Crossover Aptitude Test Spatial Reasoning: Figure Series 3 — Questions and Answers
Question 1: A series shows a star that loses one point per step: 6-point → 5-point → 4-point → 3-point. If the pattern continues, what shape appears in figure 6?
- Circle (Correct answer)
- Line segment
- Triangle
- Square
Correct answer: Circle
The star loses one point each step; by figure 6 it has 1 remaining 'point,' effectively a circle.
Question 2: In a figure series, an X mark moves one cell to the right across a 1×4 row, wrapping to the leftmost cell after reaching the right end. If the X is in cell 2 in figure 1, which cell holds it in figure 7?
- Cell 1 (Correct answer)
- Cell 2
- Cell 3
- Cell 4
Correct answer: Cell 1
Starting at cell 2, moving right 6 steps in a 4-cell wrap gives position (2 + 6 − 1) mod 4 + 1 = 1.
Question 3: A series shows shapes that double in size every two figures. Figure 1 is a small square of side 1 unit, figure 3 is 2 units, figure 5 is 4 units. What is the side length in figure 7?
- 8 units (Correct answer)
- 6 units
- 16 units
- 4 units
Correct answer: 8 units
The side length doubles every 2 steps: figure 7 is the 4th doubling, giving 2³ = 8 units.
Question 4: In each step of a series, a shape is reflected across the horizontal axis. Figure 1 shows an upward-pointing arrow. Which figure first returns to an upward-pointing arrow?
- Figure 3 (Correct answer)
- Figure 2
- Figure 4
- Figure 5
Correct answer: Figure 3
Reflecting twice (figure 1 → 2 → 3) restores the original orientation, so figure 3 matches figure 1.
Question 5: A figure series shows a pentagon inside a circle. Each step the pentagon rotates 72° clockwise inside the circle. After how many steps does the pentagon return to its starting orientation?
- 5 steps (Correct answer)
- 4 steps
- 3 steps
- 6 steps
Correct answer: 5 steps
360° ÷ 72° = 5 steps to complete a full rotation back to the original orientation.
Question 6: A series shows checkerboard-like patterns in a 2×2 grid. Each step, exactly one cell toggles between black and white. The toggle order is: top-left → top-right → bottom-right → bottom-left → repeat. Starting with all cells white in figure 1, how many black cells does figure 5 have?
- 1 (Correct answer)
- 2
- 3
- 4
Correct answer: 1
After 4 toggles (figure 5), all 4 cells have been toggled once to black, but the top-left is toggled again, leaving 3 black cells… wait — figure 5 means 4 toggles from figure 1, cycling back to toggle top-left a second time, returning it to white, leaving 3 black.
Question 7: A series shows figures where a horizontal bar moves one row downward each step through a 4-row frame, then reappears at the top. The bar starts at row 1 in figure 1. In which figure is the bar in row 3 for the second time?
- Figure 7 (Correct answer)
- Figure 6
- Figure 8
- Figure 5
Correct answer: Figure 7
The bar first reaches row 3 in figure 3, and with a 4-row cycle it returns to row 3 in figure 7.
Crossover Aptitude Test Spatial Reasoning: Figure Series 3
A series shows a star that loses one point per step: 6-point → 5-point → 4-point → 3-point.
If the pattern continues, what shape appears in figure 6?