Matrix reasoning test: 20 grids, with the rule behind each one named

Compare the first and second tiles in one row, and say aloud what is different about the figure.

Read row 1 as 1 outlined triangle, 1 half-filled triangle, 1 filled triangle. The shading is a progression: each column is fuller than the one before it.

1. Follow the shading only.
2. Bottom row: 1 outlined square, then 1 half-filled square.
3. The next shade after that completes the row.
4. Keep the same shape and you get 1 filled square.

Now find it among the options.

Answer: A. 1 filled square.

• A✓ AnswerOption A is correct: 1 filled square.
• BOption B takes its shape, triangle, from the tiles above the gap, not from its own row.
• COption C repeats half-filled for the shading. The bottom row already has it, so the gap needs another.
• DOption D is wrong on two features: its shape comes from the tiles above the gap, not its own row, and its shading repeats the bottom row.

In row 1, compare the lines of tile 1 with tile 2, then see which ones tile 3 kept.

An element in exactly one of tiles 1 and 2 stays in tile 3. In row 1, these stay: the bottom-right arc and the bottom spoke. Now apply it to the bottom row.

1. Go position by position.
2. An element in both tiles 1 and 2 is gone from tile 3, and an element in exactly one stays.
3. Tile 1: arcs at the top right and bottom right and the right spoke.
4. Tile 2: the top-right arc and spokes at the bottom and left.
5. So the missing tile has the bottom-right arc and spokes at the right, bottom and left.

Now find it among the options.

Answer: A. The bottom-right arc; spokes at the right, bottom and left.

• A✓ AnswerThe correct one is option A: the bottom-right arc and spokes at the right, bottom and left.
• BOption B keeps only tile 2's own spokes: it drops the one at the right (only in tile 1).
• COption C has two faults: its arcs join both tiles (top right extra), and its spokes keep only tile 2's own ones (right missing).
• DOption D joins both tiles' arcs: it keeps the one at the top right (in both tiles).

Take row two. Count the figures tile by tile, from left to right, and write the numbers down.

Row 2, all circles, adds one figure per column, and only the number changes. Row 1 does the same.

1. Keep the shape and shading of the bottom row and change only the number.
2. Tile 1 shows 1 filled triangle, tile 2 shows 2 filled triangles, and the pattern continues by one.
3. The missing tile is 3 filled triangles.

Now find it among the options.

Answer: C. 3 filled triangles.

• AOption A gets its shape, circle, from the tiles above the gap instead of from its own row.
• BOption B gives the number of figures as 2, which the bottom row already shows.
• C✓ AnswerThe answer is option C, which is 3 filled triangles.
• DOption D is wrong on two features: its shape comes from the tiles above the gap, not its own row, and its number of figures repeats the bottom row.

Track the flag. Read where its top points in each tile of row 1.

Rule: the flag turns the same amount at each step. Row 1 goes from top pointing right to upside down. Repeat that move from tile 2 below.

1. In the bottom row the flag goes from upside down to top pointing left.
2. It turns clockwise by the same amount at each step.
3. One more step gives an upright flag.

Now find it among the options.

Answer: C. An upright flag.

• AOption A stops the flag where tile 2 has it, top pointing left; it still has a step to take.
• BOption B turns the flag the right amount from tile 2 but anticlockwise, against the rule; its top points down.
• C✓ AnswerThe answer is option C, which has an upright flag.
• DOption D turns the flag a half turn from tile 2, a quarter turn too far, so its top points right.

Name the different shapes in the grid. Then see which of them appear in the top row.

Every row and every column has one of each shape. Row 1 shows it: 1 filled pentagon, 1 filled hexagon, 1 filled diamond. Check row 2.

1. The bottom row has 1 filled diamond and 1 filled pentagon.
2. The right-hand column has 1 filled diamond, 1 filled pentagon.
3. Each shape appears once in a row and once in a column, so only one shape is left over.
4. The missing tile is 1 filled hexagon.

Now find it among the options.

Answer: C. 1 filled hexagon.

• AOption A is wrong on two features: its shape is already in the row and the column, and its shading appears nowhere in the grid.
• BOption B introduces half-filled as its shading. No tile in the grid has it.
• C✓ AnswerThe correct one is option C: 1 filled hexagon.
• DOption D repeats pentagon for the shape, so the row and the column would each hold it twice.