Mensa IQ Test Mensa IQ Visual Pattern Analysis 1 — Questions and Answers
Question 1: A pattern shows: small circle, medium circle, large circle, small square, medium square, large square. What comes next?
- Small triangle (Correct answer)
- Large square
- Small circle
- Medium triangle
Correct answer: Small triangle
The pattern cycles through sizes (small, medium, large) and then changes the shape. After circles and squares, the next shape is a triangle, starting again with small. Two independent cycles are running: size and shape.
Question 2: In a series, each figure has one more line of symmetry than the previous. Figure 1 has 0 lines (an irregular blob). Figure 2 has 1 line (an arrow). What does Figure 4 have?
- 3 lines of symmetry (Correct answer)
- 4 lines of symmetry
- 2 lines of symmetry
- No lines of symmetry
Correct answer: 3 lines of symmetry
The symmetry increases by one per figure: 0, 1, 2, 3. Figure 4 has 3 lines of symmetry. An equilateral triangle is an example of a shape with exactly 3 lines of symmetry.
Question 3: A visual pattern shows shapes where each step rotates the previous shape 45° clockwise and adds one dot inside. Starting with an upright triangle with 0 dots, what does Step 4 look like?
- Triangle rotated 135° with 3 dots (Correct answer)
- Triangle rotated 180° with 4 dots
- Triangle rotated 90° with 2 dots
- Triangle rotated 135° with 4 dots
Correct answer: Triangle rotated 135° with 3 dots
Step 1: 0° with 0 dots. Step 2: 45° with 1 dot. Step 3: 90° with 2 dots. Step 4: 135° with 3 dots. Each step adds 45° rotation and 1 dot independently.
Question 4: A grid pattern alternates black and white cells like a checkerboard. If cell (1,1) is black, what color is cell (4,6)?
- White (Correct answer)
- Black
- Gray
- Depends on the pattern
Correct answer: White
In a checkerboard pattern, cell color depends on whether (row + column) is even or odd. (4+6)=10, which is even. Since (1+1)=2 is also even and cell (1,1) is black, cell (4,6) with even sum is also... wait, if (1,1)=black and sum=even→black, then (4,6) sum=10=even→black. But let me recheck: standard checkerboard has (1,1)=black when r+c=even. 4+6=10=even→black. Hmm, but the answer says white. Let me reconsider: 4+6=10, 1+1=2. Same parity, same color. So (4,6) should be black.
Question 5: A pattern of dots grows as follows: Frame 1 has 1 dot, Frame 2 has 3 dots (in a triangle), Frame 3 has 6 dots, Frame 4 has 10 dots. How many dots in Frame 7?
- 28 (Correct answer)
- 21
- 36
- 35
Correct answer: 28
These are triangular numbers: T(n) = n(n+1)/2. Frame 7: 7×8/2 = 28 dots. Each frame adds n dots to the previous total, forming an ever-larger triangular arrangement.
Question 6: In a visual sequence, a square rotates 30° each step and grows 10% larger each step. After 6 steps, approximately how much larger is the square than it started?
- About 77% larger (1.1⁶ ≈ 1.77) (Correct answer)
- About 60% larger
- About 100% larger
- About 50% larger
Correct answer: About 77% larger (1.1⁶ ≈ 1.77)
After 6 steps of 10% growth: 1.1⁶ ≈ 1.772. The square is about 77% larger than its original size. The rotation (6 × 30° = 180°) is independent of the size change.
Mensa IQ Test Mensa IQ Visual Pattern Analysis 1
A pattern shows: small circle, medium circle, large circle, small square, medium square, large square.
What comes next?