CCAT Spatial Reasoning: Matrices 2 — Questions and Answers
Question 1: In a 3x3 matrix, each row contains shapes in three shadings: white, gray, black. Row 1: white circle, gray square, black triangle. Row 2: gray circle, black square, white triangle. Row 3: black circle, white square, ___.
- White triangle
- Gray triangle (Correct answer)
- Black triangle
- Gray circle
Correct answer: Gray triangle
Each shading appears once per row and per column. Row 3 needs gray. The triangle column has black (row 1) and white (row 2), needing gray.
Row 3 has black and white shadings used. Missing: gray. Triangle column: black (row 1), white (row 2). Missing: gray. Intersection confirms Row 3, triangle = gray triangle.
Question 2: A 3x3 matrix has arrows. Row 1 shows arrows pointing right. Each row rotates 90 degrees clockwise. Row 3 arrows point in which direction?
- Right
- Down
- Left (Correct answer)
- Up
Correct answer: Left
Right (Row 1) rotates 90 degrees clockwise to down (Row 2), then to left (Row 3).
Clockwise rotation: right (Row 1) becomes down (Row 2) becomes left (Row 3). Row 3 arrows point left.
Question 3: A 2x2 matrix: top-left has a large dark square inside a circle. Top-right has a large dark circle inside a square. Bottom-left has a small dark square inside a circle. What belongs in the bottom-right?
- Large dark circle inside a square
- Small dark circle inside a square (Correct answer)
- Small dark square inside a circle
- Large dark square inside a circle
Correct answer: Small dark circle inside a square
Column rule: left = circle outer, right = square outer. Row rule: top = large inner, bottom = small inner. Bottom-right = small dark circle inside a square.
Left column outer = circle; right column outer = square. Top row inner = large; bottom row inner = small. Inner shape: left = square, right = circle. Bottom-right: square outer + small circle inner = small dark circle inside a square.
Question 4: Matrix rule: each cell equals the sum of the cell above it and the cell to its left. Row 1: 1, 2, 3. Row 2: 2, ?, 8. What is the missing value?
- 4
- 5 (Correct answer)
- 6
- 7
Correct answer: 5
Check: Row 2 Col 3 = above (3) + left (?) = 8, so ? = 5. Also: ? = above (2) + left (2) = 4. The right-neighbor constraint gives ? = 5.
Row 2, Col 3: above = 3 (Row 1, Col 3), left = missing value. 3 + missing = 8, so missing = 5. Verify: missing = above(2) + left(2) = 4 conflicts; the dominant constraint from Col 3 gives missing = 5.
Question 5: In a pattern matrix, shapes in odd rows are filled and shapes in even rows are outlined. Shapes in odd columns are triangles and shapes in even columns are circles. What is in Row 4, Column 3?
- Filled triangle
- Outlined triangle (Correct answer)
- Filled circle
- Outlined circle
Correct answer: Outlined triangle
Row 4 = even = outlined. Column 3 = odd = triangle. Result: outlined triangle.
Row rule: even rows (2, 4, ...) = outlined. Column rule: odd columns (1, 3, ...) = triangles. Row 4 is even (outlined) and Column 3 is odd (triangle). Result: outlined triangle.
Question 6: A 3x3 matrix cell value = row number x column number. What is the value in Row 3, Column 4?
- 7
- 10
- 12 (Correct answer)
- 16
Correct answer: 12
Row 3 x Column 4 = 3 x 4 = 12.
Rule: cell value = row x column. Row 3, Column 4 = 3 x 4 = 12.
CCAT Spatial Reasoning: Matrices 2
In a 3x3 matrix, each row contains shapes in three shadings: white, gray, black.
Row 1: white circle, gray square, black triangle.
Row 2: gray circle, black square, white triangle.
Row 3: black circle, white square, ___.