Question 1
Figure Analogy: A : B :: C : ?
Pattern: The number of sides of the outer shape becomes the number of sides of the inner shape, and the inner shape's side count determines the new outer shape's side count through a progressive relationship (Circle→Hexagon→Octagon). Apply to C.
Step-by-Step Solution:
STEP 1: Analyze Figure A
- Outer shape: Circle (can be considered as infinite or 0 sides)
- Inner shape: Diamond (4 sides)
STEP 2: Analyze Figure B
- Outer shape: Hexagon (6 sides)
- Inner shape: Circle (infinite sides)
STEP 3: Identify the Pattern
Looking at the progression:
- A: Outer Circle (∞), Inner Diamond (4)
- B: Outer Hexagon (6), Inner Circle (∞)
The transformation swaps and transforms side counts:
- The inner shape's side count (4) becomes part of the new outer shape
- The pattern shows: 4 → 6 → 8 (increasing by 2 each time)
- Circle (∞) acts as a placeholder that transforms to the next polygon in sequence
STEP 4: Analyze Figure C
- Outer shape: Hexagon (6 sides)
- Inner shape: Diamond (4 sides)
STEP 5: Apply Pattern to C
Following the established pattern:
- The inner diamond has 4 sides → following the 4→6→8 progression, this contributes to the new outer shape
- The outer hexagon has 6 sides → this becomes the new inner shape's side count
- Therefore: New outer = Octagon (8 sides), New inner = Hexagon (6 sides)
STEP 6: Verify Pattern Consistency
- A: Circle (∞) + Diamond (4) → B: Hexagon (6) + Circle (∞)
- C: Hexagon (6) + Diamond (4) → ?: Octagon (8) + Hexagon (6)
- The pattern shows that the inner shape's side count determines the progression of the outer shape
Answer: Octagon (8 sides) with hexagon (6 sides) inside
Key Insight: This problem tests recognition of progressive relationships where shapes evolve based on their side counts, with circle acting as a special case that transforms to the next polygon in the sequence.
STEP 1: Analyze Figure A
- Outer shape: Circle (can be considered as infinite or 0 sides)
- Inner shape: Diamond (4 sides)
STEP 2: Analyze Figure B
- Outer shape: Hexagon (6 sides)
- Inner shape: Circle (infinite sides)
STEP 3: Identify the Pattern
Looking at the progression:
- A: Outer Circle (∞), Inner Diamond (4)
- B: Outer Hexagon (6), Inner Circle (∞)
The transformation swaps and transforms side counts:
- The inner shape's side count (4) becomes part of the new outer shape
- The pattern shows: 4 → 6 → 8 (increasing by 2 each time)
- Circle (∞) acts as a placeholder that transforms to the next polygon in sequence
STEP 4: Analyze Figure C
- Outer shape: Hexagon (6 sides)
- Inner shape: Diamond (4 sides)
STEP 5: Apply Pattern to C
Following the established pattern:
- The inner diamond has 4 sides → following the 4→6→8 progression, this contributes to the new outer shape
- The outer hexagon has 6 sides → this becomes the new inner shape's side count
- Therefore: New outer = Octagon (8 sides), New inner = Hexagon (6 sides)
STEP 6: Verify Pattern Consistency
- A: Circle (∞) + Diamond (4) → B: Hexagon (6) + Circle (∞)
- C: Hexagon (6) + Diamond (4) → ?: Octagon (8) + Hexagon (6)
- The pattern shows that the inner shape's side count determines the progression of the outer shape
Answer: Octagon (8 sides) with hexagon (6 sides) inside
Key Insight: This problem tests recognition of progressive relationships where shapes evolve based on their side counts, with circle acting as a special case that transforms to the next polygon in the sequence.