The Canadian Forces Aptitude Test (CFAT) Study Guide by TEST PREP HACKER

One of the best ways to prepare for the CFAT is to take practice tests. Practice tests that cover the same subjects with similar questions. It has been proven that practice tests help students get better marks when it comes to the real test. That’s why there are practice questions throughout this guide. For the best prep possible, check out our CFAT Practice Tests for thousands of additional practice questions.

The problem solving section of the CFAT can also contain questions that work with time. These questions require you to use basic math. Just keep in mind that there are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.

Let’s take a look at the example from the official CFAT practice test.

It was 3:10 by Smith's watch when he left home to go to the post office.
While at the post office he corrected his watch by setting it forward from 3:35 to 3:44. It was 4:04 by his watch when he returned home. How many minutes was he away?

(A) 45 (B) 55 (C) 63 (D) 85

There are several ways to go about solving this question. First, you could calculate how long in total Smith was away by counting the minutes between when he left and when he returned home (4:04 - 3:10 = 54 minutes). Then, you could subtract the amount of time by which Smith corrected his watch (3:44 - 3:35 = 9 minutes). Therefore, Smith was gone for a total of 45 minutes (54 - 9), so the answer to this question is A.

Another way to solve this question is to count how many minutes elapsed between when Smith left and when he corrected his watch (3:35 - 3:10 = 25 minutes), and how many minutes elapsed from the corrected time and when Smith returned home (4:04 -3:44 = 20 minutes). Add the two together and you get the same answer, 45 minutes.

Numerical reasoning questions in this section of the CFAT assess your ability to solve number problems. Candidates should be comfortable with topics such as addition, subtraction, multiplication, division, decimals, fractions, percentages, averages, rates/ratios, and solving simple algebra equations.

While this level of math should not be very hard for people who have graduated from high school, keep in mind that calculators are not allowed while writing the CFAT, so everything must be done the long way, by hand. Also, the CFAT has a time limit, so not only must you be comfortable performing math by hand, you have to be able to do so quickly. The more time the math section eats up, the less time available for the rest of the test.

If you have been out of high school for a few years, or it has been a while since you have done math without a calculator, it is very important that you take the time to review all the basic concepts in math, and how to do them by hand. That should be followed by as much practice as possible. The more comfortable you are with math, the better you will do on the CFAT.

Let’s take a look at some of the math questions from the official CFAT practice test.

Example 1

If a child can run 10 meters while a car travels 30 meters, how many meters can the child run while the car travels 66 meters?

(A) 12 (B) 15 (C) 22 (D) 25

This is a simple ratio question. We are given a ratio, and must use that information to solve for an unknown value. Here’s how we can represent this question as a ratio. Let x represent how far the child can run while the car travels 66 meters.

To solve this equation, we simply cross multiply and then solve for x.

30x = 660

X = 22

That means the answer for this questions is C.

Example 2

A team of clothing workers had an output of 1,000 uniforms per week. This
output was increased by 20%, which demanded an increase of 50 uniforms per worker. How many workers are there on the team?
 

(A) 4 (B) 15 (C) 20 (D) 24

This is a two step word problem that involves percents and ratios. First, as we are given the fact that the increased demand for uniforms required 50 additional uniforms from each worker, in order to find out how many workers there are, we need to find out how many additional uniforms were output with the 20 % increase. To find that, we simply do the following:

1000 x 0.20 = 200

That means that the 20 % increase raised overall production by 200 uniforms per week. Of this total, each worker contributed 50 additional uniforms (this is given in the question). Therefore, if we divide 200 by 50, we will find out how many workers there are on the team.

200 uniforms = 50 uniforms per worker x the number of workers

Number of workers = 200 / 50

The number of workers on the team is therefore 4, and the answer to this question is A.

We say this a lot at TEST PREP HACKER. You must study hard and practice a lot if you want to get a great mark on this test. Nowhere is this more important than with basic math. The questions themselves may not be overly difficult, but all calculations must be done by hand. Things like long division by hand can bog people down and eat up a lot of time. Don’t let this happen to you. You need to be able to work through math question like these examples quickly. Practice math. A lot.

Number and letter series are another type of question that can be found in the problem solving section of the CFAT. Number series questions present a series of related numbers. The candidate must determine the relationship between the numbers, and then use that to determine which number should come next in the series. In other words, candidates’ must first determine which rule was used to create the series, and then use the rule to complete the series.

For example, here is an easy number series:

1, 2, 4, 8, 16, __

In this example, we are looking to find which number comes after 16. At first glance, it is rather obvious that there is a pattern to the numbers, with each number being double the previous number. 2 is double 1, 4 is double 2, 8 is double 4, and 16 is double 8. Using this pattern, we can easily predict that the next number will be double 16, or 32.

Don’t let this very easy example lull you into thinking that number series are all this easy. They aren’t. You will likely encounter number series where the pattern isn’t immediately obvious. It is therefore important to approach answering number series questions in a systematic way.

Prime Number Series

This type of number series uses prime numbers, or numbers greater than 1 which can only be evenly divided by the number 1, and the number itself. Some number series questions involve only prime numbers; that is, the only relationship between the numbers is that all of them are prime numbers.

Here is a list of the first 10 prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29…

For example, which number comes next in the following series?

31, 29, 19, 17, __

To start, we can see that this series is nothing more than prime numbers in descending order. So, to determine which number comes next, all we need to do is figure out which prime number comes before 17. The answer is 13.

When approaching number series questions, it is a good idea to first rule out the possibility that the numbers in the series are prime. If they are not, then you can move on to other ways of solving the problem.

Difference Number Series

A difference number series is one in which the pattern among the presented numbers can be equated to the differences between each set of numbers. The pattern is in the differences between each number. To get the differences, you simply subtract from each number in the series the previous number in the series.

For example, in the number series 5, 10, 15, 20, 25, the difference between each number is constant at 5. The next number in the series is simply the previous number + the difference of 5. The answer here is therefore 30.

In this example, the difference was constant. It was always 5. Again, this is a simple type of number series to solve.

Differences can also be increasing or decreasing. For example, in an increasing difference series, each number in the series increases by an increasing amount. In the series 1, 2, 4, 7, 11, 16, the difference between each of the numbers is increasing as you move through the series. The difference between the first pair of numbers is 1, the next pair 2, the next pair 3, the next pair 4, and the last pair 5.

Knowing this pattern, we can predict that the next number in the series is equal to the last number plus the difference (which increases by one each time). The next number in the series is therefore 22.

TIP: when working on a number series problem, if the answer isn’t readily obvious, start by calculating the differences between each pair of numbers in the series. Often a pattern will become much more clear when you look at the differences.

Product Number Series

In a product number series, each number in the series is multiplied by another number to get the next number in the series. As with difference number series, product number series can be CONSTANT, INCREASING, or DECREASING. That is, the number by which each number in the series is multiplied either remains constant throughout the series, the number increases through the series, or it decreases through the series.

For example, recall this number series from the start of this chapter: 1, 2, 4, 8, 16, 32. This is an example of a CONSTANT product number series. Each number in the series is multiplied by 2 to get the next number in the series.

Here is another example. This one involves an increasing product series in which each number in the series is multiplied by a number that increases as you go through the series.

4, 4, 8, 24, 96, __

In this series, the first number is multiplied by 1 to get the second number. The second number is multiplied by 2 to get the third number. The third number is multiplied by 3 to get the fourth number. And the fourth number is multiplied by 4 to get the fifth number. So we can see that each successive number is multiplied by an increasing number (1,2,3,4) to get the next number. The following diagram may help clarify.
 

We can therefore predict that the next number in the series is the product of 96 x 5, or 480.

TIP: if a number series has the same number twice in a row, it is a good bet that the series is a product number series.

Combination Number Series

To make things even more complex, some number series are actually a combination of number series. If when solving a number series question, and you move through the steps of determining the differences, and they don’t seem to make any sense, and there is no discernable pattern, there is a good chance it is a combination number series.

In this kind of number series, there are two series. The series skip over every other number. The first, third, and fifth numbers are in their own series, and the second, fourth and sixth numbers are in their own series.

Consider the following series:

5, 60, 8, 55, 11, 50 …

At first glance, there does not seem to be any pattern or relationship between the numbers. Now take a look at the same series:

5, 60, 8, 55, 11, 50 …

The italic numbers are in their own series, in which each successive number increases by 3, and the bold numbers are in their own series, in which the next number decreases by 5 each time.

More about Number Series

Number series can get increasingly complex. It is likely that you will encounter difficult number series on the Test of Reasoning. It is therefore very important to have a solid foundation in number series, and to have good understanding of how to systematically go about solving number series questions. To further your understanding, check out the following videos:

• Khan Academy: Finding patterns in numbers

• Khan Academy: Using inductive reasoning

• Number Series Reasoning Tricks

• Video Tutorials by MathsSmart

Figure series are another type of question that can be found in the problem solving section of the CFAT. These questions seeks to assess a candidate's ability to determine relationships and patterns in a set of objects, and then apply that pattern to predict the next object in the set. It is sometimes called non-verbal reasoning. The idea is to have you figure out the pattern, and then mentally apply the pattern to determine what should come next.

For example:

△ is to ▲, as ○ is to ______.

a) ●  b) △  c) ◀  d) ◌

With this type of question, you will be given a series of shapes or objects, usually three of them. You are then asked to pick which object or shape should come next from four provided answers.

In the example above, the relationship between the first and second triangles is one of colour or shading. The first △ has no shading, while the next ▲ is shaded in black. Applying that relationship to the next set of shapes, the ○ would become ●. The answer is therefore a).

In other words, what happened to the first triangle to make it into the second triangle? In this example, the first triangle was coloured in black to become the second triangle. If we apply that to the third shape, ○, we must fill it in black in order to get the correct answer, ●.

These kind of questions are testing what is known as inductive reasoning or abstract reasoning. That is, they are testing your ability to find the pattern in a set, and then use that pattern to predict what comes next.

Now this was a very easy example. The questions on the HOAE will be more challenging. Figuring out the relationship between the first two objects will be more complex, involving multiple movements, rotations, mirroring, and shading.  

Here is another example:

This example involves two separate transformations applied to change the first image into the second image. The first step is to figure out what changes have taken place.

• SHADING: the arrow changes from black to white

• ROTATION: the arrow rotates 90 degrees clockwise (to the right)

Now that we know the two changes required to make the first image into the second image, we can apply the changes to the third image to get the correct answer.

• First change the star from white to black

• Next, rotate the star 90 degrees clockwise

When we apply these changes, we get the image c) from the answers provided.

Again, this example was not overly tough. The questions on the HOAE can get harder. Some can have several different objects or shapes, with each shape changing in a different way. In that case, you have to figure out how each shape has changed individually, and also in relation to the other.

Here is another, harder example:

This example involves two different shapes changing in different ways. To solve this question, start by looking at what each shape is doing on its own.

WHITE CIRCLE:

• MOVES: the white circle moves clockwise across three sides of the square (across to the right, down, and then back across to the left), to end up on the bottom left corner.

• There does not appear to be any other changes to the white circle

BLACK TRIANGLE:

• MOVES: the black triangle moves clockwise across two sides of the square (up and across to the right, to end up in the top right corner

• SHADING: the black triangle changes colour to white

• ROTATION: the black triangle is rotated 90 degrees counterclockwise (to the left)

Now we can apply these separate changes to the two different shapes presented in the third image in the question, and figure out the answer.

• Move the white diamond clockwise across three sides of the square so that it ends up in the bottom left corner

• Move the partial white circle clockwise across to sides of the square so that it ends up in the top right corner

• Next change the shading of the white partial circle to black. Note that the original pattern changed the colour of the triangle from black to white. In this case we are changing the colour from white to black. The colours are different, but the pattern remains the same: the colour of the shape has changed to the opposite colour

• Finally rotate the now black partial circle 90 degrees counterclockwise

Applying these changes to the third image presented in the question, we see that the answer is the image in b).

Answer the following spatial ability practice question.