Question 1

A figure consists of a square divided into 16 equal smaller squares (4×4 grid). Some of these smaller squares are further subdivided by a diagonal line. Count the total number of rectangles (including squares) in this figure, excluding those that contain a diagonal line within them.

Given: 6 of the 16 squares have diagonal lines drawn inside them, scattered randomly across the grid.

Accepted Answer

This question tests the ability to count rectangles of various sizes while applying an exclusion constraint. Students must identify all possible rectangles in a 4×4 grid, then subtract those containing diagonals, requiring careful tracking of which cells are affected.

Question 2

A figure shows a 3×3 grid of squares. Each square in the grid is further subdivided by drawing one diagonal line. Additionally, 2 internal lines are drawn: one connecting the midpoint of the top edge to the midpoint of the bottom edge, and another connecting the midpoint of the left edge to the midpoint of the right edge (forming a cross through the center). Count the total number of triangles in this figure.

Accepted Answer

This question tests the ability to count triangles in a complex figure with multiple overlapping subdivisions created by diagonals and internal lines, requiring careful tracking of all triangle sizes and orientations.

Question 3

A figure consists of two overlapping circles. The overlapping region (lens shape) is further subdivided by 3 chords. Additionally, each non-overlapping part of the circles is divided by 2 chords. Count the total number of regions (including the overlapping region) created in this figure.

Accepted Answer

This question tests the ability to count regions created by overlapping circles and multiple chords, requiring careful tracking of how chords subdivide both overlapping and non-overlapping areas without double-counting or missing regions.

RRB NTPC Counting Figures

Counting Figures— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Counting Figures — Practice Questions

60-Second Revision — Counting Figures