Introduction: Mathematical Operations | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year PDF Download

Mathematical Operations

All these operations are represented by symbols, different from usual ones. The candidate is required to substitute the real signs in place of artificial symbols to solve the questions.We need to follow the VBODMAS rule for simplification of Mathematical operations. This rule gives us the correct order, in which various operations regarding simplification are to be performed. Order of various operations is as same as the order of letters in the 'VBODMAS'.

Types of Questions

Type #1:
 Problem Solving by Substitution

In this type of questions, you have substitutes for various mathematical symbols or numerals followed by a questions involving calculation of an expression or choosing the correct/incorrect equation.

Type #2:
 Interchanging the Signs and Numbers

In this type of questions, certain signs or numbers interchange among each other. The candidate is required to change the given signs or numbers with each other and select the equation which is correct from the given alternatives.

It can also be asked to find the correct pair of signs and numbers to be interchanged from the alternatives to make the given equation correct.

Type #3:
 Miscellaneous Patterns

In this type, questions are based on balancing the equation by replacing the actual mathematical signs with some other signs and tricks.

Type #4:
 Simple and Coded Inequalities

In this type of questions, certain relationship between different sets of elements is given (in terms of 'less than', 'greater than', or 'equal to'), using either the real symbols or substituted symbols. The candidate is required to read the given statements and then choose which of the conclusions is/are definitely true.

Solved Examples:

Q1: If '+' means '÷', 'x' means '-', '÷' means '+' and '-' means 'x', then 16 ÷ 8 x6 - 2 + 12 = ?
(a) 23
(b) 24
(c) 17
(d)  22
Ans: (a)
16 ÷ 8 x 6 - 2 + 12
Replacing the signs, 16 + 8 - 6 x 2 ÷ 12
= 16 + 8 - (6 x 2)/12 = 16 + 8 -1 = 24 - 1 = 23

Q2: If + means 'subtraction', x means 'division', '÷' means 'addition' and '-' means 'multiplication', then 15 x 5 + 78 - 5 ÷ 4 = ?
(a) - 383
(b) - 460
(c) - 475
(d) - 743
Ans: (a)
15 x 5 + 78 - 5 ÷ 4
Now, changing the signs as per the questions,
15/5 - 78 x 5 + 4 = 3 - 390 + 4 = - 390 + 7 = -383

Q3: If '+' means 'x', '-' means '÷', 'x' means '-' and '÷' means '+', then find the value of the given equation 6 + 64 - 8 ÷ 45 x 8 = ?
(a) 85
(b) 76
(c) 87
(d) 75
Ans: (a)
Given equation, 6 + 64 - 8 ÷ 45 x 8
Now, changing the sign as per the question,
6 x 64 ÷ 8 + 45 - 8 = (6 x 64)/8 + 45 - 8
6 x 8 + 45 - 8 = 48 + 45 - 8 = 93 - 8 = 85

Q4: If the mathematical signs interchange from - to +, + to ÷, x to - and ÷ to x, then find out the correct answer of the given equation 6 ÷ 8 + 2 x 5 - 8 = ?
(a) 27
(b) 18
(c) 32
(d) 28
Ans: (a)
6 ÷ 8 + 2 x 5 - 8 = 6 x 8 ÷ 2 - 5 + 8
= 6 x 4 - 5 + 8
= 24 - 5 + 8
= 32 - 5 = 27

Q5: In a certain code language, '÷' represents '+', '-' represents 'x', '+' represents '÷' and 'x' represents '-'. Find out the answer to the given question 8 - 14 + 7 x 10 ÷ 9 = ?
(a) 15
(b) 28
(c) 20
(d) 13
Ans: (a)
Given, 8 - 14 + 7 x 10 ÷ 9
Now, changing, the signs as per the questions,
8 x 14 ÷ 7 - 10 + 9
= 8 x 2 - 10 + 9 = 16 - 10 + 9
= 25 - 10 = 15