# Inductive Reasoning – Written Guide

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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 third question figure, we have our answer.

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:

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:

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 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:

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: