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Practice Questions 1

Spatial Awareness, also known as Spatial Reasoning, is a common component of Abstract Reasoning in psychometric testing. These questions are presented in two formats:

**Conforming Figure:**In these questions, you are required to identify which of the four given answer figures DOES share a common feature with the two given question figures.**Outlying Figure:**In these questions, you are required to identify which of the four given answer figures**DOES NOT**share a common feature with the two given question figures.

This question format might not be one which you encounter regularly in your day-to-day activities, but it is likely that you have experienced something similar in your childhood – spot the difference puzzles are based on many of the same principles as the spatial awareness problems posed in this test.

Let’s take a look at an example:

**Question:** The two unlabeled figures share a common feature. One of the answer figures does NOT share this same feature. bWhich figure does NOT share the common feature?

**Answer:** A. In each figure, there is a main shape containing a line segment. All lines are aligned with one side of the same shape, close to the boundary, except for in one figure. In A, the line segment is in the middle of the shape and aligned to no sides of the shape.

In this manner of question, there are 6 key attributes to observe in the answer figures:

**Shape:**Look for different shapes in the given problem figures – while this is a simple attribute, it will often constitute the key difference between figures.**Position:**Look for the position and placement of individual elements in the given problem figures.**Angle:**Look for differences in the direction, alignment, angle, pointing direction, etc. of different elements in the given figures.**Number:**Look for the number of certain things in the figures – for example, the number of sides in a shape or the number of given elements in a figure may constitute the difference between figures.**Shading:**Shading patterns in figures may constitute the difference between figures.**Size:**Look at the size of different elements, relative to the other elements, in the given figures.

In order to solve these questions, there is a three-step approach:

As this problem type is not necessarily one which can be solved through a formulaic approach, much of the solution lies in your ability to visually identify patterns and intuitively find the solution.

For the sake of demonstration, let’s walk through another question with the approach presented above:

**Question:** The two unlabelled figures share a common feature. One of the answer figures does NOT share this same feature. Which figure does NOT share the common feature?

**Observe**

In this question, we can immediately see that the relevant element from the SPANSS categories is shape. In each figure, we can see an upper horizontal line with a certain shape below it.

**Focus**

In the question figures, we can see that the shapes have open bottoms, and are composed of straight lines. By comparison, we can see that three of the question figures also share this feature. Only D comes with a closed bottom and non-straight lines.

**Answer**

Based on what we have observed, it would seem that D is the only outlier. Therefore, we can conclude that this is the correct answer.

**Answer: D**

As each question comes with a very short time limit to find a solution, it is critical that you practice this question format in order to develop your intuition so that you may discern the correct response quickly and accurately- generally speaking, this question type is not particularly difficult.

If you are unable to distinguish any form of pattern within the first 6 seconds, it is advised that you make an educated guess and move on – if you cannot find the pattern quickly then it is likely that you will lose precious time which could be better-spent on other questions. To that end, follow this decision tree when faced with such a question:

As with all the question types in this test, the key is to make an effective judgement as to whether you can solve the question in good time.

If you cannot find the first step towards solving the problem quickly, then you cannot afford to waste time on the question. These questions largely depend on intuition once you understand the basic principles of what to be looking out for in the figures.

To that end, the most appropriate way to prepare for these questions, rather than a formulaic approach, is to practice until you are familiar with the format to such a degree that you can intuitively recognize the common features between the answer figures and problem figures.

There is little more to say in terms of theory on this question format – instead, ensure that you practice thoroughly by making use of the question bank available in this module in order to get a sense how these questions are formulated so that nothing will catch you by surprise in the real exam.

So that we may effectively approach this question type in the course, let’s work through some further practice questions together.

**Question:** The two unlabelled figures share a common feature. One of the answer figures shares this same feature. Which figure DOES share the common feature?

**Observe**

Based on the SPANSS categories, it would appear that the relevant dimension here is position. Each image is composed of four rectangular shapes with an arrow protruding out of one of the two longer sides.

**Focus**

Looking closely at the question figures, we can see that two of the four shapes contained have the same bearing, as illustrated below:

**Answer**

Applying this criteria to the question figures, there is only one possible option which also has two shapes of the same bearing:

**Answer: C.**

**Question:** The two unlabelled figures share a common feature. One of the answer figures does NOT share this same feature. Which figure does NOT share the common feature?

**Observe**

Upon initial examination, we can see that each figure contains three shapes of different sizes. As such, the SPANSS elements to observe here are shape & size.

**Focus**

When examining more closely, we can see that the question figures feature a large shape containing a smaller, different shape, which in turn contains a smaller version of the first large shape:

Looking at the answer figures, all but one of the figures follows this trend, figure D:

As such, we can be confident that this figure does not share the common feature.

**Answer: D.**

**Question:** The two unlabelled figures share a common feature. One of the answer figures does NOT share this same feature. Which figure does NOT share the common feature?

**Observe**

Each figure features four circles, each containing an arrow of various bearings. The SPANSS element to observe here is positioning.

**Focus**

Looking closely at the question figures, we can see that each circle contains an arrow pointing in a different direction; there is an arrow pointing up, down, left and right across the four circles.

**Answer**

We can see that all but one of the answer figures, this feature is maintained. The only figure which deviates is figure C:

**Answer: C.**

Now that we have explored a number of Spatial Awareness questions together, it would be a good idea for you to move on to the practice questions available for this module and try to solve them without any help.

Apply the principles laid out in this guide, and you should have very little trouble overcoming this question type.

Just be careful that you do not get tripped up spending too much time on any individual question. If it turns out that a question is too difficult to solve in the time required, just take a guess and skip it.

If you find you have time left over after completing all questions, you could always consider coming back to this question to check it – though it is very uncommon to have time to spare in this exam.

Continue practicing and before long you will be adept at answering questions of this format. Good luck!

Practice Questions 2

Figural series involve questions that require the candidate to find the missing link between a number of figures. Figural series questions are within the boundaries of spatial awareness and are thus included in the question bank in numerous tests such as the CCAT.

For this, an important element known as inductive reasoning is required to be at the highest level. So, let’s have a look at it first.

**Inductive Reasoning**

Inductive Reasoning is a component of the greater Abstract Reasoning question category in psychometric tests. In these questions, you are required to analyze a series of figures in order to determine which figure comes next.

These questions can be delivered in a variety of styles:

- Inversion Sequences
- Rotation sequences
- Positioning sequences
- Counting sequences
- Size sequences

Questions of this manner can often appear to be extremely confusing, but with the correct methodology, you can overcome these obstacles quickly and effectively.

**Inversion Sequences**

In inversion sequences, you will be faced with figures in which certain elements are being inverted. It is quite straightforward to identify this question type, given that the key element to look out for is the inversion/flipping of individual elements in the image.

Let’s take a look at an example:

**Question:** What comes next in the sequence?

Now, this series of images can appear to be rather visually cluttered, but the route to solving this manner of problem is really quite straightforward when applying the correct methodology. Let’s walk through the steps for a solution.

First, we should examine the first two images in the sequence in order to find the change. This is seen below:

As we can see, an inversion has occurred. This indicates that this is an inversion problem.

Now that we have examined the change between the first two images, we should take a look at the next transition to see if we can identify a change of any similar nature:

So, it would seem that our pattern is the vertical inversion of arcs, with the arc to be inverted being the one above the previous inversion. Let’s apply this same process to the next arc up:

Given that we have found the pattern and applied it to the third question figure, we have our answer.

**Answer: B**

As we can see, by identifying the nature of the first two transitions, we can apply the rule to easily discern the third transition. To this end, we can follow a routine to identify a pattern and determine the next step in the sequence:

As we continue through the other question types, let’s follow this structure so that you can fully understand how these questions would be approached methodically.

**Rotation Sequences**

Rotation sequences feature a rotating figure, which may or may not have a number of other changes occurring with individual elements of the figure. In these questions, it is important to visually identify these problems quickly for the sake of a quick and effective solution.

Let’s take a look at an example of this question type, applying the methodology we laid out before this section:

**Question:** What comes next in the sequence?

Again, this series is a little confusing upon first examination. Let’s walk through the steps for a quick solution.

**Observe**

Take a look at the first two question figures. Let’s take a first glance at how they are different:

At a glance, we can see that the orientation of the image has changed, with some manner of rotation and the ring changing position. By identifying a clear rotation, we can easily identify this as a rotation sequence. The additional change in this figure is the movement of the ring.

**Identify**

As we have observed, there is a rotation imposed on the image, and the ring changes it’s bearing. Let’s identify exactly how this transition occurs:

As we can see, the image has a 45° clockwise rotation applied, and the ring is moved one step to clockwise with an inversion applied moving it to the opposite end of the line.

**Verify**

Now that we have identified the nature of the transition, let’s check the next transition to ensure that this is, in fact, the driving process behind the sequence:

As we can see, it is quite clear that the same process is applied for the second transition – as such, we can be confident that this is the correct process.

**Apply**

Now that we have identified the process to follow in this sequence, we can apply this to the third question figure to find our answer:

Having found the pattern and applied it to the third question figure, we now have our answer:

**Answer: D**

In this question, we can reach a quicker solution by sight. Of the available answer figures, only A and D conform to the movement of the arrow in the question figures, so it is impossible that B and C could be correct from the beginning.

All this leaves is to identify the movement of the ring, and given the movement of the ring in the question figures it is not any stretch of one’s cognitive capacity to see that D, visually, makes the most sense as the next movement of the ring out of the two options.

**Positioning Sequences**

Positioning sequences feature changes of individual elements of the figure, but do not change the bearing of the entire figure. The key to solving this manner of question lies in quickly identifying that only individual elements are moving, and identifying which of those are moving.

Let’s take a look at an example:

**Question:** What comes next in the sequence?

This question type presents a high volume of elements to visually assess. Let’s walk through the steps to solve this question.

**Observe**

Take a look at the elements contained within the figures. At a first glance, we can see that some of the letters are moving. Upon closer inspection, we can see that Y, A, X are moving, while D, G are not.

**Identify**

Now that we have identified the moving parts, let’s discern exactly how they are moving. Let’s do so by examining the first two figures.

It appears that, in the transition between these figures, Y has moved to the position of A, A has moved to the position of X, and X has moved to the position of Y. This would indicate that these elements are rotating in a clockwise fashion, as seen below:

**Verify**

Now, let’s check that this same movement occurs in the second transition:

We can see here that in the transition between these figures, Y has moved to the position of A, A has moved to the position of X, and X has moved to the position of Y. This is consistent with the first transition. As such, we have verified that this is the correct movement to make.

**Apply**

Now we have found the manner of repositioning undergone in each transition, we can find the final item.

In order to find the solution, we must move A to the position of X, X to the position of Y, and Y to the position of A. The result of this is seen below:

By rotating the three moving elements, we have found our answer:

**Answer: A**

**Counting Sequences**

In counting sequences, a given element of an image will either increase or decrease, along with other potential changes in the figure. In these questions, it is important to quickly recognize that the count of a certain element is changing, and isolate that change in order to find the solution.

Let’s take a look at an example:

**Question:** What comes next in the sequence?

**Observe**

Let’s look at the question figures in order to ascertain what is happening here.

It appears in these figures that the elements being changed are shape and shading.

**Identify**

Let’s examine the first two question figures to identify exactly what is changing here.

In the first two question figures, we can see that the second figure has one more side, and is not shaded. As such, we can see that this is a counting sequence, with alternating shading as an additional element.

**Verify**

In order to verify that we have the right manner of transition, let’s examine the second transition.

Once again, it is evident that there is one additional side added to the shape, and the shape is shaded once more. As such, we infer that the method of transition is by adding one more side and inverting the shading.

**Apply**

Now that we know we are to add one more side to the shape and invert the shading, we know that the shape is to be an unshaded hexagon, as seen below:

As such, we have our answer:

**Answer: B**

In reality, this question did not require the meticulous steps; rather it could have been solved by sight. We immediately see the alternating shading which immediately rules out C and D as answers, and A has exactly the same number of sides as the third question figure, leaving only B as a viable answer. In these questions it is often desirable to reach the answer by elimination.

**Size Questions**

In size questions, you will be presented with figures which are changing in size by some measure. These can either be shrinking or expanding, and may come with an additional element of change.

The trick with these questions is to identify the increment/position of change and apply it to find the solution.

Let’s take a look at an example:

**Question:** What comes next in the sequence?

**Observe**

Let’s examine the three question figures.

We can see here that the image is expanding horizontally with a tendency towards the upper-right.

**Identify**

In order to ascertain what is going on here, let’s take a look at the first two question figures.

Between these two question figures, we can see that a certain volume is added to the figure, increasing its size. Our hypothesis here is that the change is the addition of a certain volume to the figure.

**Verify**

In order to check this trend, let’s look at the second transition to see if the same process is taking place.

Here, it would seem that the same event has taken place. A fixed volume is being added to the shape vertically and then to the right when it cannot progress vertically. Let’s visualize this as if it were on a grid:

Using this grid, we can see that the shape begins at four units, and is increased by three units with each increment. As such, we can be certain that the addition of three units is the process taking place here.

**Apply**

Applying this process, we can easily reach the answer by visualizing a grid. We add three more units to the figure, and we reach our answer.

This final image on the grid corresponds to the correct answer:

*Answer: B*

Once again, it was perhaps unnecessary to take the time to walk through each step meticulously in reaching this answer.

When observing the answer figures, it is immediately obvious that A and D cannot be the correct response on account of the positioning of the smaller vertical component of the figure; A’s is on the bottom of the shape rather than the top, and D does not have one at all. This leaves B and C.

Looking at the question figures, we see that the rightmost component of the shape is shrinking, so it cannot be C as that part is exactly the same size as it is in the third question figure. Therefore, B must be the answer.

**Solving Inductive Reasoning Problems Quickly**

Despite walking through each problem presented step by step, we have examined after some of them how we can solve them more quickly by sight and intuition.

The point which is being put forward here is that you often will not need to approach these questions with such a formulaic approach – it is simply helpful to understand the principles so that you can effectively approach these questions in an accurate and time-efficient manner.

It is only by fully understanding a concept that we can reliably take shortcuts.

If you find that you can’t quite reach the solution to most of these questions based on your intuition, make sure that you have fully understood the principles in the meticulous step-by-step approach and apply those principles on this module’s practice questions until you find that you start noticing patterns in this question type and can take the shortcuts required to maximize your success.

In some instances, it might be the case that the question is too complicated to solve in a time-efficient manner.

It is important to remember that there will only be a very short amount of time available per question if all questions are attempted, and time can be saved by skipping the harder questions in favor of getting the easier points.

With many psychometric tests, the average score is far below the maximum possible score, in many cases being around 40% of the total possible score. In this sense, it is often favorable to skip the harder questions to pick up points as efficiently as possible.

In order to effectively make decisions in the tight time frame provided, follow this decision tree for Inductive Reasoning questions:

By following this decision process, you can effectively answer the questions which are worth answering, and not linger too long on those which are time traps. In doing so, you can maximize the efficient use of your time so that you may score as high as you possibly can on this component of your test.