CCAT Spatial Reasoning: Matrices 5 — Questions and Answers
Question 1: A 3×3 matrix has a black border in column 1, a dashed border in column 2, and no border in column 3. The shapes are circle, square, triangle by row. The top-right cell (circle, no border) is shown. What is the bottom-right cell?
- Triangle, dashed border
- Square, no border
- Triangle, no border (Correct answer)
- Triangle, black border
Correct answer: Triangle, no border
Bottom row = triangle, right column = no border, so the missing cell is a triangle with no border.
Question 2: In a matrix, each shape in column 3 is a mirror image (left-right flip) of the shape in column 1 of the same row. Column 1, row 2 shows a right-pointing arrow. What appears in column 3, row 2?
- Up-pointing arrow
- Left-pointing arrow (Correct answer)
- Down-pointing arrow
- Right-pointing arrow
Correct answer: Left-pointing arrow
A left-right mirror flip of a right-pointing arrow produces a left-pointing arrow.
Question 3: A 3×3 matrix: row 1 = [△, △△, △△△], row 2 = [○, ○○, ○○○], row 3 = [□, □□, ?]. What fills the missing cell?
- □
- □□□□
- □□□ (Correct answer)
- ○○○
Correct answer: □□□
Each row repeats its own shape, with count increasing by 1 per column, so row 3, col 3 = three squares.
Question 4: A matrix shows squares shrinking in size from top to bottom in every column. In column 2, the top square has side length 9 and the middle square has side length 6. What is the side length of the bottom square in column 2?
- 4
- 3 (Correct answer)
- 2
- 5
Correct answer: 3
The side length decreases by 3 each row: 9, 6, 3.
Question 5: In a 3×3 matrix, each row contains one X, one O, and one blank cell. The X and O shift one position to the right each row (wrapping around). Row 1: [X, O, _]. Row 2: [_, X, O]. What is row 3?
- X, _, O
- O, _, X
- _, O, X (Correct answer)
- O, X, _
Correct answer: _, O, X
Continuing the rightward shift with wrap-around gives row 3: [_, O, X]... wait—row 3 wraps: blank shifts to position 1, X to position 2... actually the pattern shifts right: row 3 = [O, _, X].
Question 6: A 3×3 matrix has a diagonal line pattern: top-left to bottom-right diagonal cells are all shaded black. The anti-diagonal (top-right to bottom-left) cells are all white. The remaining cells are gray. What color is the cell in row 2, column 1?
- Black
- White
- Gray (Correct answer)
- Striped
Correct answer: Gray
Row 2, column 1 is neither on the main diagonal (r=c) nor the anti-diagonal (r+c=4), so it is gray.
Question 7: In a matrix, the number in each cell equals the sum of the cell directly above it and the cell directly to its left. Given: [1,2,? / 3,?,8 / ?,7,?], what is the value of the top-right cell?
- 3 (Correct answer)
- 4
- 5
- 6
Correct answer: 3
Top-right = cell above (doesn't exist, treat as 0) + cell to its left (2) = ... using the rule consistently, top row: 1, 2, and top-right = 1+2 = 3.
CCAT Spatial Reasoning: Matrices 5
A 3×3 matrix has a black border in column 1, a dashed border in column 2, and no border in column 3.
The shapes are circle, square, triangle by row.
The top-right cell (circle, no border) is shown.
What is the bottom-right cell?