Raven's Progressive Matrices Logical Figure Operations Questions and Answers — Questions and Answers
Question 1: In the provided 3x3 matrix, the figure in the third column of each row is derived from a logical operation applied to the figures in the first two columns. The operation remains consistent for all rows. Given the patterns in the first two rows, which of the following options correctly completes the third row?
Row 1: (1) A 2x2 grid with top-left and bottom-right squares shaded. (2) A 2x2 grid with top-left and top-right squares shaded. (3) A 2x2 grid with only the top-left square shaded.
Row 2: (1) A circle with a vertical diameter line. (2) A circle with a horizontal diameter line. (3) A circle with a small dot at the very center.
Row 3: (1) A solid black square. (2) A hollow square outline. (3) ?
- A hollow square with a solid black dot in the center.
- A solid black square with a hollow square inside.
- An empty cell. (Correct answer)
- A solid black square.
Correct answer: An empty cell.
The rule is a logical AND operation, also known as intersection. The third figure in each row contains only the elements that are common to both the first and second figures. In Row 1, only the top-left square is shaded in both grids. In Row 2, the only common point between a vertical and horizontal diameter is the exact center. In Row 3, a solid black square (all area) and a hollow square outline (only the perimeter) have no area in common, resulting in an empty figure.
Question 2: A 2x2 matrix is presented where the relationship between the top-left and top-right figures is analogous to the relationship between the bottom-left and the missing bottom-right figure. Top-left: A hollow circle positioned above a horizontal line. Top-right: The same hollow circle is now half-submerged below the line, and the submerged portion is shaded black. Bottom-left: A hollow, upright equilateral triangle is positioned above a horizontal line. Which figure completes the analogy in the bottom-right cell?
- A hollow triangle fully below the line.
- A solid black triangle positioned on top of the line.
- A hollow triangle half-submerged below the line, with the submerged portion shaded black. (Correct answer)
- A hollow triangle that is inverted and rests its point on the line.
Correct answer: A hollow triangle half-submerged below the line, with the submerged portion shaded black.
The analogy is based on an object interacting with a line. The figure in the first cell moves down to intersect the line, and the portion of the figure that crosses below the line becomes shaded. The hollow circle becomes half-submerged and the submerged half is shaded. Therefore, the hollow triangle must also move down to become half-submerged, and its submerged triangular tip must be shaded black.
Question 3: Analyze the 3x3 matrix, which follows two simultaneous rules: one rule governs the progression across each row from left to right, and a different rule governs the progression down each column from top to bottom. If the top-left cell contains a small square, and the center cell (row 2, column 2) contains a medium circle, what is the figure in the bottom-right cell (row 3, column 3)?
- A large circle.
- A small triangle.
- A medium triangle.
- A large triangle. (Correct answer)
Correct answer: A large triangle.
The two rules are: 1. Across the rows, the size of the shape progresses from small, to medium, to large. 2. Down the columns, the shape itself changes from a square (top row), to a circle (middle row), to a triangle (bottom row). To find the figure in the bottom-right cell (row 3, column 3), we apply both rules. The row (bottom) dictates the shape is a triangle. The column (right) dictates the size is large. Therefore, the correct figure is a large triangle.
Question 4: In the following 3x3 matrix, the third figure in each row is a result of the motion between the first and second figures. Row 1: (1) A dot in the top-left corner of a square. (2) A dot in the top-right corner. (3) A horizontal line across the top of the square. Row 2: (1) A dot in the top-left corner. (2) A dot in the bottom-left corner. (3) A vertical line down the left side of the square. Row 3: (1) A dot in the top-left corner. (2) A dot in the bottom-right corner. (3) ? Which option correctly completes Row 3?
- A plus sign in the middle of the square.
- A diagonal line from the top-left to the bottom-right corner. (Correct answer)
- A dot in the center of the square.
- A circle enclosing the square.
Correct answer: A diagonal line from the top-left to the bottom-right corner.
The rule is that the figure in the third cell represents the path traced by the dot moving from its position in the first cell to its position in the second cell. In Row 1, moving from top-left to top-right creates a horizontal line. In Row 2, moving from top-left to bottom-left creates a vertical line. In Row 3, the dot moves from the top-left corner to the bottom-right corner, which traces a diagonal line.
Question 5: A 3x3 matrix is governed by a conditional transformation rule that is applied from one cell to the next across each row. The rule is: if a figure contains a straight line, it rotates 90 degrees clockwise; if it contains a curved line, it is reflected across a vertical axis. In the third row, the first figure is a capital letter 'S'. What will the third figure in that row be?
- A capital letter 'S'. (Correct answer)
- The letter 'S' rotated 90 degrees clockwise.
- A horizontally flipped 'S' (a backwards 'S').
- The letter 'S' rotated 180 degrees.
Correct answer: A capital letter 'S'.
The transformation from cell 1 to cell 2 is based on the properties of the figure in cell 1. The transformation from cell 2 to cell 3 is based on the properties of the figure in cell 2. The letter 'S' contains only curved lines. Applying the rule, the figure in cell 1 (S) is reflected vertically to get the figure in cell 2 (a backwards S). The backwards 'S' also contains only curved lines, so it is reflected vertically again to get the figure in cell 3. Reflecting a backwards 'S' vertically returns it to the original 'S'.
Question 6: In a 3x3 matrix, the figure in the third column is the result of a cumulative construction of the figures in the first two columns. The same principle applies down each column. Top Row: (1) A triangle. (2) A square. (3) A triangle inside a square. First Column: (1) A triangle. (2) A circle. (3) A triangle inside a circle. Given this logic, if the figure in the center cell (row 2, column 2) is a single dot, what must the figure in the bottom-right cell (row 3, column 3) be?
- A circle inside a square, with a dot in the center. (Correct answer)
- A dot inside a circle.
- A dot inside a square.
- A triangle inside a circle, with a dot in the center.
Correct answer: A circle inside a square, with a dot in the center.
The matrix operates on cumulative construction (superimposition) both horizontally and vertically. The bottom-right cell is the combination of the cell above it (row 2, column 3) and the cell to its left (row 3, column 2). We must first determine those two cells. Cell (2,3) is the combination of (2,1) and (2,2), which is a circle and a dot, resulting in a dot inside a circle. Cell (3,2) is the combination of (1,2) and (2,2), which is a square and a dot, resulting in a dot inside a square. Therefore, the final cell (3,3) is the combination of (a dot inside a circle) and (a dot inside a square). Superimposing these results in a dot inside a circle which is itself inside a square.
