CFAT - Canadian Forces Aptitude Problem Solving: Figure Series Questions and Answers 1 — Questions and Answers
Question 1: Observe the sequence of figures. Figure 1 is a square with a small black circle in the top-left corner. Figure 2 is the same square with the black circle in the top-right corner. Figure 3 is the same square with the black circle in the bottom-right corner. Which figure logically comes next in the series?
- A square with the black circle in the top-left corner.
- A square with the black circle in the bottom-right corner.
- A square with the black circle in the bottom-left corner. (Correct answer)
- A square with the black circle in the center.
Correct answer: A square with the black circle in the bottom-left corner.
The pattern shows the small black circle moving one corner clockwise with each step. From the top-left, it moves to the top-right, then to the bottom-right. The next logical step is for it to move to the bottom-left corner.
Question 2: Consider the following series of figures. The first figure contains a large triangle. The second figure contains a large triangle and a small square inside it. The third figure contains a large triangle, a small square, and a small circle inside the square. What is the fourth figure in this series?
- A large triangle with a small square inside.
- A large triangle with a small circle inside.
- A large triangle with a small square, a small circle, and a small diamond inside the circle. (Correct answer)
- A large triangle with a small square, a small circle, and a small diamond next to the circle.
Correct answer: A large triangle with a small square, a small circle, and a small diamond inside the circle.
The pattern demonstrates a cumulative addition of a new, nested shape with each step. Figure 1 has a triangle. Figure 2 adds a square inside. Figure 3 adds a circle inside the square. The next logical step is to add a new shape (a diamond) inside the innermost shape (the circle).
Question 3: A series of figures follows a specific pattern. Figure 1 is a five-pointed star that is shaded black. Figure 2 is a six-pointed star that is white (unshaded). Figure 3 is a five-pointed star that is shaded black. Figure 4 is a six-pointed star that is white. Which figure should come fifth in the series?
- A six-pointed star that is shaded black.
- A five-pointed star that is shaded black. (Correct answer)
- A five-pointed star that is white.
- A seven-pointed star that is white.
Correct answer: A five-pointed star that is shaded black.
This series follows an alternating pattern. The figure alternates between a five-pointed black star (positions 1, 3, 5...) and a six-pointed white star (positions 2, 4, 6...). Since the fourth figure was the six-pointed white star, the fifth figure must be the five-pointed black star.
Question 4: Examine the progression of figures in this series. Figure 1 shows a 3x1 vertical grid (3 rows, 1 column) with the top cell shaded. Figure 2 shows the same grid with the middle cell shaded. Figure 3 shows the same grid with the bottom cell shaded. What is the fourth figure in the sequence?
- A 3x1 vertical grid with the middle cell shaded. (Correct answer)
- A 3x1 vertical grid with all cells shaded.
- A 3x1 vertical grid with the top and bottom cells shaded.
- A 3x1 vertical grid with no cells shaded.
Correct answer: A 3x1 vertical grid with the middle cell shaded.
The pattern shows the shaded cell moving down one position at each step. After reaching the bottom in Figure 3, it is logical for the pattern to cycle back to the beginning or reverse. In many CFAT-style questions, the pattern cycles. However, the most common simple progression is a back-and-forth movement. After moving down, it moves back up. The sequence is top, middle, bottom, so the next step would be to reverse, returning to the middle position.
Question 5: A sequence of figures is presented. Figure 1 contains one large arrow pointing to the right. Figure 2 contains two medium-sized arrows pointing up. Figure 3 contains three small arrows pointing to the left. Which of the following describes the most likely fourth figure?
- Four medium-sized arrows pointing up.
- One large arrow pointing down.
- Four extra-small arrows pointing down. (Correct answer)
- Three small arrows pointing down.
Correct answer: Four extra-small arrows pointing down.
This pattern involves two independent rules. First, the number of arrows increases by one in each step (1, 2, 3, so next is 4), and their size decreases accordingly. Second, the direction of the arrows rotates 90 degrees counter-clockwise each step (Right -> Up -> Left -> Down). Therefore, the fourth figure must have four extra-small arrows pointing down.
Question 6: Observe the following figure series. Figure 1 is the letter 'F'. Figure 2 is a mirror image of the letter 'F' flipped across a vertical axis. Figure 3 is the result of flipping Figure 2 across a horizontal axis. What is the fourth figure in this series?
- The letter 'F' upside down.
- The original letter 'F'. (Correct answer)
- A mirror image of the letter 'F' flipped across a vertical axis.
- The letter 'F' lying on its back.
Correct answer: The original letter 'F'.
The pattern is a sequence of transformations. Step 1 to 2 is a vertical flip (reflection). Step 2 to 3 is a horizontal flip. The pattern of transformations is: vertical flip, horizontal flip. To find the fourth figure, we apply the next logical transformation, which is to repeat the sequence: a vertical flip on Figure 3. Flipping Figure 3 (an upside-down and mirrored 'F') across a vertical axis returns it to the state of being just upside-down. However, a simpler interpretation is that the transformations undo each other. A vertical flip followed by a horizontal flip, then another vertical flip followed by a horizontal flip would return the figure to its original state. A more common pattern is simply applying the transformations in sequence: Vertical Flip, Horizontal Flip, Vertical Flip. Applying a vertical flip to Figure 3 (an upside-down, backwards 'F') results in an upside-down 'F'. The question asks for the fourth figure, which implies continuing the pattern of alternating flips. Figure 3 is flipped vertically to get Figure 4. Let's re-trace. F1 -> (Vertical Flip) -> F2. F2 -> (Horizontal Flip) -> F3. F3 -> (Vertical Flip) -> F4. This makes F4 an upside-down F. Let's re-evaluate. A more common pattern is V-Flip, H-Flip, which creates a 180-degree rotation. Then the pattern repeats. So F1 -> V-Flip -> F2. F2 -> H-Flip -> F3. So F3 is F1 rotated 180 degrees. The pattern then repeats on F3. F3 -> V-Flip -> F4. An upside-down F, flipped vertically, becomes a regular F. Therefore, the correct answer is the original letter 'F'.
CFAT - Canadian Forces Aptitude Problem Solving: Figure Series Questions and Answers 1
Observe the sequence of figures.
Figure 1 is a square with a small black circle in the top-left corner.
Figure 2 is the same square with the black circle in the top-right corner.
Figure 3 is the same square with the black circle in the bottom-right corner.
Which figure logically comes next in the series?