CogAT Paper Folding Analysis Questions and Answers 1 — Questions and Answers
Question 1: A square piece of paper is folded in half vertically (left edge to right edge). Then, it is folded in half again horizontally (top edge to bottom edge). Finally, a single circular hole is punched through the center of the folded paper. How will the paper look when it is fully unfolded?
- One circle in the exact center of the paper.
- Two circles aligned vertically in the center.
- Four circles arranged in a square pattern in the center. (Correct answer)
- Two circles aligned horizontally in the center.
Correct answer: Four circles arranged in a square pattern in the center.
The paper is folded twice, creating four layers. Punching a hole through the center of the folded square means the hole goes through all four layers. When unfolded, each layer will reveal a hole, resulting in four holes arranged symmetrically around the center of the original square paper.
Question 2: Imagine a square piece of paper is folded along the diagonal from the top-right corner to the bottom-left corner. Then, a small triangular cut is made on the folded edge, near the top corner. Which of the following best describes the resulting shape when the paper is unfolded?
- A single triangular hole on the diagonal.
- A square-shaped hole in the center of the paper. (Correct answer)
- Two triangular holes along the diagonal, pointing away from each other.
- A single square hole on one edge of the paper.
Correct answer: A square-shaped hole in the center of the paper.
Folding the paper diagonally creates two layers. A triangular cut on the folded edge removes a piece from both layers. When unfolded, the two triangular cuts will combine to form a larger, symmetrical shape. Since the cut is on the fold, the two triangles will form a square (or diamond) shape in the middle of the paper.
Question 3: A rectangular piece of paper is folded in half from bottom to top. A semi-circle is then cut out from the middle of the folded edge. What will the paper look like when unfolded?
- Two semi-circles on the top and bottom edges.
- A full circle in the center of the paper. (Correct answer)
- A semi-circle on the top edge.
- An oval shape in the center of the paper.
Correct answer: A full circle in the center of the paper.
When the paper is folded, the cut is made along the fold line. A semi-circle cut along this fold will be mirrored when the paper is unfolded. The two semi-circles will join together to form a complete circle in the center of the original rectangle.
Question 4: A square piece of paper is folded in half horizontally. Then, a straight cut is made from the middle of the folded edge to the middle of the top, open edge. What is the result when the paper is unfolded?
- A single vertical slit in the middle.
- Two separate rectangular pieces of paper.
- A large triangular hole in the center. (Correct answer)
- A horizontal cut across the middle.
Correct answer: A large triangular hole in the center.
The cut starts at the fold and goes to the opposite edge, effectively cutting a triangle out of the folded paper. Because the paper is folded, this removes a triangle from both the top and bottom halves. When unfolded, these two missing triangular sections combine to create a larger, diamond or triangular-shaped hole in the center of the square.
Question 5: Which of the following folding and cutting actions would result in a single, small square hole in the very center of a square piece of paper?
- Fold the paper in half once and punch a square hole in the center of the fold.
- Fold the paper into quarters towards the center and punch one hole where the corners meet. (Correct answer)
- Fold the paper in half diagonally and cut a small triangle from the center of the folded edge.
- Fold the paper in half vertically, then horizontally, and cut off the corner where all the folded edges meet.
Correct answer: Fold the paper into quarters towards the center and punch one hole where the corners meet.
Folding the paper into quarters brings all four center points of the original paper together. Punching a single hole at this meeting point will place a hole in each of the four quadrants. When unfolded, these four holes will merge to form a single square hole in the exact center of the paper. Other methods create multiple holes or holes in different locations.
Question 6: A square paper is folded in half vertically. Then, a second fold is made, bringing the bottom edge up to meet the top edge. A single hole is punched in the bottom-left corner of the resulting rectangle. Where will the holes appear on the unfolded paper?
- One hole in the bottom-left corner.
- Two holes, one in the bottom-left and one in the top-left corner. (Correct answer)
- Four holes, one in each corner of the paper.
- Two holes, one in the bottom-left and one in the bottom-right corner.
Correct answer: Two holes, one in the bottom-left and one in the top-left corner.
The first fold (vertical) is a standard fold. The second fold (bottom to top) creates a crease in the middle. The hole is punched through the two layers in the bottom-left. When the second fold is undone (unfolding top to bottom), the existing hole remains in the bottom-left, and a new hole appears in the top-left, mirrored across the horizontal fold line. The first fold doesn't affect the vertical position of these holes.
CogAT Paper Folding Analysis Questions and Answers 1
A square piece of paper is folded in half vertically (left edge to right edge).
Then, it is folded in half again horizontally (top edge to bottom edge).
Finally, a single circular hole is punched through the center of the folded paper.
How will the paper look when it is fully unfolded?