CCAT Spatial Reasoning: Series 2 — Questions and Answers
Question 1: A shape series shows: triangle with 1 dot, triangle with 2 dots, triangle with 3 dots, ___. What comes next?
- Triangle with 4 dots (Correct answer)
- Square with 4 dots
- Triangle with 5 dots
- Square with 3 dots
Correct answer: Triangle with 4 dots
The shape (triangle) is constant; dots increase by 1 each step. Next: triangle with 4 dots.
Two independent patterns: shape = triangle (constant); dots = 1, 2, 3, 4 (arithmetic +1). Next figure = triangle with 4 dots.
Question 2: A square rotates 45 degrees clockwise at each step. After 4 steps from the original position, what does it look like?
- Diamond (45 degrees rotated)
- Square aligned with the axes (Correct answer)
- Triangle
- Circle
Correct answer: Square aligned with the axes
4 x 45 = 180 degrees. A square has 90-degree rotational symmetry, so at 180 degrees it looks the same as at 0 degrees.
Each step = 45 degrees. After 4 steps: 180 degrees. A square has 90-degree rotational symmetry — at 180 degrees it is visually identical to the original. It is back to being a square aligned with the axes.
Question 3: In a series, the number of polygon sides increases by 1 each step: triangle, square, pentagon, hexagon, ___.
- Heptagon (Correct answer)
- Octagon
- Nonagon
- Decagon
Correct answer: Heptagon
Sides: 3, 4, 5, 6, 7. After hexagon (6 sides) comes heptagon (7 sides).
Triangle=3, square=4, pentagon=5, hexagon=6, heptagon=7. Adding one side each step, after hexagon comes heptagon.
Question 4: A series of figures has lines of symmetry: Figure 1 = 1, Figure 2 = 2, Figure 3 = 3, Figure 4 = 4. Which shape has exactly 4 lines of symmetry?
- Regular pentagon
- Square (Correct answer)
- Circle
- Rhombus
Correct answer: Square
A square has exactly 4 lines of symmetry: 2 through opposite sides and 2 through opposite vertices.
Lines of symmetry: isosceles triangle=1, rectangle=2, equilateral triangle=3, square=4, regular pentagon=5. A square has exactly 4 lines of symmetry.
Question 5: A repeating tile pattern cycles: circle, square, triangle, diamond, circle, square, triangle, diamond... What is the 19th shape?
- Circle
- Square
- Triangle (Correct answer)
- Diamond
Correct answer: Triangle
Cycle length = 4. 19 mod 4 = 3. Position 3 in the cycle = triangle.
Cycle: 1=circle, 2=square, 3=triangle, 4=diamond. For position n, compute n mod 4. 19 mod 4 = 3 (since 4x4=16, 19-16=3). Position 3 = triangle.
Question 6: A figure grows by adding one square to the right each step. Step 1 = 1 square. How many unit segments (edges) does Step 5 have?
- 16 (Correct answer)
- 17
- 18
- 20
Correct answer: 16
Step 1 = 4 edges. Each added square contributes 3 new edges (1 shared). Step n = 4 + 3(n-1). Step 5 = 4 + 12 = 16.
Step 1: 4 edges. Adding each square: 3 new edges (the shared side is not counted again). Step n = 3n + 1. Step 5 = 3(5)+1 = 16 edges.
CCAT Spatial Reasoning: Series 2
A shape series shows: triangle with 1 dot, triangle with 2 dots, triangle with 3 dots, ___.
What comes next?