STEP 2: Apply to Figure C - C: 2 dot(s) (different container) - Add 2 more dot(s) - Result: 4 dots total
Answer: Circle with 4 dots (2 more than original)
Question 2
Figure Analogy: A : B :: C : ?
Figure A undergoes two transformations to become B: rotated 90° anticlockwise AND enlarged by 1.5x. Apply both to C.
Step-by-Step Solution:
STEP 1: Identify First Transformation (Rotation) - Figure A orientation: Triangle pointing right - Figure B orientation: Triangle pointing upward - First transformation: 90° anticlockwise rotation
STEP 2: Identify Second Transformation (Scaling) - Measure A dimensions: Small triangle (base ≈ 20 units) - Measure B dimensions: Larger triangle (base ≈ 30 units) - Second transformation: 1.5× scaling (enlargement by 50%)
STEP 3: Determine Transformation Sequence - Method 1: Rotate first, then scale - Method 2: Scale first, then rotate - Result: Same final figure (transformations commute) - Standard approach: Rotate, then scale
STEP 4: Apply Rotation to C (90° anticlockwise) - Original C: Vertical rectangle (height > width) - After rotation: Horizontal rectangle (width > height) - Internal dot: Rotates with figure to new position
STEP 5: Apply Scaling to Rotated C (1.5×) - Current dimensions: Already rotated rectangle - Apply 1.5× to both length and width - Internal dot: Maintains relative position, scales proportionally
STEP 6: Verify Combined Transformation - Original: Vertical rectangle, small size, dot at top - After rotation: Horizontal rectangle, small size, dot on left - After scaling: Horizontal rectangle, 1.5× larger, dot on left (scaled position)
Answer: Rectangle in horizontal orientation (rotated 90° anticlockwise), dimensions increased by 1.5×, with dot repositioned according to both transformations
Question 3
Figure Analogy: A : B :: C : ?
A→B: Rotated 45° clockwise + scaled 1.3x + colors inverted. Apply all three to C.
Step-by-Step Solution:
STEP 1: Identify First Transformation - Rotation - Figure A: Diamond (square rotated 45°) - Figure B: Diamond rotated further (additional 45° clockwise) - First transformation: 45° clockwise rotation
STEP 2: Identify Second Transformation - Scaling - Measure A diagonal span: Approximately 36 units - Measure B diagonal span: Approximately 48 units - Calculate ratio: 48/36 ≈ 1.33 (approximately 1.3) - Second transformation: 1.3× scaling (30% enlargement)
STEP 3: Identify Third Transformation - Color Inversion - Figure A fill: White (light), dot: Black (dark) - Figure B fill: Black (dark), dot: White (light) - Third transformation: Complete color/shading inversion
STEP 4: Analyze Figure C - Shape: Rectangle (horizontal orientation) - Size: Standard (40×34 units) - Colors: White background, black internal lines - Internal elements: 2 perpendicular lines (cross pattern)
STEP 5: Apply Transformations in Sequence - Rotate 45° clockwise → Rectangle becomes tilted (diamond-like) - Scale 1.3× → All dimensions multiplied by 1.3 - Invert colors → Black background, white lines
Answer: Rectangle rotated 45° clockwise, dimensions enlarged by 1.3×, with inverted coloring (black fill with white cross lines inside)
Question 4
Figure Analogy: A : B :: C : ?
In A→B, all shaded regions become unshaded and vice versa (color inversion).
Apply the same inversion to Figure C.
Step-by-Step Solution:
STEP 1: Identify Transformation - A: Light background, dark internal elements - B: Dark background, light internal elements - Rule: Complete color/shading inversion
STEP 2: Apply to Figure C - C: Light background, dark internal elements - After inversion: Dark background, light internal elements - All positions and shapes preserved
Answer: Circle with inverted shading
Question 5
Figure Analogy: A : B :: C : ?
In A→B, all shaded regions become unshaded and vice versa (color inversion).
Apply the same inversion to Figure C.
Step-by-Step Solution:
STEP 1: Identify Transformation - A: Light background, dark internal elements - B: Dark background, light internal elements - Rule: Complete color/shading inversion
STEP 2: Apply to Figure C - C: Light background, dark internal elements - After inversion: Dark background, light internal elements - All positions and shapes preserved
Answer: Square with inverted shading
Question 6
Figure Analogy: A : B :: C : ?
Figure A is rotated 90° anticlockwise to become Figure B.
What should Figure '?' look like when the same rotation is applied to Figure C?
Step-by-Step Solution:
STEP 1: Identify the Transformation - Figure A: Arrow in original orientation - Figure B: Same arrow rotated 90° anticlockwise - Transformation: 90° anticlockwise rotation
STEP 2: Apply to Figure C - Figure C: Rectangle (horizontal orientation) - After 90° anticlockwise rotation: Rectangle becomes vertical - The shape remains a rectangle, only orientation changes
STEP 3: Verify - Shape preserved ✓ - Size preserved ✓ - Only orientation changed by 90° anticlockwise ✓
STEP 2: Analyze Figure B (Result) - Shape: Pentagon (5-sided polygon - same as A) - Internal elements: One central dot added - Transformation applied: Dot added (condition met)
STEP 3: Extract Transformation Rule - Condition: Count number of sides - Decision point: Compare to 4 - If sides > 4: Add central dot - If sides ≤ 4: No change
STEP 4: Analyze Figure C Properties - Shape: Rectangle (4-sided polygon) - Sides count: 4 = 4 (NOT greater than 4) - Current internal elements: None
STEP 5: Apply Conditional Rule to C - Rectangle has 4 sides - Is 4 > 4? NO - Condition NOT met - Action: NO transformation (keep unchanged)
Answer: Rectangle remains completely unchanged (has exactly 4 sides, does not meet the "> 4" condition)
Question 8
Figure Analogy: A : B :: C : ?
Figure A is rotated 180° to become Figure B.
Apply the same 180° rotation to Figure C.
Step-by-Step Solution:
STEP 1: Identify Rotation Angle - A and B: 180° rotation (half turn) - Every point moves to opposite side
STEP 2: Apply to Figure C - Rotate C 180° around its center - Shape preserved, orientation inverted - Dot moves to opposite position
Answer: Diamond rotated 180° (upside down) with dot repositioned
Question 9
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 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.
Question 10
Figure Analogy: A : B :: C : ?
A→B: Rotated 45° clockwise + scaled 1.3x + colors inverted. Apply all three to C.
Step-by-Step Solution:
STEP 1: Identify First Transformation - Rotation - Figure A: Diamond (square rotated 45°) - Figure B: Diamond rotated further (additional 45° clockwise) - First transformation: 45° clockwise rotation
STEP 2: Identify Second Transformation - Scaling - Measure A diagonal span: Approximately 36 units - Measure B diagonal span: Approximately 48 units - Calculate ratio: 48/36 ≈ 1.33 (approximately 1.3) - Second transformation: 1.3× scaling (30% enlargement)
STEP 3: Identify Third Transformation - Color Inversion - Figure A fill: White (light), dot: Black (dark) - Figure B fill: Black (dark), dot: White (light) - Third transformation: Complete color/shading inversion
STEP 4: Analyze Figure C - Shape: Rectangle (horizontal orientation) - Size: Standard (40×34 units) - Colors: White background, black internal lines - Internal elements: 2 perpendicular lines (cross pattern)
STEP 5: Apply Transformations in Sequence - Rotate 45° clockwise → Rectangle becomes tilted (diamond-like) - Scale 1.3× → All dimensions multiplied by 1.3 - Invert colors → Black background, white lines
Answer: Rectangle rotated 45° clockwise, dimensions enlarged by 1.3×, with inverted coloring (black fill with white cross lines inside)
Question 11
Figure Analogy: A : B :: C : ?
A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:
STEP 1: Understand Set Operation in A - Component 1: Circle - Operation symbol: + (indicates union/combination) - Component 2: Rectangle - Components: Overlapping or adjacent
STEP 2: Analyze Result in B - Single unified region combining both shapes - Overlapping area counted once (not double-shaded) - Boundary: Outer perimeter of combined shape - Operation: UNION (∪) in set theory = Combined area
STEP 3: Identify Components in C - Component 1: Hexagon - Operation symbol: + (same as in A) - Component 2: Trapezoid - Relationship: Adjacent or overlapping
STEP 4: Construct Union of C - Merge hexagon and trapezoid - Create single continuous region - Outer boundary: Traces perimeter of combined shape - Interior: All area covered by either polygon
Answer: Single merged region containing all area covered by either hexagon or trapezoid
Question 12
Figure Analogy: A : B :: C : ?
Figure A has 1 dot(s). Figure B has 2 dot(s) (1 more).
Apply the same transformation to Figure C.
STEP 2: Apply to Figure C - C: 1 dot(s) (different container) - Add 1 more dot(s) - Result: 2 dots total
Answer: Circle with 2 dots (1 more than original)
Question 13
Figure Analogy: A : B :: C : ?
In A→B, the inner square becomes a circle (matching the outer circle's shape).
Apply the same transformation to C.
Step-by-Step Solution:
STEP 1: Identify Transformation Rule - A: Circle (outer) + Square (inner) - B: Circle (outer) + Circle (inner) - Rule: Inner shape transforms to match outer shape type
STEP 2: Apply to Figure C - C: Triangle (outer) + Square (inner) - Transform inner square to match outer triangle - Result: Triangle with inscribed triangle
Answer: Triangle with inscribed triangle (inner becomes triangle)
Question 14
Figure Analogy: A : B :: C : ?
Figure A has 1 dot(s). Figure B has 3 dot(s) (2 more).
Apply the same transformation to Figure C.
STEP 2: Analyze Figure B (Result) - Shape: Pentagon (5-sided polygon - same as A) - Internal elements: One central dot added - Transformation applied: Dot added (condition met)
STEP 3: Extract Transformation Rule - Condition: Count number of sides - Decision point: Compare to 4 - If sides > 4: Add central dot - If sides ≤ 4: No change
STEP 4: Analyze Figure C Properties - Shape: Rectangle (4-sided polygon) - Sides count: 4 = 4 (NOT greater than 4) - Current internal elements: None
STEP 5: Apply Conditional Rule to C - Rectangle has 4 sides - Is 4 > 4? NO - Condition NOT met - Action: NO transformation (keep unchanged)
Answer: Rectangle remains completely unchanged (has exactly 4 sides, does not meet the "> 4" condition)
Question 16
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 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.
Question 17
Figure Analogy: A : B :: C : ?
Figure A undergoes two transformations to become B: rotated 90° anticlockwise AND enlarged by 1.5x. Apply both to C.
Step-by-Step Solution:
STEP 1: Identify First Transformation (Rotation) - Figure A orientation: Triangle pointing right - Figure B orientation: Triangle pointing upward - First transformation: 90° anticlockwise rotation
STEP 2: Identify Second Transformation (Scaling) - Measure A dimensions: Small triangle (base ≈ 20 units) - Measure B dimensions: Larger triangle (base ≈ 30 units) - Second transformation: 1.5× scaling (enlargement by 50%)
STEP 3: Determine Transformation Sequence - Method 1: Rotate first, then scale - Method 2: Scale first, then rotate - Result: Same final figure (transformations commute) - Standard approach: Rotate, then scale
STEP 4: Apply Rotation to C (90° anticlockwise) - Original C: Vertical rectangle (height > width) - After rotation: Horizontal rectangle (width > height) - Internal dot: Rotates with figure to new position
STEP 5: Apply Scaling to Rotated C (1.5×) - Current dimensions: Already rotated rectangle - Apply 1.5× to both length and width - Internal dot: Maintains relative position, scales proportionally
STEP 6: Verify Combined Transformation - Original: Vertical rectangle, small size, dot at top - After rotation: Horizontal rectangle, small size, dot on left - After scaling: Horizontal rectangle, 1.5× larger, dot on left (scaled position)
Answer: Rectangle in horizontal orientation (rotated 90° anticlockwise), dimensions increased by 1.5×, with dot repositioned according to both transformations
Question 18
Figure Analogy: A : B :: C : ?
A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:
STEP 1: Understand Set Operation in A - Component 1: Circle - Operation symbol: + (indicates union/combination) - Component 2: Rectangle - Components: Overlapping or adjacent
STEP 2: Analyze Result in B - Single unified region combining both shapes - Overlapping area counted once (not double-shaded) - Boundary: Outer perimeter of combined shape - Operation: UNION (∪) in set theory = Combined area
STEP 3: Identify Components in C - Component 1: Hexagon - Operation symbol: + (same as in A) - Component 2: Trapezoid - Relationship: Adjacent or overlapping
STEP 4: Construct Union of C - Merge hexagon and trapezoid - Create single continuous region - Outer boundary: Traces perimeter of combined shape - Interior: All area covered by either polygon
Answer: Single merged region containing all area covered by either hexagon or trapezoid
Question 19
Figure Analogy: A : B :: C : ?
Figure A is rotated 180° to become Figure B.
Apply the same 180° rotation to Figure C.
Step-by-Step Solution:
STEP 1: Identify Rotation Angle - A and B: 180° rotation (half turn) - Every point moves to opposite side
STEP 2: Apply to Figure C - Rotate C 180° around its center - Shape preserved, orientation inverted - Dot moves to opposite position
Answer: Diamond rotated 180° (upside down) with dot repositioned
Question 20
Figure Analogy: A : B :: C : ?
A→B: Rotated 45° clockwise + scaled 1.3x + colors inverted. Apply all three to C.
Step-by-Step Solution:
STEP 1: Identify First Transformation - Rotation - Figure A: Diamond (square rotated 45°) - Figure B: Diamond rotated further (additional 45° clockwise) - First transformation: 45° clockwise rotation
STEP 2: Identify Second Transformation - Scaling - Measure A diagonal span: Approximately 36 units - Measure B diagonal span: Approximately 48 units - Calculate ratio: 48/36 ≈ 1.33 (approximately 1.3) - Second transformation: 1.3× scaling (30% enlargement)
STEP 3: Identify Third Transformation - Color Inversion - Figure A fill: White (light), dot: Black (dark) - Figure B fill: Black (dark), dot: White (light) - Third transformation: Complete color/shading inversion
STEP 4: Analyze Figure C - Shape: Rectangle (horizontal orientation) - Size: Standard (40×34 units) - Colors: White background, black internal lines - Internal elements: 2 perpendicular lines (cross pattern)
STEP 5: Apply Transformations in Sequence - Rotate 45° clockwise → Rectangle becomes tilted (diamond-like) - Scale 1.3× → All dimensions multiplied by 1.3 - Invert colors → Black background, white lines
Answer: Rectangle rotated 45° clockwise, dimensions enlarged by 1.3×, with inverted coloring (black fill with white cross lines inside)
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