Raven's Progressive Matrices Element Combination and Subtraction Questions and Answers — Questions and Answers
Question 1: Consider a 3x3 matrix where each cell contains a shape. The first row contains: a circle, a triangle, and a circle with a triangle inside. The second row contains: a square, a plus sign, and a square with a plus sign inside. The third row contains: a diamond, a vertical line, and a missing shape. Which of the following shapes completes the matrix?
- A diamond with a vertical line inside. (Correct answer)
- A circle with a square inside.
- A diamond.
- A vertical line inside a circle.
Correct answer: A diamond with a vertical line inside.
The rule for each row is that the third cell is a combination of the shapes from the first and second cells. The first shape forms the outer boundary and the second shape is placed inside it. Therefore, the diamond from the first cell of the third row should contain the vertical line from the second cell.
Question 2: In a 3x3 grid, the first row shows: (1) a large square with a small black circle, (2) a large square, (3) a small black circle. The second row shows: (1) a large triangle with a small star, (2) a small star, (3) a large triangle. The third row shows: (1) a large pentagon with a small cross, (2) a large pentagon, (3) a missing shape. Which shape belongs in the missing cell?
- A large pentagon.
- A small star.
- A small cross. (Correct answer)
- A large pentagon with a small circle.
Correct answer: A small cross.
The logic across each row involves subtraction. The shape in the third cell is what remains after the shape in the second cell is removed from the first cell. In the first row, removing the large square from the 'large square with a small circle' leaves the small circle. In the second row, removing the small star from the 'large triangle with a small star' leaves the large triangle. Following this pattern, removing the large pentagon from the 'large pentagon with a small cross' leaves the small cross.
Question 3: A 3x3 matrix operates on a principle of element combination down each column. Column 1 contains: a solid black circle, a hollow circle, and a solid black circle with a hollow center. Column 2 contains: a solid black square, a smaller solid black square, and a solid black square with a smaller, hollow square in the center. Column 3 contains: a solid black triangle, a small hollow circle, and a missing shape. Which of the following completes the pattern?
- A solid black square with a hollow circle inside.
- A solid black triangle.
- A hollow triangle with a solid black circle inside.
- A solid black triangle with a small hollow circle in the center. (Correct answer)
Correct answer: A solid black triangle with a small hollow circle in the center.
The rule operates vertically. The third cell in each column is a combination of the first two cells. The shape from the top cell becomes the main figure, and the shape from the second cell is placed in its center, but as a hollow version. Therefore, the solid black triangle from the top of column 3 should be combined with the small hollow circle from the middle cell, resulting in a solid black triangle with a small hollow circle in its center.
Question 4: Which of the following completes the matrix? Row 1: (1) Three horizontal lines, (2) One horizontal line, (3) Two horizontal lines. Row 2: (1) A square and a circle, (2) A circle, (3) A square. Row 3: (1) Two triangles and a diamond, (2) Two triangles, (3) ?
- A circle.
- A diamond. (Correct answer)
- Two triangles.
- A square and a diamond.
Correct answer: A diamond.
The pattern in each row is based on subtraction. The elements in the second cell are subtracted from the elements in the first cell to produce the elements in the third cell. In Row 1, three lines minus one line equals two lines. In Row 2, a square and a circle minus a circle equals a square. Therefore, in Row 3, two triangles and a diamond minus two triangles equals a diamond.
Question 5: You are presented with a 3x3 matrix scenario. Across each row, the third figure is the result of overlaying the first two figures. When two identical lines overlap, they are removed. Row 1: (1) A plus sign (+), (2) A cross (x), (3) A star shape with eight points. Row 2: (1) A vertical line (|), (2) A horizontal line (-), (3) A plus sign (+). Row 3: (1) A square (□), (2) A cross (x), (3) A missing figure. What is the missing figure?
- A square.
- A square with a plus sign inside.
- A square with a cross (x) inscribed inside. (Correct answer)
- An empty cell.
Correct answer: A square with a cross (x) inscribed inside.
The rule is a form of logical XOR or subtraction upon combination. When the first two figures in a row are combined, any overlapping lines are cancelled out. In Row 3, overlaying a cross (x) onto a square (□) results in a square with the cross inscribed inside it, as there are no overlapping lines to be removed.
Question 6: Consider a 3x3 matrix where the pattern works down the columns. Column 1: A grid of four squares (2x2), a single black square in the top-left, a grid with only the top-left square missing. Column 2: A circle divided into four quadrants, a black shading in the bottom-right quadrant, a circle with only the bottom-right quadrant empty. Column 3: A diamond shape, a small black dot in the center, a missing figure. What is the missing figure?
- A small black dot.
- A diamond with a small white dot in the center. (Correct answer)
- A diamond.
- A circle with a diamond inside.
Correct answer: A diamond with a small white dot in the center.
The rule is subtraction operating vertically. The figure in the second cell of the column is 'subtracted' from the figure in the first cell to produce the third. In Column 1, the top-left black square is removed from the grid. In Column 2, the shaded bottom-right quadrant is removed from the circle. Therefore, in Column 3, the small black dot in the center must be removed from the diamond, leaving a diamond with a hole (or a white dot) in the center.
