Raven's Progressive Matrices Matrix Structure and Logic Questions and Answers — Questions and Answers
Question 1: In a 3x3 matrix, the figure in the third cell of each row is determined by a rule of subtraction. The elements of the second figure are removed from the first figure. Row 1 shows: (A large square with 4 small circles in the corners) - (A large square with 2 small circles on the left side) = (A large square with 2 small circles on the right side). Row 2 shows: (A plus sign inside a circle) - (A vertical line inside a circle) = (A horizontal line inside a circle). Following this rule, what is the missing figure in Row 3: (A shape with 8 sides and 2 diagonals forming an 'X') - (A shape with 8 sides and 1 diagonal line leaning right '/') = ?
- A shape with 8 sides
- A shape with 8 sides and 1 diagonal line leaning left '\' (Correct answer)
- A shape with 8 sides and a plus sign '+'
- A shape with 2 diagonal lines forming an 'X'
Correct answer: A shape with 8 sides and 1 diagonal line leaning left '\'
The governing rule for each row is that the third figure is the result of the first figure minus any overlapping elements from the second figure. In the third row, the first figure is an octagon with two diagonals ('X'). The second figure is an octagon with one right-leaning diagonal ('/'). Subtracting the common elements (the octagon shape and the '/' diagonal) from the first figure leaves only the octagon shape and the left-leaning diagonal ('\').
Question 2: A 3x3 matrix operates on a cumulative rule set. Moving one cell to the right adds a specific feature, and moving one cell down adds a different feature. The starting cell (top-left) is a blank square. Moving right adds concentric circles (one for each step right). Moving down adds radial lines from the center (one for each step down). What would the figure in the bottom-right cell (row 3, column 3) look like?
- A square with three concentric circles and three radial lines
- A square with two concentric circles and two radial lines (Correct answer)
- A square with three concentric circles
- A square with two radial lines
Correct answer: A square with two concentric circles and two radial lines
To reach the bottom-right cell (3,3) from the top-left (1,1), one must move two steps to the right and two steps down. Each step right adds a concentric circle, so two steps right results in two concentric circles. Each step down adds a radial line, so two steps down results in two radial lines. Therefore, the final figure combines both transformations, resulting in a square containing two concentric circles and two radial lines.
Question 3: A 2x2 matrix presents a visual analogy. The top-left cell contains a U-shape. The top-right cell shows the same U-shape with a horizontal line across the top, forming a closed square-like shape. The bottom-left cell contains a V-shape. Which figure completes the analogy in the bottom-right cell?
- An upward-pointing triangle (Correct answer)
- A diamond shape
- An inverted V-shape
- A W-shape
Correct answer: An upward-pointing triangle
The relationship in the top row is 'closure'; a line is added to close the open part of the U-shape, turning it into a complete figure. Applying this same analogical reasoning to the bottom row, a line must be added to close the open part of the V-shape. This creates a complete, upward-pointing triangle.
Question 4: In a 3x3 matrix, the rule is a 'distribution of three values'. Each row and each column must contain exactly one of each of the following: a curved shape, a shape with 3 sides, and a shape with 4 sides. The top row contains a triangle and a square. The first column contains a triangle and a circle. The center cell of the matrix contains a diamond. What must the figure in the bottom-right cell be?
- A square
- An oval
- A triangle (Correct answer)
- A pentagon
Correct answer: A triangle
This problem follows a Sudoku-like distribution rule. The three shape categories are curved (circle/oval), 3-sided (triangle), and 4-sided (square/diamond). Let's analyze the bottom row (Row 3). The first cell must be a circle (from Column 1's logic). The second cell must be a triangle (because Column 2 needs a 3-sided shape, as Row 1 and Row 2 have a 4-sided and curved shape respectively). Since the bottom row now has a curved shape and a 3-sided shape, the final cell (bottom-right) must be a 4-sided shape. Now let's analyze the rightmost column (Column 3). The top cell must be a circle (from Row 1's logic). The middle cell must be a triangle (because Row 2 needs a 3-sided shape). Thus, Column 3 has a curved and a 3-sided shape, meaning the bottom-right cell must be a 4-sided shape. Both lines of logic point to a 4-sided shape, but we need to be more specific. Let's re-evaluate. Column 3 needs one of each. Row 1 has a 3-side and 4-side, so cell (1,3) is curved. Row 2 has a 4-side (center) and needs a curved and 3-side. Column 3 will have a curved shape in (1,3). The bottom row (Row 3) has a curved shape in (3,1). So the shape in (3,3) must be a 3-sided shape, a triangle, to satisfy the distribution rule for both its row and column.
Question 5: You are analyzing a 3x3 matrix where the principle is a logical combination. The third figure in each row contains only the features (e.g., dots, lines, shading) that are unique to EITHER the first figure OR the second figure, but not features common to both. Row 1: [Striped Circle], [Striped Square], [Circle, Square]. Row 2: [Square with a Dot], [Triangle with a Dot], [Square, Triangle]. Row 3: [Hollow Star], [Hollow Star with a Circle around it], [?]. What is the missing figure?
- A Hollow Star with a Circle around it
- A Hollow Star
- A Circle (Correct answer)
- An empty cell
Correct answer: A Circle
The rule is a logical XOR (exclusive OR). The output in the third cell contains elements that appear in the first or second cell, but not in both. In Row 3, the 'Hollow Star' is a common feature to both the first and second cells, so it is excluded. The 'Circle around it' is a feature unique to the second cell. Therefore, the resulting figure is just the Circle.
Question 6: Which of the following scenarios in a 3x3 matrix BEST describes the application of a 'Progressive Change' principle?
- The third column is a superposition of the first two columns.
- Each row and column contains one circle, one square, and one triangle.
- Moving left-to-right, a central figure rotates 45 degrees clockwise per cell. (Correct answer)
- The relationship from cell A to B is the same as from cell C to D.
Correct answer: Moving left-to-right, a central figure rotates 45 degrees clockwise per cell.
'Progressive Change' refers to a continuous, step-by-step transformation of a figure across a row or down a column. The rotation of a figure by a set amount in each subsequent cell is a classic example of this principle. Superposition is a combination rule, distribution is a frequency rule, and the A:B::C:D structure is reasoning by analogy.
