Crossover Aptitude Test Spatial Reasoning: Figure Series 5 — Questions and Answers
Question 1: A figure series shows nested squares. Figure 1 has 1 square, figure 2 has 2 nested squares, and so on. The innermost square is always shaded. In figure 6, how many unshaded squares are there?
- 5 (Correct answer)
- 4
- 6
- 3
Correct answer: 5
Figure 6 has 6 nested squares total, with only the innermost shaded, leaving 5 unshaded.
Question 2: A series of figures shows an equilateral triangle that flips upward (△) and downward (▽) alternately, while also rotating 60° clockwise at each step. What orientation does figure 7 show?
- Upward-pointing (△) (Correct answer)
- Downward-pointing (▽)
- Sideways-left
- Sideways-right
Correct answer: Upward-pointing (△)
The flip alternation is independent of rotation; figure 7 is odd, so it points upward like figure 1.
Question 3: In a figure series, a shaded region grows by adding one row from the bottom each step inside a 5-row rectangle. Figure 1 has 1 shaded row; figure 5 is fully shaded. What fraction of the rectangle is shaded in figure 3?
- 3/5 (Correct answer)
- 2/5
- 1/2
- 4/5
Correct answer: 3/5
In figure 3, three of the five rows are shaded, giving a fraction of 3/5.
Question 4: A figure series shows a clock face where the hour hand advances 3 hours each step. If the hand points to 12 in figure 1, where does it point in figure 9?
- 12 (Correct answer)
- 3
- 6
- 9
Correct answer: 12
The hand moves 3 × 8 = 24 hours total, which is exactly 2 full rotations, returning to 12.
Question 5: A figure series shows overlapping shapes: in figure 1, a circle overlaps a square with a small overlap; in each subsequent figure the circle moves further right, increasing the overlap area. In figure 5, the circle is entirely inside the square. What does figure 6 show?
- Circle emerging from the right side of the square (Correct answer)
- Circle fully outside the square
- Circle centered in the square
- Circle and square separated
Correct answer: Circle emerging from the right side of the square
Continuing the rightward movement past full containment, the circle begins to emerge from the right edge of the square in figure 6.
Question 6: A series shows figures where small triangles point in rotating directions: up, right, down, left, repeating. A second row of triangles is offset by one step. If row 1 figure 1 points up, and row 2 figure 1 points right, which direction does row 2 point in figure 6?
- Down (Correct answer)
- Up
- Right
- Left
Correct answer: Down
Row 2 starts at 'right' (step 2 of the cycle) and advances 5 more steps to position 7 in the cycle (7 mod 4 = 3), which is 'down'.
Question 7: In a figure series, a diagonal striped pattern inside a rectangle shifts one stripe to the right each step. The rectangle holds exactly 4 stripes, and the pattern wraps. Figure 1 shows stripes in columns 1 and 3 (alternating shaded). What does figure 5 look like?
- Same as figure 1 (Correct answer)
- Same as figure 2
- Same as figure 3
- All stripes shaded
Correct answer: Same as figure 1
A 4-stripe wrap means the pattern repeats every 4 steps; figure 5 = figure 1 (5 mod 4 = 1).
Crossover Aptitude Test Spatial Reasoning: Figure Series 5
A figure series shows nested squares.
Figure 1 has 1 square, figure 2 has 2 nested squares, and so on.
The innermost square is always shaded.
In figure 6, how many unshaded squares are there?