Page 84 - Concepts of Reasoning-8

CHAPTER

Analytical Reasoning 3

Getting Started
m Two types of problems will be dealt with in this chapter. They are:
I. To count the number of straight lines, triangles, squares, parallelograms etc. in a given

complex geometrical figure and tell their exact number.
II. To arrange the given number of persons either in a row or in a circle on the basis of given
information

Let us Understand

Type I. Problem based on counting of geometrical figures:

Example 1. Find the number of triangles in the given figure:

(a) 18 (b) 13 (c) 17 (d) 15

Solution (a). Given figure is:

T1

Q1
T2 T3

T4 T5 T6
T7 T8

Triangles are

Simple triangles: T , T , T , T , T , T , T , T ® 8
4
7
6
5
2
1
3
8
Triangles consisting of 2 components: (T + T ), (T + T ), (T + T ), (T + T ), (Q + T ) ® 5
5
6
5
4
4
2
1
3
6
5
Triangles consisting of 3 components: (T + T + T ), (T + T + T ), (T + T + T ) ® 3
4
5
7
6
4
6
8
2
3
Triangles consisting of 4 components: (T + T + Q + T ) ® 1
3
2
1
1
Complete triangle: (T + T + Q + T + T + T + T + T + T ) ® 1
3
1
1
2
8
6
7
4
5
Thus, there are 8 + 5 + 3 + 1 + 1 = 18 triangles.
So, option (a) is correct.
84 Reasoning - 8