Odd Figure Out - Intermediate Level: different shading INTERMEDIATE

Step-by-step Solution:

Step 1: Analyze symmetry in all figures
- Check each figure for lines of symmetry
- Determine if figures have rotational or reflective symmetry

Step 2: Identify common symmetry property
- Figures other than E all possess clear symmetry
- These shapes have at least one line of symmetry (vertical, horizontal, or both)
- Circles have infinite lines of symmetry
- Regular polygons have multiple lines of symmetry

Step 3: Detect the asymmetric figure
- Figure E is an irregular polygon with no lines of symmetry
- This figure cannot be divided into mirror-image halves

Step 4: Verification
- Four figures: Symmetric shapes
- One figure: Asymmetric shape (Figure E)

Symmetry Check Method:
- Draw imaginary lines through the center
- Check if both halves are mirror images
- Figure E fails this test

Common Mistake: Confusing similar-looking shapes with truly symmetric ones.

Step-by-step Solution:

Step 1: Identify the geometric shapes
- Count the number of sides for each polygon
- Classify each shape by its number of sides

Step 2: Analyze the mathematical property
- Four figures are polygons with an EVEN number of sides (4 or 6 sides)
- These include squares (4 sides) and hexagons (6 sides)
- Even-sided polygons share specific symmetry properties

Step 3: Detect the odd polygon
- Figure D is a pentagon with 5 sides (ODD number)
- This breaks the even-sided polygon pattern
- Pentagon belongs to the odd-sided polygon category

Step 4: Mathematical verification
- Even numbers: 4, 6 (divisible by 2)
- Odd number: 5 (not divisible by 2)
- Four figures have even sides; one (Figure D) has odd sides

Advanced Property Analysis:
- Even-sided regular polygons have both diagonal and edge-to-edge symmetry
- Odd-sided regular polygons only have vertex-to-edge symmetry
- This is a deeper mathematical distinction beyond visual appearance

Systematic Counting Method:
- Count sides carefully for each polygon
- Classify as even or odd
- Identify the numerical outlier

Common Mistakes:
- Confusing shape names with their properties
- Not counting sides systematically
- Missing the even/odd mathematical distinction
- Focusing on size rather than side count

Step-by-step Solution:

Step 1: Analyze all figures for common properties
- Examine each figure to identify the basic shape used
- Figure A through E each contain a single geometric shape

Step 2: Identify the pattern
- Figures at positions other than E all contain squares
- These four figures share the common property of being the same shape

Step 3: Find the odd figure
- Figure E contains a triangle, which is different from the others
- This figure breaks the pattern of uniformity

Step 4: Verify the answer
- Four figures: square
- One figure: triangle
- Figure E is clearly the odd one out

Common Mistake to Avoid:
Don't focus on size or color variations; focus on the fundamental shape property.

Step-by-step Solution:

Step 1: Analyze angles in all figures
- Examine each interior angle of every polygon
- Classify angles as acute (<90°), right (=90°), or obtuse (>90°)

Step 2: Identify the common angle property
- Four figures contain ONLY acute angles (<90°) or right angles (=90°)
- Squares have all 90° angles (right angles)
- Equilateral triangles have all 60° angles (acute)
- These figures never exceed 90° in any interior angle

Step 3: Detect the figure with obtuse angle
- Figure E contains at least one OBTUSE angle (>90°)
- This triangle has one angle greater than 90 degrees
- This breaks the "no angles greater than 90°" property

Step 4: Mathematical verification
- Acute angle: 0° < angle < 90°
- Right angle: angle = 90°
- Obtuse angle: 90° < angle < 180°
- Figure E is the only one with an obtuse angle

Advanced Geometric Analysis:
- This tests understanding of angle classification
- Requires visual estimation or calculation of angles
- Triangle types: Acute-angled, Right-angled, Obtuse-angled
- Figure E is an obtuse-angled triangle

Angle Identification Strategy:
1. Focus on each corner/vertex
2. Mentally compare each angle to 90° (right angle)
3. Classify each angle
4. Look for the figure with an angle type that differs from others

Common Mistakes:
- Not carefully examining all angles in each figure
- Confusing angle size with side length
- Missing subtle obtuse angles in triangles
- Not knowing angle classifications (acute, right, obtuse)
- Estimating angles incorrectly

Step-by-step Solution:

Step 1: Analyze the nesting structure
- Each figure contains two shapes in a nested arrangement
- Identify the outer shape and inner shape for each figure
- Note the relationship between outer and inner elements

Step 2: Identify the common nesting pattern
- Four figures have a SQUARE as the outer shape and a CIRCLE as the inner shape
- This establishes the pattern: Square → Circle (from outside to inside)
- The outer-to-inner relationship is consistent

Step 3: Detect the reversed nesting
- Figure B has a CIRCLE as the outer shape and a SQUARE as the inner shape
- This is the REVERSE nesting order: Circle → Square
- The hierarchical relationship is inverted

Step 4: Verification through layer analysis
- Four figures: Outer = Square, Inner = Circle
- One figure (Figure B): Outer = Circle, Inner = Square
- The nesting sequence is opposite

Advanced Relationship Analysis:
- Nesting implies containment hierarchy
- The order matters: A contains B is different from B contains A
- This tests understanding of spatial relationships and ordering

Systematic Approach:
1. Identify outer boundary shape
2. Identify inner contained shape
3. Note the outer→inner sequence
4. Compare sequences across all figures
5. Find the one with different sequence

Common Mistakes:
- Only noticing that both shapes are present, missing the order
- Confusing size differences with nesting order
- Not recognizing that nesting direction is the key property
- Thinking all nested figures are equivalent regardless of which is outer

Step-by-step Solution:

Step 1: Analyze symmetry in all figures
- Check each figure for lines of symmetry
- Determine if figures have rotational or reflective symmetry

Step 2: Identify common symmetry property
- Figures other than C all possess clear symmetry
- These shapes have at least one line of symmetry (vertical, horizontal, or both)
- Circles have infinite lines of symmetry
- Regular polygons have multiple lines of symmetry

Step 3: Detect the asymmetric figure
- Figure C is an irregular polygon with no lines of symmetry
- This figure cannot be divided into mirror-image halves

Step 4: Verification
- Four figures: Symmetric shapes
- One figure: Asymmetric shape (Figure C)

Symmetry Check Method:
- Draw imaginary lines through the center
- Check if both halves are mirror images
- Figure C fails this test

Common Mistake: Confusing similar-looking shapes with truly symmetric ones.

Step-by-step Solution:

Step 1: Analyze internal element positioning
- Each figure contains an outer square and an inner circle
- Examine where the inner circle is positioned within the square

Step 2: Identify the common position
- Four figures have the inner circle in the top right position
- This positioning is consistent across these four figures
- The corner placement establishes the pattern

Step 3: Find the differently positioned figure
- Figure C has the inner circle in the center position
- This is a fundamentally different placement
- The central position breaks the corner-based pattern

Step 4: Verification through spatial analysis
- Divide each square into quadrants or use center reference
- Four figures: Circle in top right
- One figure (Figure C): Circle in center

Positional Analysis Strategy:
- Mentally divide shapes into grid sections
- Use coordinates (top/bottom, left/right, center)
- Compare relative positions systematically
- Look for the position that doesn't match the majority

Common Mistakes:
- Not establishing a clear reference frame
- Confusing approximate positions with exact positions
- Focusing on shape types instead of positions

Step-by-step Solution:

Step 1: Check if each shape is open or closed
- Closed shapes: Continuous boundary with enclosed area
- Open shapes: Boundary has a gap or doesn't fully enclose area

Step 2: Identify the common property
- Four figures are CLOSED shapes (complete boundaries)
- These enclose a finite area

Step 3: Find the open shape
- Figure E is an OPEN shape (arc with gaps)
- This figure does not enclose any area

Step 4: Verification
- Four figures: Closed shapes
- One figure: Open shape (Figure E)

🔍 Key Insight: Trace the boundary - if you return to start without lifting your finger, it's closed.

Step-by-step Solution:

Step 1: Analyze internal element positioning
- Each figure contains an outer square and an inner circle
- Examine where the inner circle is positioned within the square

Step 2: Identify the common position
- Four figures have the inner circle in the bottom left position
- This positioning is consistent across these four figures
- The corner placement establishes the pattern

Step 3: Find the differently positioned figure
- Figure B has the inner circle in the center position
- This is a fundamentally different placement
- The central position breaks the corner-based pattern

Step 4: Verification through spatial analysis
- Divide each square into quadrants or use center reference
- Four figures: Circle in bottom left
- One figure (Figure B): Circle in center

Positional Analysis Strategy:
- Mentally divide shapes into grid sections
- Use coordinates (top/bottom, left/right, center)
- Compare relative positions systematically
- Look for the position that doesn't match the majority

Common Mistakes:
- Not establishing a clear reference frame
- Confusing approximate positions with exact positions
- Focusing on shape types instead of positions

Step-by-step Solution:

Step 1: Analyze angles in all figures
- Examine each interior angle of every polygon
- Classify angles as acute (<90°), right (=90°), or obtuse (>90°)

Step 2: Identify the common angle property
- Four figures contain ONLY acute angles (<90°) or right angles (=90°)
- Squares have all 90° angles (right angles)
- Equilateral triangles have all 60° angles (acute)
- These figures never exceed 90° in any interior angle

Step 3: Detect the figure with obtuse angle
- Figure B contains at least one OBTUSE angle (>90°)
- This triangle has one angle greater than 90 degrees
- This breaks the "no angles greater than 90°" property

Step 4: Mathematical verification
- Acute angle: 0° < angle < 90°
- Right angle: angle = 90°
- Obtuse angle: 90° < angle < 180°
- Figure B is the only one with an obtuse angle

Advanced Geometric Analysis:
- This tests understanding of angle classification
- Requires visual estimation or calculation of angles
- Triangle types: Acute-angled, Right-angled, Obtuse-angled
- Figure B is an obtuse-angled triangle

Angle Identification Strategy:
1. Focus on each corner/vertex
2. Mentally compare each angle to 90° (right angle)
3. Classify each angle
4. Look for the figure with an angle type that differs from others

Common Mistakes:
- Not carefully examining all angles in each figure
- Confusing angle size with side length
- Missing subtle obtuse angles in triangles
- Not knowing angle classifications (acute, right, obtuse)
- Estimating angles incorrectly

Step-by-step Solution:

Step 1: Count elements in each figure
- Systematically count the number of shapes in each figure
- Record the count for each figure A through E

Step 2: Identify the common count
- Four figures contain exactly 4 elements each
- This establishes the standard pattern

Step 3: Find the figure with different count
- Figure B contains 5 elements
- This breaks the numerical pattern established by the other four

Step 4: Verify by elimination
- Figures except B: 4 elements each
- Figure B: 5 elements
- Clear quantitative difference identified

Counting Strategy:
- Count systematically from left to right
- Double-check your count to avoid errors
- Look for the outlier in quantity

Common Mistake: Miscounting due to overlapping shapes or rushing.

Step-by-step Solution:

Step 1: Analyze symmetry in all figures
- Check each figure for lines of symmetry
- Determine if figures have rotational or reflective symmetry

Step 2: Identify common symmetry property
- Figures other than D all possess clear symmetry
- These shapes have at least one line of symmetry (vertical, horizontal, or both)
- Circles have infinite lines of symmetry
- Regular polygons have multiple lines of symmetry

Step 3: Detect the asymmetric figure
- Figure D is an irregular polygon with no lines of symmetry
- This figure cannot be divided into mirror-image halves

Step 4: Verification
- Four figures: Symmetric shapes
- One figure: Asymmetric shape (Figure D)

Symmetry Check Method:
- Draw imaginary lines through the center
- Check if both halves are mirror images
- Figure D fails this test

Common Mistake: Confusing similar-looking shapes with truly symmetric ones.

Step-by-step Solution:

Step 1: Analyze all figures for common properties
- Examine each figure to identify the basic shape used
- Figure A through E each contain a single geometric shape

Step 2: Identify the pattern
- Figures at positions other than C all contain triangles
- These four figures share the common property of being the same shape

Step 3: Find the odd figure
- Figure C contains a square, which is different from the others
- This figure breaks the pattern of uniformity

Step 4: Verify the answer
- Four figures: triangle
- One figure: square
- Figure C is clearly the odd one out

Common Mistake to Avoid:
Don't focus on size or color variations; focus on the fundamental shape property.

Step-by-step Solution:

Step 1: Analyze angles in all figures
- Examine each interior angle of every polygon
- Classify angles as acute (<90°), right (=90°), or obtuse (>90°)

Step 2: Identify the common angle property
- Four figures contain ONLY acute angles (<90°) or right angles (=90°)
- Squares have all 90° angles (right angles)
- Equilateral triangles have all 60° angles (acute)
- These figures never exceed 90° in any interior angle

Step 3: Detect the figure with obtuse angle
- Figure C contains at least one OBTUSE angle (>90°)
- This triangle has one angle greater than 90 degrees
- This breaks the "no angles greater than 90°" property

Step 4: Mathematical verification
- Acute angle: 0° < angle < 90°
- Right angle: angle = 90°
- Obtuse angle: 90° < angle < 180°
- Figure C is the only one with an obtuse angle

Advanced Geometric Analysis:
- This tests understanding of angle classification
- Requires visual estimation or calculation of angles
- Triangle types: Acute-angled, Right-angled, Obtuse-angled
- Figure C is an obtuse-angled triangle

Angle Identification Strategy:
1. Focus on each corner/vertex
2. Mentally compare each angle to 90° (right angle)
3. Classify each angle
4. Look for the figure with an angle type that differs from others

Common Mistakes:
- Not carefully examining all angles in each figure
- Confusing angle size with side length
- Missing subtle obtuse angles in triangles
- Not knowing angle classifications (acute, right, obtuse)
- Estimating angles incorrectly

Step-by-step Solution:

Step 1: Analyze division lines in figures
- Count the number of lines dividing each figure
- Determine how many sections each figure is divided into

Step 2: Identify common division pattern
- Four figures are divided by ONE line into TWO equal sections
- This creates a simple bisection pattern
- The division is consistent across these figures

Step 3: Detect different division pattern
- Figure C is divided by MULTIPLE lines into MORE sections
- This creates a more complex division pattern
- The number of divisions differs significantly

Step 4: Verification
- Count dividing lines in each figure
- Four figures: 1 dividing line (2 sections)
- One figure (Figure C): Multiple dividing lines (more sections)

Division Analysis Method:
- Count all internal lines that divide the figure
- Determine the number of resulting sections
- Compare division complexity across figures

Common Mistake: Confusing external boundaries with internal division lines.

Step-by-step Solution:

Step 1: Analyze division lines in figures
- Count the number of lines dividing each figure
- Determine how many sections each figure is divided into

Step 2: Identify common division pattern
- Four figures are divided by ONE line into TWO equal sections
- This creates a simple bisection pattern
- The division is consistent across these figures

Step 3: Detect different division pattern
- Figure C is divided by MULTIPLE lines into MORE sections
- This creates a more complex division pattern
- The number of divisions differs significantly

Step 4: Verification
- Count dividing lines in each figure
- Four figures: 1 dividing line (2 sections)
- One figure (Figure C): Multiple dividing lines (more sections)

Division Analysis Method:
- Count all internal lines that divide the figure
- Determine the number of resulting sections
- Compare division complexity across figures

Common Mistake: Confusing external boundaries with internal division lines.

Step-by-step Solution:

Step 1: Identify the geometric shapes
- Count the number of sides for each polygon
- Classify each shape by its number of sides

Step 2: Analyze the mathematical property
- Four figures are polygons with an EVEN number of sides (4 or 6 sides)
- These include squares (4 sides) and hexagons (6 sides)
- Even-sided polygons share specific symmetry properties

Step 3: Detect the odd polygon
- Figure A is a pentagon with 5 sides (ODD number)
- This breaks the even-sided polygon pattern
- Pentagon belongs to the odd-sided polygon category

Step 4: Mathematical verification
- Even numbers: 4, 6 (divisible by 2)
- Odd number: 5 (not divisible by 2)
- Four figures have even sides; one (Figure A) has odd sides

Advanced Property Analysis:
- Even-sided regular polygons have both diagonal and edge-to-edge symmetry
- Odd-sided regular polygons only have vertex-to-edge symmetry
- This is a deeper mathematical distinction beyond visual appearance

Systematic Counting Method:
- Count sides carefully for each polygon
- Classify as even or odd
- Identify the numerical outlier

Common Mistakes:
- Confusing shape names with their properties
- Not counting sides systematically
- Missing the even/odd mathematical distinction
- Focusing on size rather than side count

Step-by-step Solution:

Step 1: Count elements in each figure
- Systematically count the number of shapes in each figure
- Record the count for each figure A through E

Step 2: Identify the common count
- Four figures contain exactly 3 elements each
- This establishes the standard pattern

Step 3: Find the figure with different count
- Figure C contains 2 elements
- This breaks the numerical pattern established by the other four

Step 4: Verify by elimination
- Figures except C: 3 elements each
- Figure C: 2 elements
- Clear quantitative difference identified

Counting Strategy:
- Count systematically from left to right
- Double-check your count to avoid errors
- Look for the outlier in quantity

Common Mistake: Miscounting due to overlapping shapes or rushing.

Step-by-step Solution:

Step 1: Multi-property systematic analysis
- This is an advanced problem requiring analysis of MULTIPLE properties
- Check: (1) Shape type, (2) Number of elements, (3) Shading/fill

Step 2: Analyze Property 1 - Shape Type
- Four figures contain CIRCLES
- One figure (Figure E) contains TRIANGLES
- First difference detected: Shape type

Step 3: Analyze Property 2 - Element Count
- Four figures contain 3 shapes each
- One figure (Figure E) contains 2 shapes
- Second difference detected: Quantity

Step 4: Analyze Property 3 - Shading/Fill
- Four figures have UNFILLED (outline only) shapes
- One figure (Figure E) has FILLED (solid) shapes
- Third difference detected: Shading

Step 5: Comprehensive verification
- Four figures: 3 circles, unfilled
- One figure (Figure E): 2 triangles, filled
- ALL THREE properties differ in Figure E

Advanced Multi-Property Analysis:
This is a CAT/GMAT/UPSC level problem testing:
- Ability to analyze multiple dimensions simultaneously
- Systematic comparison methodology
- Not being distracted by partial similarities
- Understanding that multiple properties can define a group

Systematic Multi-Property Approach:
1. Create a property checklist
2. Evaluate each property across all figures
3. Note which figures share each property
4. Identify the figure that differs on most/all properties
5. Verify your conclusion across all dimensions

Common Mistakes:
- Stopping after finding one difference (may not be conclusive)
- Not checking all properties systematically
- Being distracted by irrelevant properties (like position)
- Missing that ALL properties differ, not just one
- Rushing without systematic analysis

Expert Tip: In complex problems, create a mental or written table comparing all properties.

Step-by-step Solution:

Step 1: Count elements in each figure
- Systematically count the number of shapes in each figure
- Record the count for each figure A through E

Step 2: Identify the common count
- Four figures contain exactly 3 elements each
- This establishes the standard pattern

Step 3: Find the figure with different count
- Figure C contains 4 elements
- This breaks the numerical pattern established by the other four

Step 4: Verify by elimination
- Figures except C: 3 elements each
- Figure C: 4 elements
- Clear quantitative difference identified

Counting Strategy:
- Count systematically from left to right
- Double-check your count to avoid errors
- Look for the outlier in quantity

Common Mistake: Miscounting due to overlapping shapes or rushing.