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SBI PO Counting Figures

Study Material — 2 PYQs (2024–2024) · Concept Notes · Shortcuts

SBI PO Counting Figures is a frequently tested subtopic — 2 previous year questions from 2024–2024 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

SBI PO Counting Figures — Past Exam Questions

2 questions from actual SBI PO papers · all shown free · click option to reveal solution

Exam Q 12024Previous Year Pattern

A hexagon is divided into 6 equilateral triangles by drawing lines from the center to each vertex. Each of these 6 triangles is further subdivided into 4 smaller equilateral triangles by connecting the midpoints of its sides. Count the total number of equilateral triangles of all sizes and orientations (both upward △ and downward ▽) in the entire figure.

Exam Q 22024Previous Year Pattern

A figure consists of a 3×3 grid of squares, where each small square is further divided into 4 smaller squares by drawing one horizontal and one vertical line through its center. Additionally, one diagonal is drawn in each of the 9 small squares from top-left to bottom-right. Count the total number of quadrilaterals (4-sided figures) of all sizes in the entire figure.

Concept Notes

Counting Figures— Rules & Concept

Core ConceptRead this first — the foundation of the topic
CORE CONCEPT

You are given a complex figure made of triangles, squares, rectangles, lines, or other shapes. Your job is to count ALL shapes of a specific type (or all shapes total) without missing any or double-counting

KEY RULES

Count systematically — start from one corner and move in order (left to right, top to bottom). 2. Count individual shapes first, then combinations of 2, 3, 4 shapes, etc. 3. Overlapping shapes count as separate shapes. 4. Don't recount the same shape twice when moving to combinations. 5.

Use different colors or marks mentally to track what you've counted.

Exam PatternsWhat examiners ask — read before attempting PYQs

— Count total triangles in a figure — Count total squares/rectangles — Count total line segments — Count figures formed by combining smaller shapes — Questions ask: "How many triangles are there?" or "Find the total number of squares." SHORTCUT/TRICK: Use the "Layer Method" — Count shapes by size. First count the smallest individual shapes. Then count shapes made of 2 units, then 3 units, and so on. This prevents overlap and ensures nothing is missed.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Count 1×1 squares = 4 (the four small squares)

2
Step 2

Count 2×2 squares = 1 (the entire large square)

3
Step 3

Add them up = 4 + 1 = 5 total squares Answer: 5 squares

Exam TrapsCommon mistakes students make — avoid these

Students often count only the smallest individual shapes and forget to count larger shapes formed by combining smaller ones. For example, in a 2×2 grid, many count only the 4 small squares and give 4 as the answer, missing the 1 large square. Always count combinations systematically. FORMULA (For grid-based counting): For an n×n grid of squares: Total = 1² + 2² + 3² + ... + n² Example: For a 3×3 grid = 1 + 4 + 9 = 14 squares

Key Points to Remember

  • Count shapes systematically from one direction to avoid missing or double-counting.
  • Always count individual shapes first, then combinations of 2, 3, 4 units.
  • For an n×n grid of squares, use formula: Total = 1² + 2² + 3² + ... + n²
  • Overlapping shapes and shapes formed by combinations are counted separately.
  • Common error: forgetting to count larger shapes made from combining smaller ones.
  • Mark mentally or use colors to track which shapes you've already counted.

Exam-Specific Tips

  • In a 2×2 square grid, total number of squares = 5 (four 1×1 squares + one 2×2 square).
  • In a 3×3 square grid, total number of squares = 14 (calculated as 1² + 2² + 3² = 1 + 4 + 9).
  • For a figure with straight lines, each intersection point can create multiple segments to count.
  • In triangle counting problems, overlapping triangles of different sizes must be counted as separate entities.
  • The sum formula for square counting in n×n grids is: n(n+1)(2n+1)/6 for advanced calculations.
  • SSC CGL typically presents 2-3 figure counting questions in the Non-Verbal Reasoning section.
  • Time limit per counting figure question is approximately 1-1.5 minutes in actual exam.
  • Grid-based counting (squares and rectangles) appears more frequently than line segment counting.
Practice MCQs

Counting Figures — Practice Questions

4graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

How many squares are present in a 3×3 grid (a grid with 3 rows and 3 columns of small squares)?

Practice 2medium

A figure consists of a large circle divided into 8 equal sectors by radii. Additionally, there are 2 concentric circles inside, creating 3 rings. How many distinct regions (sectors and rings combined) are created in total?

Practice 3medium

How many squares of all sizes are present in a 4×4 grid? [A square grid with 4 rows and 4 columns of unit squares]

Practice 4hard

A rectangular grid contains horizontal and vertical lines forming a 4×5 array of small rectangles. How many rectangles of all possible sizes can be formed by selecting any two horizontal lines and any two vertical lines?

60-Second Revision — Counting Figures

  • Remember: Count systematically by size — small shapes first, then combinations. Never skip larger combined shapes.
  • Formula for n×n square grid: Total = 1² + 2² + 3² + ... + n². For 3×3 grid = 14 squares.
  • Trap: Students miss composite shapes. In a divided square, the outer boundary also counts as one shape.
  • Layer method works best: identify all 1-unit shapes, then 2-unit shapes, then larger combinations.
  • Verify your count: Use a different mental path to recount. If answers match, you're likely correct.
  • Mark shapes mentally as you count to avoid recounting or skipping in complex figures.
  • Practice on grid patterns (2×2, 3×3, 3×4) — these dominate SSC CGL counting questions.
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