In a sequence of star patterns: 1 star, 3 stars in triangle, 6 stars in triangle, 10 stars in triangle, ?
A
15 stars
B
12 stars
C
14 stars
D
16 stars
Correct Answer:
A. 15 stars
Triangular numbers: 1, 3, 6, 10, 15. Each is sum of consecutive integers: 1, 1+2, 1+2+3, 1+2+3+4, 1+2+3+4+5.
A diamond shape rotates: 0°, 45°, 90°, 135°, 180°, ?. What is the next rotation?
A
225°
B
270°
C
315°
D
360°
Rotation increases by 45° each step. 180° + 45° = 225°.
Colors alternate in pattern: Red, Blue, Red, Blue, Green, Red, Blue, Red, Blue, Green, ?
A
Red
B
Green
C
Blue
D
Yellow
Pattern repeats every 5: (Red, Blue, Red, Blue, Green). The 11th position is the 1st in the next cycle, which is Red.
A sequence shows: 1 square, then 4 small squares in 2×2 arrangement, then 9 small squares in 3×3 arrangement. The 4th figure has ?
A
16 squares in 4×4 arrangement
B
25 squares in 5×5 arrangement
C
12 squares
D
20 squares
Correct Answer:
A. 16 squares in 4×4 arrangement
Pattern: 1² = 1, 2² = 4, 3² = 9, 4² = 16. Each figure shows n² small squares arranged in an n×n grid.
In a 3×3 grid pattern, corners have stars, edges have circles, and center has a square. If the pattern repeats in a 5×5 grid, how many stars appear?
In any rectangular grid, corners always number 4 (constant), regardless of grid size. Stars only appear at corners.
Numbers in boxes follow pattern: 2, 6, 12, 20, 30, ?. What is the next number?
Differences are: 4, 6, 8, 10, 12. Pattern: n(n+1) where n=1,2,3,4,5,6. So 6×7=42.
Squares are shaded progressively: 1st square half-shaded, 2nd square three-quarters shaded, 3rd square fully shaded, 4th square ?
A
Fully shaded with additional border
B
Half-shaded
C
Empty
D
Three-quarters shaded
Correct Answer:
A. Fully shaded with additional border
Shading increases: 1/2, 3/4, 1, then continues to fully shaded with a distinguishing feature (border) to indicate the pattern extends.
Figures show nested rectangles: 1 rectangle, 3 rectangles, 5 rectangles, 7 rectangles. This follows which pattern?
A
Odd numbers (2n-1)
B
Even numbers
C
Prime numbers
D
Fibonacci sequence
Correct Answer:
A. Odd numbers (2n-1)
The sequence 1, 3, 5, 7 follows the odd number pattern 2n-1 where n=1,2,3,4...
A grid pattern shows shapes moving in an L-shape: Start position, Right 1 cell, Down 1 cell, Left 1 cell, Down 1 cell. Where is it after these 4 moves?
A
Same column, 2 rows down
B
2 columns right, 2 rows down
C
1 column right, 2 rows down
D
Left 1 column, 1 row down
Correct Answer:
A. Same column, 2 rows down
Right 1 (+1 col), Down 1 (+1 row), Left 1 (-1 col), Down 1 (+1 row) = 0 columns net, +2 rows net.
In a fractal-like pattern: Stage 1 has 1 triangle, Stage 2 has 3 triangles, Stage 3 has 9 triangles. How many triangles in Stage 4?
A
27 triangles
B
15 triangles
C
21 triangles
D
18 triangles
Correct Answer:
A. 27 triangles
Each stage triples: 1×3=3, 3×3=9, 9×3=27.
