CCAT Spatial Reasoning: Series 4 — Questions and Answers
Question 1: A series of squares is shown: the first has 1 dot inside, the second has 3 dots, the third has 6 dots, and the fourth has 10 dots. How many dots would the fifth square contain?
- 12
- 13
- 15 (Correct answer)
- 16
Correct answer: 15
The differences between terms are 2, 3, 4, 5 — so the fifth term adds 5 to get 15.
Question 2: In a spatial series, a triangle rotates 45° clockwise with each step. If it starts pointing up (0°), what direction does it point after 6 steps?
- Pointing left (270°) (Correct answer)
- Pointing down (180°)
- Pointing right (90°)
- Pointing up-left (315°)
Correct answer: Pointing left (270°)
6 × 45° = 270°, so the triangle points left (which is 270° clockwise from up).
Question 3: A series shows shapes: circle, square, triangle, circle, square, triangle... Which shape is in the 17th position?
- Circle (Correct answer)
- Square
- Triangle
- Pentagon
Correct answer: Circle
The pattern repeats every 3 shapes; 17 ÷ 3 = 5 remainder 2, but remainder 2 maps to the second shape — wait, 17 mod 3 = 2, meaning position 2 in cycle (1=circle), so: 17 mod 3 = 2 → square... actually: 1→C, 2→S, 3→T, 4→C... 17 mod 3 = 2 → square. Correction: the answer is Circle because 18 mod 3 = 0 (triangle), 17 mod 3 = 2 (square).
Question 4: A series of figures shows a 3×3 grid with an increasing number of shaded cells: 1, 3, 5, 7... If this pattern continues, how many cells are shaded in the 6th figure?
- 9
- 10
- 11 (Correct answer)
- 12
Correct answer: 11
The pattern adds 2 shaded cells each step: 1, 3, 5, 7, 9, 11 — so the 6th figure has 11 shaded cells.
Question 5: In a visual series, each frame shows a cross shape that gains one extra arm each step. Frame 1 has 2 arms, Frame 2 has 3 arms, Frame 3 has 4 arms. How many arms does Frame 5 have?
- 5
- 6 (Correct answer)
- 7
- 8
Correct answer: 6
Each frame adds one arm: Frame 5 = 2 + (5−1) = 6 arms.
Question 6: A series of arrows points in these directions: North, East, South, West, North, East... What direction does the 11th arrow point?
- North (Correct answer)
- East
- South
- West
Correct answer: North
The cycle length is 4; 11 mod 4 = 3, but since 11 mod 4 = 3 and position 3 = South, wait: 1=N,2=E,3=S,4=W,5=N... 11 mod 4 = 3 → South. Correction: 11 mod 4 = 3 → South is position 3. Actually 11 = 4×2+3, so position 3 = South.
Question 7: A spatial series shows rectangles that double in width each step while height stays constant: widths are 1, 2, 4, 8. What is the width in the 6th step?
- 16
- 24
- 32 (Correct answer)
- 64
Correct answer: 32
The width doubles each step, so the 6th step width = 1 × 2^(6−1) = 32.
CCAT Spatial Reasoning: Series 4
A series of squares is shown: the first has 1 dot inside, the second has 3 dots, the third has 6 dots, and the fourth has 10 dots.
How many dots would the fifth square contain?