- Col1: solid L, outline L-90, solid L-180; Col2: outline T, solid T-90, outline T-180; Col3: solid F, outline F-90, ?
Answer: solid F-180
Each column cycles rotations 0, 90, 180 degrees while the fill alternates. Column 3 starts solid, then outline, so the missing third must be solid; the rotation is 180, giving solid F-180. The tempting wrong choice is outline F-180: it gets the rotation right but ignores that the fill should return to solid.
- Examine the figure matrix shown. Determine the column rule and choose the figure that completes the matrix.
Answer: An arrow pointing down with three stripes
In each column, the arrow rotates 90° clockwise from row 1 to row 2 and another 90° clockwise from row 2 to row 3. The number of stripes in each column is constant. Column 3 shows: up-arrow with 3 stripes (row 1), right-arrow with 3 stripes (row 2), so row 3 must be down-arrow with 3 stripes. (A) has wrong direction and stripe count. (B) rotates counterclockwise. (D) doesn't rotate far enough and has wrong stripe count.
- Col1: solid ▲, outline ▷, solid ▼; Col2: outline ▷, solid ▼, outline ◁; Col3: solid ▼, outline ◁, ?
Answer: solid ▲
Read the grid in diagonal bands from upper left to lower right: one solid up-triangle, then two outline right-triangles, then three solid down-triangles, then two outline left-triangles. The missing lower-right cell begins the next band, so it must be solid, and the direction cycle up, right, down, left repeats to up. The tempting outline up-triangle gets the direction right but ignores the solid/outline alternation, which makes this cell solid.
- Col1: solid tri, outline sq, solid pent; Col2: outline sq, solid pent, outline hex; Col3: solid pent, outline hex, ?
Answer: solid 7-sided
Follow the shapes diagonally: each step right or down adds one side, and the fill alternates solid and outline. The missing cell continues row 3 as solid pentagon - outline hexagon - solid 7-sided. The tempting wrong answer is outline 7-sided, but row 3 starts solid, so the missing shape must be solid, not outline.
- Col1: 3 sides, 4 sides, 7 sides; Col2: 4 sides, 5 sides, 9 sides; Col3: 5 sides, 6 sides, ?
Answer: 11 sides
In each column, the first two numbers add to the third: 3 + 4 = 7, 4 + 5 = 9, so 5 + 6 = 11. The tempting wrong answer is 10 sides, which comes from guessing a pattern across rows instead of adding down each column. Count column by column and you'll land on 11 sides.
- Refer to the 3×3 figure matrix. Based on the column relationship, what figure should appear in the empty cell?
Answer: A triangle inscribed in a square inscribed in a circle
Each column nests shapes, with a new outer shape added each row. Row 1 of column 3 is a triangle; row 2 adds a square outside it (square containing triangle); row 3 adds a circle outside the square (circle containing square containing triangle). (A) reverses the nesting. (C) and (D) use incorrect combinations of shapes in the wrong order.
- Look at the figure matrix. Identify the column relationship and select the figure that belongs in the empty box.
Answer: A star with a white center and black points
Each column's rule: row 1 shows a fully white figure, row 2 shows the figure with ONLY the center shaded black, and row 3 shows the figure with ONLY the points/edges shaded black (inverse of row 2). In column 3, row 1 is a white star, row 2 is a star with a black center, so row 3 must be a star with black points and white center. (A) reverses the pattern. (C) and (D) ignore the partial-shading rule entirely.
- Based on the figure matrix shown, which figure fits the empty cell by following the column rule?
Answer: A square grid with the bottom-right corner shaded
Each column shows a 2×2 grid where the shaded cell moves one position clockwise each row. In column 3: row 1 has top-left shaded, row 2 has top-right shaded, so row 3 must have bottom-right shaded. (B) repeats row 1. (C) isn't a corner. (D) repeats row 2.
- Based on the 3×3 figure matrix shown, which figure completes the pattern in the missing cell?
Answer: A large circle containing three small triangles
In each column, the outer shape is constant, and the number of inner shapes increases by 1 each row. The inner shape in each column matches the outer shape of the NEXT column to the right (with column 3 wrapping to column 1). Column 3 outer shape is a circle; column 1's outer shape is a triangle, so inner shapes are triangles. Row 3 of column 3 needs 3 triangles inside a circle. (A) has wrong count. (C) and (D) swap inner and outer shapes.
- Examine the 3×3 figure matrix below. What figure completes the pattern according to the column rule?
Answer: Five overlapping circles forming a ring
In each column, the number of overlapping circles increases by 1 per row (3, 4, 5). Column 3 row 1 has 3 circles, row 2 has 4 circles, so row 3 must have 5 circles. (B) repeats row 2. (C) repeats row 1. (D) increases by too much.
- Refer to the figure matrix below. Which figure correctly completes the matrix according to the column rule?
Answer: Three black dots in a vertical column
Down each column, the number of dots stays constant but the arrangement rotates 90° clockwise. Column 3 shows 3 dots diagonally (row 1), 3 dots horizontally (row 2), so row 3 should be 3 dots vertically. (A) and (D) change the dot count. (B) repeats the row-2 arrangement.
- Study the figure matrix below. Identify the column rule and choose the missing figure.
Answer: A right-pointing arrow with a double line and a black tail
Each column has three independent features that change down the rows: (1) line thickness goes single→double→double, (2) tail color goes white→white→black, and (3) direction stays constant within each column. Column 3's arrows all point right. Row 3 needs: double line (matches row 2 rule), black tail (new feature appearing at row 3), right-pointing. (B) flips direction. (C) and (D) fail to apply the cumulative feature rules.
- Look at the figure matrix. Choose the figure that completes the empty cell based on how items in each column are related.
Answer: A clock face showing 9:00
Down each column, the hour hand rotates 90° counterclockwise each step while the minute hand stays on 12. In column 3, row 1 shows 3:00, row 2 shows 12:00, so row 3 should show 9:00. (A) follows clockwise rotation instead. (C) repeats row 1. (D) repeats row 2.
- Study the 3×3 matrix of figures below. Based on how the figures change going down each column, choose the correct figure for the missing cell.
Answer: A hexagon with a small square inside
Each column's rule: the outer shape gains one side per row (square→pentagon→hexagon), and the inner shape repeats the outer shape of row 1 but shrunk. In column 3, row 1 is a small square, row 2 is a pentagon with a small square inside, so row 3 should be a hexagon with a small square inside. (B) ignores the side-increase rule. (C) confuses the inner shape with the row-1 shape of a different column. (D) mixes both errors.
- Col1: solid tri, outline sq, solid tri; Col2: solid sq, outline pent, solid sq; Col3: solid pent, outline hex, ?
Answer: solid 5-sided
Each column repeats its starting solid shape after an outlined shape with one extra side: solid triangle, outline square, solid triangle; solid square, outline pentagon, solid square. So after solid pentagon and outline hexagon, the third must be another solid pentagon. The outline hexagon is a distractor because it completes only the middle pair, not the solid-outline-solid cycle.
- Look at the 3×3 figure matrix. Determine which figure belongs in the empty cell based on how figures change down each column.
Answer: A large diamond containing two small black diamonds and one small white diamond
Each column's rule: the outer shape stays the same; the total number of inner shapes increases by 1 per row (1, 2, 3); the number of BLACK inner shapes equals the row number minus 1, with remaining shapes white. Row 3 col 3: 3 total inner diamonds, 2 black, 1 white. (A) has only 1 black. (B) has all black. (C) has only 1 shape total.
