Mensa IQ Test Mensa IQ Spatial and Abstract Reasoning Questions and Answers 2 — Questions and Answers
Question 1: In a figure series, shapes increase by 1 side each step: triangle, square, pentagon, hexagon. What comes next?
- Heptagon (Correct answer)
- Octagon
- Circle
- Star
Correct answer: Heptagon
Triangle=3 sides, Square=4, Pentagon=5, Hexagon=6, Heptagon=7. The next shape has 7 sides.
The pattern adds one side per step: 3→4→5→6→7 sides. A heptagon has 7 sides. An octagon has 8 (skips a step). The answer is heptagon.
Question 2: Which shape looks the same after a 90-degree clockwise rotation?
- Equilateral triangle
- Square (Correct answer)
- Regular pentagon
- Rectangle
Correct answer: Square
A square has 4-fold rotational symmetry — it looks identical after each 90° rotation.
A square has 4-fold rotational symmetry — it maps onto itself after rotations of 90°, 180°, 270°, and 360°. An equilateral triangle has 3-fold symmetry (120°). A rectangle (non-square) only looks the same after 180°. A pentagon has 5-fold symmetry (72°).
Question 3: A pattern of dots: Row 1 has 1 dot, Row 2 has 3 dots, Row 3 has 6 dots, Row 4 has 10 dots. How many dots are in Row 5?
- 12
- 14
- 15 (Correct answer)
- 16
Correct answer: 15
These are triangular numbers. Row 5 has 5 more than Row 4: 10+5=15.
Row 1: 1 (+1), Row 2: 3 (+2), Row 3: 6 (+3), Row 4: 10 (+4), Row 5: 15 (+5). Each row adds one more dot than the previous increment. Row 5 = 10+5 = 15.
Question 4: Two overlapping circles: circle A area = 20, circle B area = 16, overlap area = 5. What is the total area of the union (combined area covered by both circles)?
- 31 (Correct answer)
- 36
- 41
- 36
Correct answer: 31
Union = A + B - Overlap = 20 + 16 - 5 = 31.
Area of union = Area(A) + Area(B) - Area(overlap) = 20 + 16 - 5 = 31. If you simply added A and B, you'd count the overlap twice, so you subtract it once.
Question 5: In abstract pattern matrices, a 2×2 grid uses four unique shapes. Top-left = circle, top-right = square, bottom-left = triangle. What shape belongs in bottom-right?
- Circle
- Square
- Triangle
- Diamond (Correct answer)
Correct answer: Diamond
The no-repetition rule means each cell contains a unique shape. Circle, square, triangle are used, so diamond completes the set.
In a 2×2 matrix using unique shapes: circle, square, triangle occupy three cells. The fourth position must be a different shape — diamond/rhombus. This tests recognition of the unique-element pattern rule.
Question 6: A figure shows a square grid 4×4. The diagonal from top-left to bottom-right passes through how many unit squares?
- 4 (Correct answer)
- 7
- 8
- 16
Correct answer: 4
The main diagonal of a 4×4 grid passes through exactly 4 unit squares (one on each row/column of the diagonal).
In an n×n square grid, the main diagonal passes through exactly n unit squares (one per row, one per column). For a 4×4 grid: 4 squares. This is because the diagonal moves exactly diagonally without crossing any vertical or horizontal interior lines at non-corner points.
Mensa IQ Test Mensa IQ Spatial and Abstract Reasoning Questions and Answers 2
In a figure series, shapes increase by 1 side each step: triangle, square, pentagon, hexagon.
What comes next?