GMA Abstract Reasoning 2 — Questions and Answers
Question 1: In a 3×3 matrix, the number of dots in each row increases by 1. The first row has 1, 2, 3 dots; the second row has 2, 3, 4 dots. What should the third row contain?
- 2, 3, 4 dots
- 3, 4, 5 dots (Correct answer)
- 4, 5, 6 dots
- 1, 2, 3 dots
Correct answer: 3, 4, 5 dots
Each row starts with one more dot than the previous row. Row 1: 1,2,3. Row 2: 2,3,4. Row 3: 3,4,5.
Matrix reasoning requires identifying rules across rows AND columns. Row 1 starts at 1, Row 2 starts at 2, Row 3 must start at 3 — giving 3, 4, 5. Also, within each row the count increases by 1. Both rules confirm the answer: 3, 4, 5 dots.
Question 2: A sequence of symbols rotates 45° clockwise each step. If the first symbol is a vertical up arrow (↑), what does the fifth symbol look like?
- ↗ (upper-right diagonal)
- → (right)
- ↓ (downward) (Correct answer)
- ↙ (lower-left diagonal)
Correct answer: ↓ (downward)
Each step adds 45° clockwise: ↑(step1) → ↗(step2) → →(step3) → ↘(step4) → ↓(step5). After 4 rotations of 45°, the total is 180°, so the arrow now points downward.
Starting at ↑ and rotating 45° clockwise each step: Step 1=↑, Step 2=↗, Step 3=→, Step 4=↘, Step 5=↓. After 4 rotations of 45° (total 180°), the arrow points directly downward (↓). This tests sequential spatial rotation tracking through eight cardinal/diagonal positions.
Question 3: In an abstract pattern, shapes alternate between filled (black) and outline (white) in a checkerboard fashion across a 3×3 grid. The top-left is filled. What is the centre cell?
- Filled (black) (Correct answer)
- Outline (white)
- Half-filled
- No shape
Correct answer: Filled (black)
In a checkerboard pattern, same-coloured cells are on the same diagonal. The centre is at position (2,2). Since (1,1) is filled, and the sum 2+2=4 is even (same parity as 1+1=2), the centre is also filled.
Checkerboard patterns alternate fill so that adjacent cells differ. If we label positions (row, col) starting at 1, cells where (row+col) is even have one colour and cells where (row+col) is odd have the other. Top-left (1,1): sum=2 (even) → filled. Centre (2,2): sum=4 (even) → also filled. Bottom-right (3,3): sum=6 (even) → also filled.
Question 4: Each figure in a series gains one side: triangle, square, pentagon... What is the 7th figure in the series?
- Hexagon
- Heptagon
- Octagon (Correct answer)
- Nonagon
Correct answer: Octagon
Triangle=3 sides (figure 1), square=4 (figure 2), pentagon=5 (figure 3). Pattern: figure n has n+2 sides. Figure 7 has 7+2=9 sides — a nonagon.
The series increases the number of sides by 1 each step, starting at 3 (triangle). Figure n has n+2 sides: Figure 1=3, Figure 2=4, Figure 3=5, Figure 4=6, Figure 5=7, Figure 6=8, Figure 7=9. A 9-sided polygon is a nonagon. Note: the answer listed as 'Octagon' (8 sides) is Figure 6, not Figure 7.
Question 5: In a number matrix, each row sums to the same total. Row 1: 3, 7, 2 (sum=12). Row 2: 5, ?, 4 (sum must be 12). What is the missing number?
- 1
- 2
- 3 (Correct answer)
- 4
Correct answer: 3
Row 2 must sum to 12: 5 + ? + 4 = 12. So ? = 12 - 5 - 4 = 3.
Matrix completion with a constant row-sum rule: Total for each row = 12. For Row 2: 5 + ? + 4 = 12. Solving: ? = 12 - 9 = 3. This tests the ability to identify a constant property (row sum) and apply it to find a missing element.
Question 6: A pattern shows: ★★○, ★○○, ○○○. What rule describes this pattern across rows?
- Stars increase by 1 each row
- Stars decrease by 1 each row (Correct answer)
- Circles increase by 1 each row
- The pattern alternates
Correct answer: Stars decrease by 1 each row
Row 1: 2 stars, 1 circle. Row 2: 1 star, 2 circles. Row 3: 0 stars, 3 circles. Stars decrease by 1 each row (equivalently, circles increase by 1).
Counting the stars: Row 1=2, Row 2=1, Row 3=0 — decreasing by 1 each time. Counting circles: Row 1=1, Row 2=2, Row 3=3 — increasing by 1 each time. Both observations describe the same pattern differently. Either 'stars decrease by 1' or 'circles increase by 1' is a valid description, but option B (stars decrease by 1) is the primary rule.
GMA Abstract Reasoning 2
In a 3×3 matrix, the number of dots in each row increases by 1.
The first row has 1, 2, 3 dots; the second row has 2, 3, 4 dots.
What should the third row contain?