plugging M = 15:

(P + F) + 30 = 93

So:

P + F = 63

Now, let’s plug both M = 15 and P + F = 63 into equation 4 to find E:

E + 63 + 15 = 100

E = 22

We now have M and E. the next step would be to look for an equation to plug those into and reveal a new variable (either P or F). for that, we can easily use Equation 1:

E + 2P = 76

22 + 2P = 76

2P = 54

P = 27

Tip: If we have 3 out of 4 variables, we can save time by NOT calculating the remaining variable (in this case, F). The interactivity of the pie chart will make sure that F is automatically derived from the last 3.

Pretty similarly to question #3 in this guide – this one is a classic case of systems of equations used to find several variables.

In this case, we have 6 variables – let’s arrange them in a table for convenience:

Note: This table is for the sake of explanation only. During the real test, don’t spend time arranging it, and simply name the variables as is most convenient for you.

Out of the 4 data items, the first and last ones on the list are the best place to start, as they can immediately reveal the number of clients in each method.

Let’s dismantle these pieces of data to their components:

A total of 540 new clients were acquired this year

Referrals accounted for 1/3 of all new clients

Therefore, Cold Calls and Client-Initiated account for the remaining 2 thirds of new clients:

Cold Calls + Client-Initiated = 540 - 180  = 360

Using the last bit of information - Cold Calls accounted for twice as many as Client-Initiated:

2 (Client-Initiated) + Client-Initiated = 360

Client-Initiated = 120 Clients

Cold Calls = 240 Clients

So, we can now rearrange the graph as:

Tip: The pale grey lines above the graph means that you are able to change the value below the line. In this case, the total value of all bars can be changed, but the division of Client Initiated between Northern (60%) and Southern (40%) is pre-determined.

Now, let’s form some other equations using the other data items.

We should try and focus on data items containing the least variables. Data item 2 is the best for this purpose:

The Northern region produced 40% more Referrals than the Southern region.

Or in the form of an equation:

(I) NR = 1.4 x SR

We already know the total number of referrals:

(II) NR + SR = 180

Plugging (I) into (II):

2.4 x SR = 180

SR = 75

NR = 105

Converting to percentages (Don’t forget that!):

And again, we can rearrange the graphs as:

It is time to approach the last piece of information – data item 2:

The Southern region produced 84 more clients through cold calls than those that were Client Initiated.

Or in the shape of an equation:

SC = SI + 84

Since we already know the percentages in the Client-Initiated bar, we can easily deduce SI:

SI = 0.4 x 120 = 48

Plugging into the previous equation:

SC = 48 + 84 = 132

Again, converting into percentages:

And rearranging the graph to its final position:

If you remember the tip regarding the pale grey lines from the previous question, you can immediately see that the number of people at School A is given as 200. That is also supported from data item 3.

Let’s start with data item 1 to determine the percentage of students and teachers at School A.

Since we need only the percentage and not the number of students and teachers at the school, we can consider the whole as 100 (percent), and not 200 (number of people).

Teachers : Students = 1 : 9

It is simple to deduce, then, that 90% of the school population are students, and 10% are teachers.

We shall rearrange the graph, then:

The only remaining data item is 2

School B has half as many students as School A and 10 more teachers.

We can immediately form the two equations:

Converting into percentages:

So, the final graph shall appear so:

In this question, all the total numbers of phone owners are given, and we only need to determine the percentages of smartphone and non-smartphone users.

Tip: If you see one data item given per year, it is recommended to solve for one year at a time.

2010

Of the 200 million adults who owned cellphones in 2010, 70 million owned smartphones.

This data item gives a quick answer to the ownership division in 2010:

Let’s move on with the rest of the data and rearrange the graph in the end.

2014

By 2014, 230 million adults owned cellphones, and 56.5 million more adults owned smartphones than in 2010.

The first half of the sentence is already known (230 total cellphone owners). Let’s take a look at the second half, then:

By 2014… 56.5 million more adults owned smartphones than in 2010.

Quickly formulating an equation:

As ever, not forgetting to convert to percentages:

Tip: Remember that in percentage questions, you can save some precious seconds of calculating the complementary percentage (e.g., 45% in the example above). The interactivity of the question will make sure that both percentages sum up to 100%.

2018

In 2018, 250 million adults owned cellphones and non-smartphone users dropped by 72.5 million compared to 2010.

Again, we know the first half (250 million owners in 2018), so we regard only the second half of the data item:

In 2018…non-smartphone users dropped by 72.5 million compared to 2010.

This statement in the form of an equation yields:

Note that the 130 is derived from the calculation for 2010, in which we determined 70 million smartphone users out of 200 million total.

In percentage:

So, the final graph will be:

This question is a simple question of matching conditions, let’s go very briefly over the solution:

Order 1

Since the contract length is longer than 6 months but shorter than 12, the discount can be either 0% or 5%. To figure out which, we should calculate the average monthly spending.

Therefore, the correct discount is 5%.

Note: The question requires that both terms regarding average monthly spending AND contract length of a specific type, must apply.

(E.g., average monthly spending of $30 or more AND a contract length of 12 months or longer for a discount rate of 10%).

Therefore, in this case (as mentioned earlier), as long as the average monthly spending is above $20, 5% discount will be given.

Order 2

The contract length is longer than 12 months, the discount can be any of the three discounts – 0%, 5%, or 10%. Again, we shall calculate the average monthly spending to determine.

Since we have average monthly spending of less than $20, the correct discount is 0%.

Orders 3 and 4

A fast way to solve the question is using a table, and we will demonstrate how to use it for orders 3 and 4:

So, the final answer is:

• Order 1 - 5%
• Order 2 - 0%
• Order 3 - 5%
• Order 4 - 10%

To solve this question effectively and quickly, we will use one formula to find the desired metric, namely, the agent’s number of successful calls, and fill the data in a table, leaving the ranking to the end.

The formula is given by:

To find an agent’s number of successful calls, we need to divide the total time he or she spends on calls by the average call length:

Note: Pay attention to make all calculations in the same time unit (hours/minutes). For convenience, we will use minutes in this case (1 hour = 60 minutes).

We will show a detailed calculation for Beatrice:

So, Beatrice takes 72 calls a day, out of which 30% are successful – that is, 21.6 calls on average.

We will repeat the same process for all agents:

The best place to start is with the team member whose plants we know accurately and see what other team members can be expressed by it.

The only team member for whom we have a numerical value is Edward.

Edward = 160

Now, here comes a catch. Although it seems we can easily deduce Beatrice’s number of planted trees can be calculated using Edward’s data:

Beatrice planted a quarter of what Edward planted and a third of what George planted.

However, we still do not have enough data to calculate Beatrice’s plants, since we need George’s plants first (The word “and” here comes in the meaning of “plus”, and not in the meaning of “and also”).

At the end of the question, we will show the wrong calculation done for Beatrice.

Therefore, we will calculate for Diana first:

Diana planted a quarter of what Edward planted, plus 50 more.

Diana = (160/4) + 50 = 90

We can now calculate for George:

George planted half of the trees that Diana planted.

George = Diana/2 = 90/2 = 45

As we go back to Beatrice, we can understand that her data item means that she planted a quarter of what Edward did PLUS a third of what George did, namely:

Beatrice = (160/4) + (45/3) = 55

And we can now proceed to Fei:

Fei planted double what Beatrice planted.

Fei = Beatrice x 2 = 55 x 2 = 110

And lastly, Phillip:

Phillip planted half of what Fei planted, plus 20 more.

Phillip = (Fei/2) + 20 = (110/2) + 20 = 75

Now let’s sum everyone up, to see we did not make any calculation errors along the way:

160 + 90 + 45 + 55 + 110 + 75 = 535

Arranging the data in ranking order:

• Edward - 160 - 6
• Diana - 90 - 4
• George - 45 - 1
• Beatrice - 55 - 2
• Fei - 110 - 5
• Phillip - 75 - 3

Tip: Pay attention to the definition of the rankings! In some questions, such as this one, 1 will be defined as least, and 6 as most. In others (such as question 8), the opposite will be true.

Wrong solution for George and Diana:

Let’s assume Beatrice indeed planted a quarter of what Edward did (160), which is ALSO a third of what George did.

Beatrice = 160/4 = 40

And therefore:

George = Beatrice x 3 = 40 x 3 = 120

And Diana:

Diana planted a quarter of what Edward planted, plus 50 more.

Diana = 160/4 + 50 = 90

Now we will see if George’s data is satisfied:

George planted half of the trees that Diana planted.

George = 90/2 = 45

So, we have a contradiction, with 120 trees calculated from Beatrice’s data item, but 45 from George’s. Therefore, this solution cannot be correct.

Ratings

Firstly, we know that in any case in which the average ratings are lower than 5, no award is given.

So, before calculating the sales, let’s first see which person deserves an award, to begin with – this will eliminate the need to calculate sales for persons with ratings lower than 5.

The average ratings are calculated simply as:

Sales

Thanks to this pre-check of ratings, we now need to calculate sales for only 3 out of 4 persons.

To calculate how well the person has exceeded his or her sales goal, we use:

Forming a table again (remember that Person B receives no reward due to low ratings).

Remember – there is no need to waste time forming these tables in the actual test! The detailed tables are given here only for convenience and for explanatory purposes.