A geometric pattern shows: First square divided into 4 parts, Second square divided into 9 parts, Third square divided into 16 parts. Fourth square should be divided into how many parts?
A sequence uses conditional logic: If figure has odd sides, shade it. If figure has even sides, leave it unshaded. In sequence: Triangle (shaded), Square (unshaded), Pentagon (?), Hexagon (?). What should be the shading pattern?
AShaded, Shaded
BShaded, Unshaded
CUnshaded, Shaded
DUnshaded, Unshaded
Correct Answer:
B. Shaded, Unshaded
EXPLANATION
Pentagon has 5 sides (odd)→Shaded. Hexagon has 6 sides (even)→Unshaded. Pattern follows conditional odd/even rule.
A pattern shows reflection symmetry: Left half contains pattern X, right half should contain its mirror image. If left half shows a spiral turning clockwise, right half should show?
ASame clockwise spiral
BCounter-clockwise spiral
CStraight line
DCurved shape
Correct Answer:
B. Counter-clockwise spiral
EXPLANATION
Mirror reflection reverses direction. Clockwise becomes counter-clockwise. This follows the principle of reflection symmetry.
A complex figure shows: Primary color (Red) at position A, Secondary color (Orange) at position B, Tertiary color (Green) at position C. Following color theory hierarchy, what should appear at position D?
ABlue
BYellow
CPurple
DBrown
Correct Answer:
A. Blue
EXPLANATION
Pattern follows color wheel sequence: Red→Orange→Yellow→Green. But given sequence shows tertiary (Green), next logical step in color progression is Blue.
A figure shows nested shapes: Outermost hexagon contains pentagon, which contains square, which contains triangle. Following this pattern, what comes next inside the triangle?
ACircle
BDiamond
CSmaller triangle
DLine segment
Correct Answer:
A. Circle
EXPLANATION
Pattern reduces polygon sides: 6→5→4→3. Next logical shape with no straight sides is circle, or following geometric reduction principle.
A pattern displays: Small circle inside large square, medium circle inside large triangle, small square inside medium circle. What logical principle is being applied?
ASize variation only
BShape and size systematic variation
CRandom arrangement
DColor-based pattern
Correct Answer:
B. Shape and size systematic variation
EXPLANATION
Both the outer shape and inner shape vary systematically with size relationships changing. This demonstrates systematic variation in two attributes.
In a 2×3 grid with alternating shaded and unshaded squares, if positions (1,1), (1,3), (2,2) are shaded, which position should be shaded next following the checkerboard variant pattern?
A(2,1)
B(2,3)
C(1,2)
DNone
Correct Answer:
A. (2,1)
EXPLANATION
The pattern shows alternating shading in a modified checkerboard. Position (2,1) maintains the alternation pattern.
