Question 1

A rectangular paper is cut into 3 equal vertical strips. Each strip is then cut into 2 equal horizontal pieces. How many total pieces of paper will result?

Accepted Answer

First cut: 3 vertical strips. Second cut: each of the 3 strips is cut into 2 pieces. Total = 3 × 2 = 6 pieces.

Question 2

A circular piece of paper is folded in half to form a semicircle, then folded in half again. When unfolded, how many sections will the original circle be divided into?

Accepted Answer

First fold creates 2 semicircular sections. Second fold (perpendicular to the first) divides each semicircle into 2 parts. Total = 2 × 2 = 4 sections when unfolded.

Question 3

A rectangular paper is folded in half vertically, then folded in half horizontally. How many rectangular sections will appear when the paper is completely unfolded?

Accepted Answer

First fold (vertical) divides the paper into 2 sections. Second fold (horizontal) divides each section into 2 more. Total sections = 2 × 2 = 4 rectangular sections when unfolded.

Question 4

A square piece of paper is folded once along its diagonal. How many layers of paper will be visible if you look at the folded shape from above?

Accepted Answer

When a square is folded along its diagonal, one triangular half folds over the other, creating a double-layered triangle. From above, you see 2 layers of paper stacked together.

Question 5

A square paper is folded in half to form a rectangle, then folded in half again to form a smaller square. If a small hole is punched through the folded paper, how many holes will appear when the paper is completely unfolded?

Accepted Answer

After two folds, the paper is folded 2 times, creating 2² = 4 layers. One hole punched through all layers creates 4 holes when unfolded.

Question 6

A clock shows 3:15. What time will be shown in its mirror image?

Accepted Answer

This question tests understanding of how clock positions are reflected horizontally in a mirror.

Question 7

A shape consists of a triangle pointing upward with a circle attached to its base. When this shape is reflected in a horizontal mirror (top-bottom flip), which element's position relative to the other will change?

Accepted Answer

This question tests understanding of how spatial relationships between elements change under vertical (top-bottom) mirror reflection.

Question 8

A sequence of symbols is written as: ◄ ► ▲ ▼. When viewed in a mirror (left-right reflection), what will be the 2nd symbol from the left in the mirror image?

Accepted Answer

This question tests understanding of both the reversal of sequence order and the individual transformation of directional symbols under horizontal mirror reflection.

Question 9

A word 'REASONING' is written on a paper. When the paper is held in front of a mirror, how many letters appear the same in both the original and mirror image?

Accepted Answer

This question tests understanding of which letters remain visually identical when mirrored horizontally.

Question 10

A figure shows a pattern of dots arranged as: Row 1 has 2 dots, Row 2 has 4 dots, Row 3 has 6 dots. When this figure is reflected in a vertical mirror (left-right flip), which row will have the same number of dots in the same positions?

Accepted Answer

This question tests understanding that vertical mirror reflection preserves the count and arrangement symmetry of elements.

Question 11

A sequence of digits 2, 5, 8, 9, 6 is written horizontally. When viewed in a water image (horizontal mirror below), the sequence appears reversed and each digit is vertically flipped. How many digits will appear identical to their original form in the water image?

Accepted Answer

Water image: sequence reverses to 6, 9, 8, 5, 2 AND each digit is vertically flipped. Vertically symmetric digits: 0, 1, 2, 5, 8. In the sequence 2, 5, 8, 9, 6: digits 2, 5, 8 are vertically symmetric. In water image (6, 9, 8, 5, 2): digits 8, 5, 2 are vertically symmetric. Identical appearances: 2 (position changes but looks same), 5 (position changes but looks same), 8 (position changes but looks same). Count = 3 digits appear identical despite position change.

Question 12

A rectangular paper (8cm × 6cm) is folded such that the top-right corner touches the bottom-left corner. The paper is then cut along the fold line. How many pieces result, and what is the shape of the largest piece?

Accepted Answer

Tests understanding of fold geometry, the resulting crease line equation, and how a single cut along a fold line divides a rectangle.

Question 13

A square paper is folded in half vertically, then in half horizontally, then in half diagonally. A single straight cut is made through all layers. After unfolding, which of the following is IMPOSSIBLE?

Accepted Answer

Tests understanding of how multiple sequential folds create layers and how a single cut through all layers produces symmetric patterns.

Question 14

A rectangular paper (12cm × 8cm) is folded such that the top-left corner is brought to touch the bottom-right corner. The paper is then cut along the fold line. One of the resulting pieces is then folded in half along its longest dimension and cut again. How many total pieces exist after both cuts?

Accepted Answer

Tests sequential cutting operations on folded paper, requiring tracking of piece count through multiple folds and cuts.

Question 15

A word is written as REASONING. When this word is seen in a mirror placed vertically on the right side, how many letters will appear identical to their original form?

Accepted Answer

In a vertical mirror placed on the right, letters are horizontally flipped. Only letters that are horizontally symmetric appear identical: A, H, I, M, O, T, U, V, W, X, Y. In REASONING: R(no), E(no), A(yes), S(no), O(yes), N(no), I(yes), N(no), G(no). Count = 3 letters (A, O, I).

Question 16

A word PLATFORM is written in capital letters. When viewed in a water image (horizontal mirror), how many letters will have the same appearance as in the original?

Accepted Answer

In a water image (horizontal mirror placed below), letters are vertically flipped. Only vertically symmetric letters appear identical: B, C, D, E, H, I, K, O, X. In PLATFORM: P(no), L(no), A(no), T(no), F(no), O(yes), R(no), M(no). Count = 1 letter (O).

Question 17

A figure consists of a square with a diagonal line from top-left to bottom-right, and a small circle in the top-right corner. When this figure is reflected in a vertical mirror placed on the right, which of the following correctly describes the mirror image?

Accepted Answer

Original: square with diagonal from top-left to bottom-right, circle at top-right. Vertical mirror on right flips horizontally. Mirror image: square with diagonal from top-right to bottom-left (reversed), circle at top-left. The diagonal direction reverses from \ to /.

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