- Study the 3×3 matrix below. Which answer completes the missing cell?
Answer: A square divided into 4 quadrants with no quadrants shaded
In each row, the three shaded-quadrant patterns cover each of the four quadrants exactly once across columns 1 and 2, and column 3 shows whatever remains. In row 3, columns 1 and 2 together cover all four quadrants, so nothing remains — column 3 is blank. (A) and (B) are diagonal patterns that don't follow the rule. (C) would be the complement rule, not the remainder rule.
- Look carefully at the 3×3 matrix below. Which figure completes the matrix?
Answer: A cluster of 9 small dots arranged in a 3×3 square pattern
The number of dots in each cell equals the row number multiplied by the column number. Row 3, column 3 requires 3 × 3 = 9 dots. Within each row, the dot arrangements follow a pattern: the third column uses a square/grid arrangement. Therefore, the missing cell needs 9 dots arranged in a 3×3 square pattern.
- Examine the matrix of figures below. Which figure completes the pattern in the missing cell?
Answer: A large circle containing a small white square and a small black triangle
Row rule: the outer shape in row 3 is constant (circle). Column rule: column 3 contains the two inner shapes that did NOT appear in the first two columns of that row. Row 3 columns 1 & 2 show (square+circle) and (triangle+circle), so column 3 contains square+triangle. Color rule: the small shape that was black in column 1 becomes white in column 3, and vice versa — so white square + black triangle inside a circle. (A) flips the colors. (C) and (D) use the wrong outer shape.
- Look at the 3×3 matrix of figures below. Which figure belongs in the empty cell (bottom-right) to complete the matrix according to the row and column rules?
Answer: A white pentagon with 3 small black circles inside
Row rule: the outer shape gains one side across each row (triangle→square→pentagon in row 3). Column rule: the outer shape's fill color rotates black→white→white down column 3, so the pentagon is white. The number of inner dots equals (row number), so row 3 has 3 dots; the inner dots' color alternates opposite the outer shape's color, so black dots. Result: white pentagon with 3 black dots. (A) inverts both colors. (C) keeps the outer shape black (ignores column color rotation). (D) makes the inner dots white (ignores the inversion rule).
- 3x3: Row1: white circle, gray square, black triangle. Row2: gray square, black triangle, white circle. Bottom-right?
Answer: gray square
Each row shifts the three shapes one place to the left, wrapping the first shape to the end. Row 1 is white circle, gray square, black triangle; Row 2 is gray square, black triangle, white circle; so Row 3 is black triangle, white circle, gray square. The bottom-right cell is therefore the gray square. The tempting white circle is wrong because it belongs in the middle of the third row, not the last cell.
- Refer to the figure matrix below. Which choice correctly completes it?
Answer: Two overlapping circles with both circles shaded black and overlap white
Row rule: the third cell of each row is the XOR (symmetric difference) of the first two cells — regions shaded in exactly one of the first two figures become shaded in the third. In row 3, cell 1 has both circles black with overlap white, and cell 2 has only the overlap black; applying XOR leaves both circles black and overlap white. (A) is the intersection only. (C) ignores overlap structure. (D) adds an extraneous element.
- Matrix: dots +1 across rows/columns; shapes down are square, circle, triangle. Top-left square, 1 dot. Bottom-right?
Answer: triangle with 5 dots
Moving right or down adds one dot, so from the top-left square with 1 dot, the bottom-right is two steps right and two steps down: 1 + 2 + 2 = 5. Shapes run square, circle, triangle down each column, so the bottom-right shape is triangle. Triangle with 6 dots is wrong because it overcounts the steps; the correct increase is only 4 dots.
- 2x2: top-left white square, dot top; top-right white square, dot right; bottom-left gray square, dot top. Bottom-right?
Answer: gray square, dot right
Each row keeps the square color: top row is white, bottom row is gray. Each column keeps the dot position: left column has dot top, right column has dot right. So the missing cell must be a gray square with a dot right. The tempting answer, gray square with dot top, only follows the row color and ignores the column dot rule.
- Study the figure matrix below. Which option best completes the missing cell?
Answer: A clock face showing 7:30 (hands at 7 and 6)
Moving across each row from left to right, the time advances by 1 hour and 30 minutes each step. In row 3: first cell shows 4:30, second cell shows 6:00, so the third cell should show 7:30 (advancing another 1 hour 30 minutes).
- Study the 3×3 figure matrix shown. Which answer choice correctly completes the bottom-right cell?
Answer: An arrow pointing up-right with 4 tick marks on the shaft
Across each row the arrow rotates 45° clockwise. Row 3 begins with an arrow pointing left, so the cells go left→up-left→up-right. Down each column the number of tick marks increases by 1 (row 1:2, row 2:3, row 3:4). So bottom-right is up-right with 4 ticks. (B) reverses the arrow direction. (C) uses column-2's tick count. (D) combines both errors.
- Each row/column has one W/G/B and one C/S/T. Row1: WC, GS, BT. Col1: WC, GT, BS. Bottom-right?
Answer: gray circle
Top row uses W/G/B and C/S/T, and the left column forces row 2 as GT, BC, WS, so row 3 starts BS. Column 2 then needs white triangle, and column 3 needs gray circle to complete each color and shape once. The tempting gray square is wrong because row 3 already has a square in column 1 and column 3 already has a square in row 2.
- Examine the matrix provided. Which choice completes it?
Answer: Three horizontal parallel lines with a small circle below the bottom line
The circle moves down one level per column (column 1: above top; column 2: between top-middle; column 3: between middle-bottom) — and down one additional level per row. Row 3, column 3: start at above-top, add 2 column steps + 2 row steps = 4 downward moves, landing below the bottom line. (A) no movement applied. (B) only row movement. (D) only column movement.
- Refer to the matrix shown. Which option correctly fills the missing cell?
Answer: An L-shape made of 4 squares in the top-right corner orientation
The shape in each row is constant (row 3 uses L-tetromino). Across each row, the shape rotates 90° clockwise. Row 3 col 1 is L in standard orientation (bottom-left), col 2 rotated 90° CW (bottom-right), col 3 rotated 180° = top-right corner. (A) is the starting orientation, unrotated. (C) and (D) use the wrong shape entirely (T-tetromino).
- Look at the figure matrix shown. Which figure completes the matrix correctly?
Answer: A circle with 6 radial spokes and 2 concentric inner rings
Spokes: across each row, the spoke count increases by 1 (row 3: 4→5→6). Rings: down each column, the ring count increases by 1 (col 3: 0→1→2). So bottom-right has 6 spokes and 2 rings. (A) uses row 3 column 2's spoke count. (C) uses wrong ring count. (D) confuses the ring increment.
- Look at the 3×3 figure matrix. Select the choice that completes the matrix.
Answer: A hexagon with three lines through the center (like an asterisk) and no dot
Number of internal lines equals the row number (row 1:1 line, row 2:2 lines, row 3:3 lines). The dot appears only in columns 1 and 2; column 3 never has a dot. Thus bottom-right: 3 lines, no dot. (A) uses row-1 line count. (B) uses row-2 line count and adds a dot. (D) correctly has 3 lines but incorrectly adds a dot.
