CFAT Problem Solving: Figure Series 3 — Questions and Answers
Question 1: In a 3×3 grid, one cell is shaded and moves one position to the right each step, wrapping from column 3 back to column 1. Starting at row 1, column 1 in figure 1, where is the shaded cell in figure 4?
- Row 1, Column 1 (Correct answer)
- Row 1, Column 2
- Row 1, Column 3
- Row 2, Column 1
Correct answer: Row 1, Column 1
The cell moves right: column 1→2→3→1 (wrap); figure 4 completes the full cycle and returns to column 1.
Question 2: A figure series shows a rectangle divided by horizontal lines. Figure 1 has 1 line (2 sections), figure 2 has 2 lines (3 sections). How many sections does figure 6 contain?
- 5 sections
- 6 sections
- 7 sections (Correct answer)
- 8 sections
Correct answer: 7 sections
Each figure n has n lines and n+1 sections, so figure 6 has 6 lines creating 7 sections.
Question 3: A series shows a black square moving diagonally down-right one step at a time in a 4×4 grid. Starting at row 1, column 1 in figure 1, where is the square in figure 3?
- Row 2, Column 2
- Row 3, Column 3 (Correct answer)
- Row 3, Column 2
- Row 2, Column 3
Correct answer: Row 3, Column 3
Moving diagonally down-right: (1,1)→(2,2)→(3,3), placing the square at row 3, column 3 in figure 3.
Question 4: In a figure series, the shaded region alternates between the top half and bottom half of a square. Starting with the top half shaded in figure 1, which figure first shows the bottom half shaded?
- Figure 2 (Correct answer)
- Figure 3
- Figure 4
- Figure 5
Correct answer: Figure 2
The shading alternates each step, so figure 2 is the first to show the bottom half shaded.
Question 5: A triangular arrangement shows circles in rows: row 1 has 1 circle, row 2 has 2, row 3 has 3, and so on. How many circles total appear in a figure showing 5 complete rows?
- 10
- 12
- 15 (Correct answer)
- 20
Correct answer: 15
The total follows triangular numbers: 1+2+3+4+5 = 15.
Question 6: In a 2×2 grid, one quadrant is shaded and rotates clockwise each step: top-left → top-right → bottom-right → bottom-left → top-left. Starting at top-left in figure 1, which quadrant is shaded in figure 7?
- Top-left
- Top-right
- Bottom-right (Correct answer)
- Bottom-left
Correct answer: Bottom-right
The 4-step cycle repeats: figure 5=top-left, figure 6=top-right, figure 7=bottom-right.
Question 7: A series shows nested shapes where the outer and inner shapes always have the same number of sides. Figure 1: triangle inside triangle. Each step adds 1 side to both shapes. What shapes appear in figure 6?
- Hexagon inside hexagon
- Heptagon inside heptagon
- Octagon inside octagon (Correct answer)
- Pentagon inside pentagon
Correct answer: Octagon inside octagon
Starting at 3 sides and adding 1 per figure: figure 6 has 3+5=8 sides, making an octagon inside an octagon.
CFAT Problem Solving: Figure Series 3
In a 3×3 grid, one cell is shaded and moves one position to the right each step, wrapping from column 3 back to column 1.
Starting at row 1, column 1 in figure 1, where is the shaded cell in figure 4?