In a wave pattern: Amplitude starts at 1, increases to 3, then 5, then 7. Simultaneously, wavelength starts at 4, decreases to 3, then 2, then 1. If pattern repeats after 8 figures, what is amplitude and wavelength of figure 9?
A three-variable pattern shows: (Triangles=2, Lines=3, Circles=1), (T=3, L=4, C=2), (T=4, L=5, C=3), (T=5, L=6, C=4), ?. What are the values in the 6th figure?
A(T=7, L=8, C=6)
B(T=6, L=7, C=5)
C(T=7, L=8, C=5)
D(T=6, L=8, C=5)
Correct Answer:
C. (T=7, L=8, C=5)
EXPLANATION
Each variable increases by 1 each step. Figure 6: T=2+5=7, L=3+5=8, C=1+4=5.
In a conditional transformation: IF figure has even sides → add 1 line inside. IF figure has odd sides → add 2 lines inside. Starting with pentagon (5 sides, 1 line), after 4 transformations, how many lines total?
A complex overlay pattern shows: Blue circle overlaps Red square (creating purple overlap area of 2 cm²), next Blue rectangle overlaps Red circle (creating 3 cm² overlap), next Blue triangle overlaps Red rectangle (creating 4 cm² overlap), ?. What is the overlap area in the 5th figure?
A5 cm²
B6 cm²
C7 cm²
D8 cm²
Correct Answer:
B. 6 cm²
EXPLANATION
Overlap areas: 2, 3, 4, 5, 6 cm². Following arithmetic progression with difference of 1.
In a progressive complexity pattern: 1 object, then 2 different objects, then 3 different objects, then 2 objects again. What describes this pattern's nature?
ALinear increase
BCyclical/Wave pattern
CExponential growth
DRandom arrangement
Correct Answer:
B. Cyclical/Wave pattern
EXPLANATION
Pattern shows increase (1→2→3) followed by decrease (→2), suggesting cyclical or wave-like behavior rather than linear.
In an overlapping shape pattern: Circle overlaps Square (creates intersection area), Square overlaps Triangle (creates intersection area). What principle determines the intersection area?
ASum of shapes
BLarger shape determines area
CCommon area between overlapping boundaries
DAlternating pattern
Correct Answer:
C. Common area between overlapping boundaries
EXPLANATION
Intersection area in overlapping pattern geometry is the common region shared by both shapes' boundaries.