# Spatial Reasoning Study Guide for the CCAT

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## General Information

The Spatial Reasoning questions on the CCAT all require visual skills, but they also involve reasoning. Usually, you also have to determine the basis for your reasoning by finding a pattern, so this skill is very important, too. Read on to find some valuable tips for addressing this type of question and some examples so you’ll know what to expect.

## Patterns

A number of spatial reasoning questions on the CCAT require you to work with patterns that include shapes and their placement. You’ll need to do two things:

Determine the pattern. Find the answer choice that shows the shape that would continue that pattern.

Many of the shapes are complex, and the patterns may require a variety of reasoning skills.

### Matrix Patterns

A matrix (the plural is matrices) is a rectangular arrangement of numbers, symbols, or expressions displayed in rows and columns. To fill in a matrix pattern means to identify the logical or numerical relationship between the arrangement of elements in the matrix. This involves analyzing the given elements to determine a rule or pattern and then applying the rule to find the missing element.

Example 1:

Answer: A. The numbers in each row are changing by 2 every time, based on the first number in the row. In the first row, 1 + 2 = 3, 3 + 2 = 5. In the second row 2 + 2 = 4, 4 + 2 = 6. To complete the final row, add 2 to 6 to get the answer 8.

Example 2:

Answer: B. The arrows are rotating clockwise 90 degrees in the row. To complete the matrix, 90 degrees clockwise from a left arrow is an up arrow.

#### Shapes in a Matrix

Shapes in a matrix are very similar to matrix patterns but they exclusively include shapes, and you must identify the shape that logically fits into the missing space to complete the pattern.

Tips

Matrix pattern questions usually follow the rules of progression, rotation, or motion.

1. Progression is when the element changes every step in a row and column. This change can be the number of elements, or their size, shape, or color.

2. Rotation is when the element will rotate in the pattern across either rows or columns.

3. Motion is when the element moves or changes position with each step.

Example 1:

Answer: D. There are three types of shapes and two filling patterns (filled or empty). The cloud and sun shapes appear three times, two of which are filled in. The moon only appears twice, and both times it is filled in. The missing shape must be the moon and empty to complete the matrix.

Example 2:

Answer: B. There are three different shapes. Each row and column contains each shape one time. To complete this matrix, the last row must contain one of each shape. Thus the missing shape is the square.

#### Matrices in a Matrix

Matrices in a matrix questions involve multiple matrices within a larger matrix. You need to determine the pattern that governs the entire structure to find the missing element.

Example 1:

Answer: C. This matrix has two rules based on shape. The heart always remains in the same row but moves one column to the right in the following frame. Therefore, it needs to be in the far right column in the answer. Only answers C and D satisfy that.

The star always remains in the same column but moves up one row in the following frame. To complete the matrix, the heart would need to move one column to the right, placing it in the last column of the second row. The star would need to move up one row, placing it in the first row of the first column.

Example 2:

Answer: A. There are always two colored boxes in the first column, four in the second column, and six in the third column. Thus, the missing matrix must contain four colored boxes.

### Complex Shape Patterns

Complex shape patterns involve more intricate designs and relationships between shapes. These questions differ from simple shapes as multiple parts are often placed in multiple orientations within each complex shape. Complex shape patterns can be challenging as they require recognizing subtle changes in transformation.

Tips

1. Analyze all elements by looking at the shapes, their position, and their relationship.

2. Look for cycles or sequences as many patterns involve repetition or transformations.

3. Check patterns in multiple directions, considering both the vertical and the horizontal.

#### Finishing a Complex Shape Pattern

In this type of question, you are given a sequence of complex shapes, and you must determine which completes the pattern. These pattern questions can show a series of three or four.

Example 1: Series of 3

Which of the figures below comes next in this sequence of figures?

Answer: C. The top-left cell in the frame contains an hourglass shape. It moves clockwise throughout the cells and wipes out the pie-shaped circle. In the fourth and missing frame, we expect the cell to move to the left, so it continues its clockwise travel, and to have a circle missing from the bottom-right cell. Thus, the correct answer is C.

Example 2: Series of 3

Which of the figures comes next in the sequence of figures shown below?

Answer: D. First, let’s identify the pattern of color of each frame. It alternates between light and dark, so the next frame should be light, eliminating answers B and C. Next, the arrow switches between down and up. The next frame should have an up arrow, making answer choice D the only option. You may have noted that the hexagon is shaded when the background is dark, but this does not affect your answer choice. Be aware that you may see distractors like this in these questions.

Example 3: Series of 4

Which of the following boxes should replace the question mark (?) to complete the pattern?

Answer: C. From left to right, in each step, a new shape is added, leaving the final answer needing five total shapes. This eliminates answer choice A. Additionally, in each step, the entire element rotates 90 degrees counterclockwise. Therefore, the missing element must have the diamond shape at the bottom, which is only in answer choice C.

Example 4: Series of 4

Which of the figures below comes next in the sequence of figures shown above?

Answer: E. Each of the three shapes in this series has its own movement, so it’s best to look at them individually. The concave shape rotates 45 degrees clockwise; if it continues this pattern, it would appear as it does in answers C, D, and E (A and B are eliminated). The right triangle flips horizontally back and forth in the sequence; to follow this pattern, the right triangle should be in its original position, eliminating choice D. Finally, the arrow rotates 90 degrees each time in the sequence, thus the arrow should be pointing to the bottom right, making E the answer.

#### Finding Missing Items in a Complex Shape Pattern

In these questions, a complex pattern with one or more missing items is given. Based on the pattern, you must determine what the missing item(s) should be. The missing pattern might appear at the beginning, middle, or end of the series.

Example 1:

Which of the figures in the second row completes the sequence of the figures shown in the top row?

Answer: B. The square in the middle is surrounded by circles, with one added around it in each step. The circles swap colors every step. They begin white, then swap to black, then back to white, and so forth. The missing frame must have the lower-right circle in white, which leaves our answer choices as B or D. We can eliminate D because the circles’ order is different from the one seen in the sequence.

Example 2:

Which of the boxes in the bottom row should replace the question mark (?) in the top row to complete the pattern?

Answer: A. Each element contains four arrows aligned horizontally. From left to right, the leftmost arrow of an element becomes the rightmost of the next element. In its new location, the arrow is also flipped horizontally. To complete the pattern, the leftmost rounded arrow must become the rightmost and flip horizontally, making A the correct answer.

### Letter Pair Patterns

Letter pair patterns involve sequences or arrangements of letter pairs. You must identify the rule or relationship governing the pairs and use it to determine the next pair or fill in the missing pair.

Example 1:

Choose the correct pair of letters that continues this series:

Answer: A. The first letter of each pair moves backward in the alphabet from Z to A. The second letter moves forward normally from A to Z.

Example 2:

What would be the next group of letters in the following series?

Answer: C. The first letter of each pair moves forward one letter in the alphabet from A to Z. The second letter moves backward by two letters in the alphabet from Z to A based on the prior sequences’ letters. The third letter moves forward by two letters (A to Z), and the fourth letter moves backward (Z to A) by one letter. Thus, the answer should move forward one from F, which is G, two letters backward from R, which is P, two letters forward from M, which is O, and one letter backward from P, which is also O.

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