Inserting the Missing Character | CSAT Preparation - UPSC PDF Download

Introduction

Inserting a missing figure problems are generally asked in various competitive exams, which mainly consist of a figure divided into various regions. In between these regions, there will be numbers, letters or it may be the combination of letters and numbers following certain sequence. They are in a series inside the given figure. The question may contain single figure or combination of two or more than two figures. The question figure may be any geometrical figure such as rectangle, triangle, circle or other any type of unusual figure to have set of numbers or letters in it. The figure may be divided into many parts according to logic and sequence behind the question. In question figure, the numbers or letters given will be changing in each step by following certain sequence or logic. Reader has to analyze sequence or number or logic and to choose correct answer from given options.
Questions, which ask to insert the missing number, come under this category.  In most cases one of the following will be given:

• A diagram or a set of diagrams
  
• Or a matrix
  
• Or  any random figure e.g. star

Each of these has some characters. These characters can be numbers or letters or a combination of number and letters that follow a particular pattern. We need to crack the reasoning or logic behind this pattern so as to find the missing term.

Most common patterns

Different types of patterns could be there, some of the patterns are as following:

• It could be sum of two numbers divided by a constant.
• It could be average of numbersIt could be in the form of alphabets, where alphabets are increased by constant or increased by square of numbers or increased by prime numbers.
• It could be the difference of product of two diametrically opposite numbers.
• It could be the difference of sum of adjacent numbers.
• The difference of the numbers could be in the pattern   1³±1, 2³±1,  and so on.
• The difference of the numbers could be in the pattern 12±1, 22±1, and so on.
• Numbers could be 1², 2², 3² and so on  or 1³, 2³, 3³… and so on.
• The difference could be prime numbers or difference could be square of prime numbers.
• The difference could be in the form of N²± N or N³± N.
• The difference could be in the form of ×N + N or ×2 + 1, ×2 + 2, ×2 + 3…and so on.
• The difference could be in the form of ×2 ± 1 alternatively.
• Numbers could be ×1, ×2, ×3…… and so on.

Type of Question

Type – 1: In this type of questions, a single figure will be given which consists of letters or numbers inside it following certain sequence or logic as explained by following example.

Example 1:
(a) 83
(b) 54
(c) 65
(d) 60

Correct Answer is Option (c)
In this example, the question figure has four regions inside which there are numbers which are interchanging their position in next step so 56 may be written as 65 to replace question mark.

Example 2:
(a) 150
(b) 145
(c)165
(d) 162

Correct Answer is Option (d)
The numbers at the bottom row are obtained as (28 - 10) × 10 = 180, (29 - 17) × 11 = 132, (3524) × 14 = 154, therefore missing number is (54 - 36) × 9 = 162.

Type - 2: In type of figure, the question will consist of two or more than two figures of which 1st one or two figures giving information about sequence or logic of question, reader has to analyze them and choose the correct answer as explain by the following example.
Example 3:
(a) 36
(b) 40
(c) 45
(d) None of these

Correct Answer is Option (c)
In the above figure, the numbers are related as from 1^st and 2^nd figure that 5 + 3 = 8 = 2315, similarly answer can be found as 34 + 11 = 45 = 90 - 45. Therefore missing number is 45.

Solved Example

Example 1: Insert the missing number in each of the following.
(a) 185
(b) 126
(c) 239
(d) 145

Correct Answer is Option (a)
The Pattern is 4 × 2 + 1 = 9, 9 × 2 + 2 = 20, 20 × 2 +3 = 43, 43 × 2 + 4 = 90, 90 × 2 + 5= 185. So missing number is 185.

Example 2: Insert the missing number in each of the following.
(a) 5
(b) 6
(c) 14
(d) 8

Correct Answer is Option (a)
The Pattern is 4 × 2 + 1 = 9, 9 × 2 + 2 = 20, 20 × 2 + 3 = 43, 43 × 2 + 4 = 90, 90 × 2 + 5 = 185. So missing number is 185.

Example 3:  Insert the missing number in each of the following.
(a) 19
(b) 28
(c) 32
(d) 34

Correct Answer is Option (b)
Going clockwise starting from 16, numbers are increasing by 2 every time. So the missing term is 28.