Mathematical Operations: Definition, Questions, Examples

Types of Mathematical Operations Questions in Reasoning (SSC, Banking, RRB Exams)

Understanding the different types of mathematical operations questions is essential to solve operation reasoning questions quickly and accurately. In competitive exams, these questions are mainly based on symbol changes and logical number placement, testing your knowledge of BODMAS rules and calculation skills.

Interchanging Symbol-Based Questions in Mathematical Operations Reasoning

These are the most common mathematical operations reasoning questions, where arithmetic symbols like +, −, ×, and ÷ are interchanged.

What are Interchanging Symbol Questions?

In these operation reasoning questions, the given mathematical expression uses incorrect or swapped symbols. You need to replace them with the correct ones to make the equation valid.

How to Solve Symbol Interchange Questions (Step-by-Step)

• Identify the incorrect symbols in the expression

• Replace them with the correct operations logically

• Apply BODMAS rule in mathematical operations

• Verify the final equation

Example of Mathematical Operations Question (Symbol Interchange)

If + means ×, − means ÷, × means +, and ÷ means −, then solve:
$8 + 4 × 2$

(Apply replacement and solve using BODMAS)

Fill in the Blanks Based Mathematical Operations Questions

These questions are slightly more analytical and are commonly asked in SSC mathematical operations questions.

What are Fill in the Blanks Questions in Mathematical Operations?

In these mathematical operations questions with answers, a blank is given in an equation, and you need to find the correct number or operator that satisfies the equation.

How to Solve Fill in the Blanks Questions Quickly

• Analyze the given equation carefully

• Apply BODMAS rule step by step

• Try possible values logically

• Check which value satisfies the equation

Example of Mathematical Operations Question (Fill in the Blank)

$6 × _ + 4 = 16$
(Find the missing number using proper calculation)

Let’s understand these types with the help of the examples -

1. Interchanging Symbol-Based Question

As it is clear by the word interchange itself, the process of interchanging the place of the elements will be seen in these types of questions. This type of mathematical operation is divided into two parts again -

Interchanging Symbol-Based Questions

In such types of questions, the symbols given in the equation need to be interchanged with the mathematical signs as directed in the question and then solve the obtained equation using the BODMAS rule. Let’s understand this with the help of an example.

Example: If + means ×, – means ÷, ÷ means + and × means –

then, 74 ÷ 11 – 33 + 42 × 16 = ?

1. 64

2. 68

3. 76

4. 72

Answer: In this example, simply interchange the signs as directed in the question. For, + will be interchanged with ×, – will be interchanged with ÷, ÷ will be interchanged with +, and × will be interchanged with –. So, after interchanging, the equation becomes 74 + 11 ÷ 33 × 42 – 16. Now, solve the equation using the BODMAS rule.

= 74 + 11 ÷ 33 × 42 – 16

= 74 + 0.33 × 42 – 16 = 74 + 14 – 16 = 88 – 16 = 72

So, 72 is the required answer to the given equation.

Interchanging Symbols and Numbers-Based Questions

In such types of questions, both the symbols and numbers given in the equation need to be interchanged as directed in the question and then solve the obtained equation using the BODMAS rule. Let’s understand this with the help of an example.

Example: After interchanging the given two numbers and two signs, what will be the value of the equation?

+ and ×, 5 and 4
4 + 6 × 5 – 7 ÷ 1

1. 30

2. 20

3. 27

4. 25

Answer: In this example, simply interchange the signs and numbers as directed in the question. Like, + will be interchanged with ×, and × will be interchanged with +. Also, interchange the numbers as directed. So, after interchanging, the equation becomes 5 × 6 + 4 – 7 ÷ 1, now solve the equation using the BODAMS rule.
= 5 × 6 + 4 – 7 ÷ 1
= 5 × 6 + 4 – 7 = 30 + 4 – 7 = 34 – 7 = 27
So, 27 is the required answer to the given equation.

2. Fill in the blanks-based questions

In these types of questions, an equation is given with a set of numbers and blanks. The equation needs to be completed by filling in the blanks with mathematical signs given in the different options one by one. One of the options will satisfy the equation, resulting in L.H.S. being equal to R.H.S. Let’s understand this with the help of an example.

Example: Select the correct combination of mathematical signs to replace the * signs and balance the given equation sequentially.
65 * 45 * 25 * 5 * 35 * 60

1. −, +, −, +, =

2. +, ×, +, −, =

3. +, −, +, −, =

4. −, +, ÷, +, =

Replace the * symbol with the mathematical signs given in the options one by one and solve the equation using the BODMAS rule. Only option D) satisfies the equation as shown below:

65 − 45 + 25 ÷ 5 + 35 = 60

Solving the L.H.S. of the equation –

= 65 − 45 + 5 + 35

= 105 − 45

= 60

Recommended Books and Resources for Mathematical Operations

1. A Modern Approach to Verbal & Non-Verbal Reasoning by R.S. Aggarwal

2. SSC Reasoning by Rakesh Yadav

3. How to Crack Test of Reasoning by Arihant Publications

4. A New Approach to Reasoning Verbal, Non-Verbal & Analytical by B.S. Sijwali & Indu Sijwali

5. Analytical Reasoning by M.K. Pandey

Question Weightage of Mathematical Operations in Competitive Exams

The number of questions based on mathematical operations varies from exam to exam -

1) Questions asked in SSC exams, i.e. SSC MTS, SSC CGL, SSC CHSL, SSC CPO, Steno - 3 to 4 questions.

2) Questions asked in the Railways exam, i.e. Group D, NTPC, JE, ALP, etc - 2 to 3 questions.

3) Questions asked in Banking exams, Bank PO, Bank Clerk - 3 to 4 questions.

Mathematical Operations Practice Questions PDF Download

The candidates must practice the e-book of mathematical operations and reasoning questions, PDF given below.

Download Now: Mathematical Operations Questions with Solutions PDF

Best Books for Mathematical Operations Reasoning Preparation (SSC, Banking, RRB)

This section covers the most recommended books for mastering mathematical operations reasoning questions, including concept clarity, shortcut tricks, and practice sets to improve speed and accuracy in competitive exams.

Practice Questions for Interchanging Symbol-Based Questions

Q1. Directions: What will come in the place of (?) in the following equation, if + and × are interchanged and also – and ÷ are interchanged?

20 ÷ 5 × 10 – 5 + 2 = ?

1. 4

2. 19 (Correct)

3. 12

4. 2

Solution:
Given:
20 ÷ 5 × 10 – 5 + 2 = ?
After interchanging the given mathematical signs, we get –
= 20 – 5 + 10 ÷ 5 × 2
= 20 – 5 + 2 × 2
= 20 – 5 + 4
= 19
So, 19 is the answer to the given equation. Hence, the second option is correct.

Q2. Directions: By interchanging which two signs, the given equation will be correct?

39 – 3 ÷ 13 + 16 × 8 = 17

1. × and – (Correct)

2. + and –

3. ÷ and –

4. × and ÷

Solution:
Given:
39 – 3 ÷ 13 + 16 × 8 = 17
Let's check the options –
First option: × and –
39 – 3 ÷ 13 + 16 × 8 = 17
On interchanging the mathematical signs, we get –
⇒ 39 × 3 ÷ 13 + 16 – 8 = 17
⇒ 9 + 16 – 8
⇒ 25 – 8
⇒ 17
Second option: + and –
39 – 3 ÷ 13 + 16 × 8 = 17
On interchanging the mathematical signs, we get –
⇒ 39 + 3 ÷ 13 – 16 × 8 = 17
⇒ 39 + 0.23 – 16 × 8
⇒ 39 + 0.23 – 128
⇒ – 88.77 ≠ 17
Third option: ÷ and –
39 – 3 ÷ 13 + 16 × 8 = 17
On interchanging the mathematical signs, we get –
⇒ 39 ÷ 3 – 13 + 16 × 8 = 17
⇒ 13 – 13 + 16 × 8
⇒ 13 – 13 + 128
⇒ 128 ≠ 17
Fourth option: × and ÷
39 – 3 ÷ 13 + 16 × 8 = 17
On interchanging the mathematical signs, we get –
⇒ 39 – 3 × 13 + 16 ÷ 8 = 17
⇒ 39 – 3 × 13 + 2
⇒ 39 – 39 + 2
⇒ 2 ≠ 17
Here, only the first option satisfies the R.H.S. of the equation. Hence, the first option is correct.

Q3. Directions: If A means +, B means –, C means ÷, and D means ×, then 63 C 9 A 16 B 32 D 3 C 8 = ?

1. 11 (Correct)

2. 13

3. 10

4. 9

Solution:
Given:
63 C 9 A 16 B 32 D 3 C 8 = ?
On replacing the alphabet with the symbols, we get –
= 63 ÷ 9 + 16 – 32 × 3 ÷ 8
= 7 + 16 – 12
= 23 – 12
= 11
Hence, the first option is correct.

Q4.Directions: If × means +, ÷ means ×, − means ÷, and + means −, then what will be the value of the following expression?

32 × 6 + 10 − 4 ÷ 8 = ?

1. 18 (Correct)

2. 20

3. 22

4. 24

Solution:
Given:
32 × 6 + 10 – 4 ÷ 8 = ?

On interchanging the mathematical signs, we get –
= 32 + 6 – 10 ÷ 4 × 8
= 32 + 6 – 2.5 × 8
= 32 + 6 – 20
= 18

Hence, the first option is correct.

Q5. Directions: Which two signs should be interchanged to make the given equation correct?

12 + 156 ÷ 13 × 6 – 100 = 50

1. ÷ and ×

2. + and × (Correct)

3. – and ×

4. ÷ and –

Solution:
Given:
12 + 156 ÷ 13 × 6 – 100 = 50
Let's check the options –
First option: ÷ and ×
⇒ 12 + 156 × 13 ÷ 6 – 100 = 50
Solving the L.H.S. of the equation –
= 12 + 338 – 100
= 250 ≠ 50
Second option: + and ×
⇒ 12 × 156 ÷ 13 + 6 – 100 = 50
Solving the L.H.S. of the equation –
= 12 × 12 + 6 – 100
= 144 + 6 – 100
= 50
Third option: – and ×
⇒ 12 + 156 ÷ 13 – 6 × 100 = 50
Solving the L.H.S. of the equation –
= 12 + 12 – 6 × 100
= 12 + 12 – 600
= –576 ≠ 50
Fourth option: ÷ and –
⇒ 12 + 156 – 13 × 6 ÷ 100 = 50
Solving the L.H.S. of the equation –
= 12 + 156 – 13 × 0.06
= 12 + 156 – 0.78
= 167.22 ≠ 50
So, only the second option satisfies the given equation. Hence, the second option is correct.

Practice Questions for Interchanging Symbols and Numbers-Based Questions

Q1. Directions: Which two signs and two numbers (Not digits) should be interchanged in the given equation to make it correct?

9 ÷ 3 + 7 × 4 – 5 = 20

1. ÷ and –, 5 and 4

2. × and –, 3 and 5

3. + and ×, 9 and 7 (Correct)

4. ÷ and –, 7 and 5

Solution:

Given:
9 ÷ 3 + 7 × 4 – 5 = 20

Let's check the given options –
First Option: ÷ and –, 5 and 4
⇒ 9 – 3 + 7 × 5 ÷ 4 = 20
Solving the L.H.S. of the equation –
= 9 – 3 + 7 × 1.25
= 9 – 3 + 8.75
= 14.75 ≠ 20
Second option: × and –, 3 and 5
⇒ 9 ÷ 5 + 7 – 4 × 3 = 20
Solving the L.H.S. of the equation –
= 1.8 + 7 – 4 × 3
= 1.8 + 7 – 12
= –3.2 ≠ 20
Third option: + and ×, 9 and 7
⇒ 7 ÷ 3 × 9 + 4 – 5 = 20
Solving the L.H.S. of the equation –
= 21 + 4 – 5
= 20
Fourth option: ÷ and –, 7 and 5
⇒ 9 – 3 + 5 × 4 ÷ 7 = 20
Solving the L.H.S. of the equation –
= 9 – 3 + 5 × 0.57
= 9 – 3 + 2.85
= 8.85 ≠ 20

So, only the third option satisfies the given equation. Hence, the third option is correct.

Q2. Directions: By interchanging the given two signs and numbers, which of the following equations will be correct?

× and +, 9 and 6

1. 7 × 6 ÷ 3 + 9 – 8 = 17 (Correct)

2. 6 × 8 – 9 ÷ 3 + 5 = 50

3. 7 + 6 × 4 ÷ 9 – 8 = 8

4. 9 × 7 + 4 ÷ 1 – 6 = 7

Solution:
Let's check the options –
First option: 7 × 6 ÷ 3 + 9 – 8 = 17
On interchanging the given numbers and symbols, the equation becomes –
= 7 + 9 ÷ 3 × 6 – 8
= 7 + 18 – 8
= 17
Second option: 6 × 8 – 9 ÷ 3 + 5 = 50
On interchanging the given numbers and symbols, the equation becomes –
= 9 + 8 – 6 ÷ 3 × 5
= 9 + 8 – 10
= 17 – 10
= 7 ≠ 50
Third option: 7 + 6 × 4 ÷ 9 – 8 = 8
On interchanging the given numbers and symbols, the equation becomes –
= 7 × 9 + 4 ÷ 6 – 8
= 63 + 0.66 – 8
= 63.66 – 8
= 55.66 ≠ 8
Fourth option: 9 × 7 + 4 ÷ 1 – 6 = 7
On interchanging the given numbers and symbols, the equation becomes –
= 6 + 7 × 4 ÷ 1 – 9
= 6 + 7 × 4 – 9
= 6 + 28 – 9
= 25 ≠ 7
Hence, the first option is correct.

Q3. Directions: Which two signs and two numbers (Not digits) of the equation should be interchanged to make it correct?

13 × 12 ÷ 36 + 11 – 7 = 35

1. + and ×, 36 and 7

2. + and –, 12 and 7

3. × and ÷, 13 and 36

4. × and ÷,11 and 7 (Correct)

Solution:
Given:
13 × 12 ÷ 36 + 11 – 7 = 35
Let's check the given options –
First option: + and ×, 36 and 7
13 × 12 ÷ 36 + 11 – 7 = 35
On interchanging the mathematical signs and numbers, we get –
= 13 + 12 ÷ 7 × 11 – 36
= 13 + 1.71 × 11 – 36
= 13 + 18.81 – 36
= 31.81 – 36
= –4.19 ≠ 35
Second option: + and –, 12 and 7
13 × 12 ÷ 36 + 11 – 7 = 35
On interchanging the mathematical signs and numbers, we get –
= 13 × 7 ÷ 36 – 11 + 12
= 13 × 0.19 – 11 + 12
= 2.47 – 11 + 12
= 3.47 ≠ 35
Third option: × and ÷, 13 and 36
13 × 12 ÷ 36 + 11 – 7 = 35
On interchanging the mathematical signs and numbers, we get –
= 36 ÷ 12 × 13 + 11 – 7
= 3 × 13 + 11 – 7
= 39 + 11 – 7
= 50 – 7
= 43 ≠ 35
Fourth option: × and ÷,11 and 7
13 × 12 ÷ 36 + 11 – 7 = 35
On interchanging the mathematical signs and numbers, we get –
= 13 ÷ 12 × 36 + 7 – 11
= 39 + 7 – 11
= 46 – 11
= 35
So, the fourth option satisfies the R.H.S. of the equation. Hence, the fourth option is correct.

Q4. Directions: By interchanging the given two numbers (not digits) which of the following equations will not be correct?

4 and 6

1. 2 + 6 × 5 – 4 = 16

2. 4 + 5 – 6 = 7

3. 6 ÷ 2 – 4 × 5 = –28

4. 6 × 3 – 4 ÷ 1 = 3 (Correct)

Solution:
Let's check the options –
First option: 2 + 6 × 5 – 4 = 16
On interchanging the given numbers, the equation becomes –
⇒ 2 + 4 × 5 – 6 = 16
Solving the L.H.S. of the equation –
= 2 + 20 – 6
= 22 – 6
= 16
Second option: 4 + 5 – 6 = 7
On interchanging the given numbers, the equation becomes –
⇒ 6 + 5 – 4 = 7
Solving the L.H.S. of the equation –
= 11 – 4
= 7
Third option: 6 ÷ 2 – 4 × 5 = –28
On interchanging the given numbers, the equation becomes –
⇒ 4 ÷ 2 – 6 × 5 = –28
Solving the L.H.S. of the equation –
= 2 – 6 × 5
= 2 – 30
= –28
Fourth option: 6 × 3 – 4 ÷ 1 = 3
On interchanging the given numbers, the equation becomes –
⇒ 4 × 3 – 6 ÷ 1 = 3
Solving the L.H.S. of the equation –
= 4 × 3 – 6
= 12 – 6
= 6 ≠ 3
So, only the equation in the fourth option does not satisfy the R.H.S. of the given equation. Hence the fourth option is correct.

Q5. Directions: Which two numbers (not digits) should be interchanged to make the given equation correct?

5 – 6 ÷ 3 × 9 + 1 = 0

1. 1 and 0

2. 6 and 9

3. 5 and 9

4. 6 and 3

Solution:
Given:
5 – 6 ÷ 3 × 9 + 1 = 0
Let's check the options –
First option: 1 and 0
5 – 6 ÷ 3 × 9 + 1 = 0
On interchanging the numbers, we get –
⇒ 5 – 6 ÷ 3 × 9 + 0 = 1
⇒ 5 – 2 × 9 + 0 = 1
⇒ 5 – 18 + 0 = 1
⇒ –13 ≠ 1
Second option: 6 and 9
5 – 6 ÷ 3 × 9 + 1 = 0
On interchanging the numbers, we get –
⇒ 5 – 9 ÷ 3 × 6 + 1 = 0
⇒ 5 – 3 × 6 + 1 = 0
⇒ 5 – 18 + 1 = 0
⇒ –12 ≠ 0
Third option: 5 and 9
5 – 6 ÷ 3 × 9 + 1 = 0
On interchanging the numbers, we get –
⇒ 9 – 6 ÷ 3 × 5 + 1 = 0
⇒ 9 – 2 × 5 + 1 = 0
⇒ 9 – 10 + 1 = 0
⇒ 0
Fourth option: 6 and 3
5 – 6 ÷ 3 × 9 + 1 = 0
On interchanging the numbers, we get –
⇒ 5 – 3 ÷ 6 × 9 + 1 = 0
⇒ 5 – 0.5 × 9 + 1 = 0
⇒ 5 – 4.5 + 1 = 0
⇒ 1.5 ≠ 0
Here, only the third option satisfies the equation. Hence, the third option is correct.

Important Rules of Mathematical Operations (BODMAS Concept Explained for Reasoning Exams)

Understanding the BODMAS rule in mathematical operations reasoning is the foundation for solving all types of mathematical operations questions. Whether it’s symbol interchange or missing value problems, applying the correct order of operations ensures accurate answers in SSC, Banking, and other competitive exams.

BODMAS Rule in Mathematical Operations Reasoning (Core Concept)

The BODMAS rule defines the correct sequence to solve any mathematical expression.

BODMAS stands for:

• B – Brackets

• O – Orders (powers, roots)

• D – Division

• M – Multiplication

• A – Addition

• S – Subtraction

Rule: Solve expressions from left to right following this order.

Example:
$8 + 4 × 2$
= $8 + 8 = 16$

This rule is essential for solving operation reasoning questions accurately.

Order of Operations with Examples in Mathematical Operations Questions

In mathematical operations reasoning questions, applying the correct order is crucial.

Example 1:
$12 - 6 ÷ 3$
= $12 - 2 = 10$

Example 2:
$(10 + 5) × 2$
= $15 × 2 = 30$

These examples show how BODMAS in reasoning helps avoid mistakes in calculations.

Best Mathematical Operations Tricks for Quick Solving in Exams

Using smart mathematical operations tricks can save time and improve accuracy in competitive exams.

Short Tricks to Solve Mathematical Operations Questions Faster

• Always apply BODMAS rule first before trying shortcuts

• Simplify brackets early to reduce complexity

• Memorize common patterns in operation reasoning questions

• Replace symbols carefully in symbol interchange questions

• Practice mathematical operations questions with answers regularly

These tricks are highly useful for SSC, Banking, and RRB exams.

Common Mistakes in Operation Reasoning Questions (Avoid These Errors)

• Ignoring the BODMAS rule and solving left to right directly

• Misinterpreting symbols in mathematical operations reasoning questions

• Skipping brackets or solving them incorrectly

• Calculation errors due to lack of practice

• Rushing without verifying the final answer

Avoiding these mistakes improves accuracy in mathematical operations questions.

Step-by-Step Approach to Solve Mathematical Operations Questions

A structured method helps in solving even tricky operation reasoning questions efficiently.

Easy Method to Solve Operation-Based Reasoning Questions

Follow these steps:

1. Read the question carefully

2. Identify if symbols are interchanged or values are missing

3. Apply correct replacements (if needed)

4. Solve using BODMAS rule

5. Verify the final answer

This method works for all types of mathematical operations reasoning questions.

Shortcut Techniques for Mathematical Operations Reasoning

• Use elimination method in MCQs

• Break complex expressions into smaller parts

• Memorize quick calculation tricks

• Practice previous year mathematical operations questions with answers

• Focus on accuracy along with speed

These shortcut techniques for mathematical operations reasoning help you solve questions faster and score better in competitive exams.

Verbal Reasoning Topics

The candidates who are preparing for the upcoming entrance and Government exams can also refer to the links given below and master the reasoning ability section:

Practice Questions for Fill-in-the-Blanks-Based Questions

Q1. Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation.

99 * 33 * 66 * 22 * 44 * 50

1. ÷, +, ×, +, =

2. +, −, ÷, −, =

3. ÷, +, ÷, +, =

4. ÷, −, +, ×, =

Solution:
Given:
99 * 33 * 66 * 22 * 44 * 50
Let's check the given options –
First Option: ÷, +, ×, +, =
⇒ 99 ÷ 33 + 66 × 22 + 44 = 50
Solving the L.H.S. of the equation –
= 3 + 66 × 22 + 44
= 3 + 1452 + 44
= 1499 ≠ 50
Second Option: +, −, ÷, −, =
⇒ 99 + 33 − 66 ÷ 22 − 44 = 50
Solving the L.H.S. of the equation –
= 99 + 33 − 3 − 44
= 132 − 3 − 44
= 85 ≠ 50
Third Option: ÷, +, ÷, +, =
⇒ 99 ÷ 33 + 66 ÷ 22 + 44 = 50
Solving the L.H.S. of the equation –
= 3 + 3 + 44
= 50
Fourth Option: ÷, −, +, ×, =
⇒ 99 ÷ 33 − 66 + 22 × 44 = 50
Solving the L.H.S. of the equation –
= 3 − 66 + 22 × 44
= 3 − 66 + 968
= 905 ≠ 50
So, only the third option satisfies the given equation. Hence, the third option is correct.

Q2. Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation.
21 * 3 * 36 * 2 * 23 = 68

1. ÷, −, ×, +

2. ÷, ×, +, −

3. +, ×, −, ÷

4. ×, −, ÷, +

Solution:
Given:
21 * 3 * 36 * 2 * 23 = 68
Let's check the given options –
First option: ÷, −, ×, +
⇒ 21 ÷ 3 − 36 × 2 + 23 = 68
Solving the L.H.S. of the equation –
= 7 − 36 × 2 + 23
= 7 − 72 + 23
= −42 ≠ 68
Second option: ÷, ×, +, −
⇒ 21 ÷ 3 × 36 + 2 − 23 = 68
Solving the L.H.S. of the equation –
= 7 × 36 + 2 − 23
= 252 + 2 − 23
= 231 ≠ 68
Third option: +, ×, −, ÷
⇒ 21 + 3 × 36 − 2 ÷ 23 = 68
Solving the L.H.S. of the equation –
= 21 + 3 × 36 − 0.09
= 21 + 108 − 0.09
= 128.91 ≠ 68
Fourth option: ×, −, ÷, +
⇒ 21 × 3 − 36 ÷ 2 + 23 = 68
Solving the L.H.S. of the equation –
= 21 × 3 − 18 + 23
= 63 − 18 + 23
= 68
So, only the fourth option satisfies the given equation. Hence, the fourth option is correct.

Q3. Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation.
268 * 4 * 8 * 5 * 14 = 41

1. +, ×, −, ÷

2. ×, ÷, +, −

3. ÷, ×, +, −

4. ÷, −, ×, +

Solution:
Given:
268 * 4 * 8 * 5 * 14 = 41
Let's check the options –
First option: +, ×, −, ÷
⇒ 268 + 4 × 8 − 5 ÷ 14 = 41
Solving the L.H.S. of the equation –
⇒ 268 + 4 × 8 − 0.36
⇒ 268 + 32 − 0.36
⇒ 299.64 ≠ 41
Second option: ×, ÷, +, −
⇒ 268 × 4 ÷ 8 + 5 − 14 = 41
Solving the L.H.S. of the equation –
⇒ 268 × 0.5 + 5 − 14
⇒ 134 + 5 − 14
⇒ 125 ≠ 41
Third option: ÷, ×, +, −
⇒ 268 ÷ 4 × 8 + 5 − 14 = 41
Solving the L.H.S. of the equation –
⇒ 67 × 8 + 5 − 14
⇒ 536 + 5 − 14
⇒ 527 ≠ 41
Fourth option: ÷, −, ×, +
⇒ 268 ÷ 4 − 8 × 5 + 14 = 41
Solving the L.H.S. of the equation –
⇒ 67 − 8 × 5 + 14
⇒ 67 − 40 + 14
⇒ 41
Here, only the fourth option satisfies the equation. Hence, the fourth option is correct.

Q4. Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation.
(130 * 4) * 21 * 485 * (28 * 2)

1. +, −, =, −, ×

2. ÷, +, =, −, ×

3. ×, −, =, −, ÷

4. ×, −, =, +, ÷

Solution:
Given:
(130 * 4) * 21 * 485 * (28 * 2)
Let's check the options −
First option: +, −, =, −, ×
⇒ (130 + 4) − 21 = 485 − (28 × 2)
L.H.S. = (130 + 4) − 21 = 134 − 21 = 113
R.H.S. = 485 − (28 × 2) = 485 − 56 = 429
L.H.S. ≠ R.H.S.
Second option: ÷, +, =, −, ×
⇒ (130 ÷ 4) + 21 = 485 − (28 × 2)
L.H.S. = (130 ÷ 4) + 21 = 32.5 + 21 = 53.5
R.H.S. = 485 − (28 × 2) = 485 − 56 = 429
L.H.S. ≠ R.H.S.
Third option: ×, −, =, −, ÷
⇒ (130 × 4) − 21 = 485 − (28 ÷ 2)
L.H.S. = (130 × 4) − 21 = 520 − 21 = 499
R.H.S. = 485 − (28 ÷ 2) = 485 − 14 = 471
L.H.S. ≠ R.H.S.
Fourth option: ×, −, =, +, ÷
⇒ (130 × 4) − 21 = 485 + (28 ÷ 2)
L.H.S. = (130 × 4) − 21 = 520 − 21 = 499
R.H.S. = 485 + (28 ÷ 2) = 485 + 14 = 499
L.H.S. = R.H.S.
Hence, the fourth option is correct.

Q5. Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation.
54 * 6 * 72 * 8 * 3 * 15

1. ÷, +, ÷, −, =

2. ÷, −, −, +, =

3. +, ÷, ×, +, =

4. ×, −, −, +, =

Solution:
Given:
54 * 6 * 72 * 8 * 3 * 15
Let's check the given options –
First option: ÷, +, ÷, −, =
⇒ 54 ÷ 6 + 72 ÷ 8 – 3 = 15
Solving the L.H.S. of the equation –
= 9 + 9 – 3
= 18 – 3
= 15
Second option: ÷, –, –, +, =
⇒ 54 ÷ 6 – 72 – 8 + 3 = 15
Solving the L.H.S. of the equation –
= 9 – 72 – 8 + 3
= 12 – 72 – 8
= –68 ≠ 15
Third option: +, ÷, ×, +, =
⇒ 54 + 6 ÷ 72 × 8 + 3 = 15
Solving the L.H.S. of the equation –
= 54 + 0.67 + 3
= 57.67 ≠ 15
Fourth option: ×, –, –, +, =
⇒ 54 × 6 – 72 – 8 + 3 = 15
Solving the L.H.S. of the equation –
= 324 – 72 – 8 + 3
= 327 – 72 – 8
= 247 ≠ 15
So, only the first option satisfies the given equation. Hence, the first option is correct.

Mathematical Operations Questions for SSC/ RRB exams

Q-1. Directions: If A denotes addition, B denotes multiplication, C denotes subtraction, and D denotes division, then what will be the value of the following equation:
27 B 3 C (11 A 3) A 14 B (100 D 10) = ?
1) 207
2) 117
3) 221
4) 111

Solution:
27 B 3 C (11 A 3) A 14 B (100 D 10) = ?
After replacing the letters with the mathematical signs, we get:
= 27 × 3 – (11 + 3) + 14 × (100 ÷ 10)
= 27 × 3 – 14 + 14 × 10
= 81 – 14 + 140
= 207
So, 207 is the answer to the given equation. Hence, the first option is correct.

Q-2. Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct:
19 × 12 - 51 ÷ 34 + 17 = 197
1) 17 and 51, × and –
2) 51 and 17, × and ÷
3) 34 and 51, × and +
4) 34 and 51, + and ÷

Solution:
Interchanging the numbers and signs according to the options, to balance the equation –
Let's check the options –
First option: 17 and 51, × and –
⇒19 – 12 × 17 ÷ 34 + 51 = 197
19 – 12 × 0.5 + 51 = 197
19 – 6 + 51 = 197
64 ≠ 197
Second option: 51 and 17, × and ÷
⇒19 ÷ 12 – 17 × 34 + 51 = 197
1.58 – 17 × 34 + 51 = 197
1.58 – 578 + 51 = 197
– 525.42 ≠ 197
Third option: 34 and 51, × and +
⇒19 + 12 – 34 ÷ 51 × 17 = 197
19 + 12 – 0.66 × 17 = 197
19 + 12 – 11.22 = 197
19.78 ≠ 197
Fourth option: 34 and 51,+ and ÷
⇒19 × 12 – 34 + 51 ÷ 17 = 197
19 × 12 – 34 + 3 = 197
228 – 34 + 3 = 197
197 = 197
So, the fourth option satisfies the given equation. Hence, the fourth option is correct.

Q-3. Directions: Select the correct combination of the mathematical signs to replace star symbols (*) in the below equation and thereby balance it.
65 * 5 * 17 * 24 * 21 * 224

1) ÷, ×, +, –, =

2) +, ×, –, ÷, =

3) ÷, ×, –, +, =

4) ×, +, –, ÷, =

Solution:

Replace * with the mathematical signs and solve the equations one by one using BODMAS.

First options: ÷, ×, +, –, =

65 ÷ 5 × 17 + 24 – 21 = 224

On solving the L.H.S. of the given equation –

= 65 ÷ 5 × 17 + 24 – 21

= 13 × 17 + 24 – 21

= 221 + 24 – 21

= 224

Second option: +, ×, –, ÷, =

65 + 5 × 17 – 24 ÷ 21 = 224

On solving the L.H.S. of the given equation –

= 65 + 5 × 17 – 24 ÷ 21

= 65 + 5 × 17 – 1.143

= 65 + 85 – 1.143

= 148.857 ≠ 224

Third option: ÷, ×, –, +, =

65 ÷ 5 × 17 – 24 + 21 = 224

On solving the L.H.S. of the given equation –

= 13 × 17 – 24 + 21

= 221 – 24 + 21

= 218 ≠ 224

Fourth option: ×, +, –, ÷, =

65 × 5 + 17 – 24 ÷ 21 = 224

On solving the L.H.S. of the given equation –

= 65 × 5 + 17 – 1.14

= 325 + 17 – 1.14

= 340.86 ≠ 224

So, the first option satisfies the equation. Hence, the first option is correct.

Mathematical Operations Questions for Bank Clerk/ Insurance Assistant exams

Q-1. Directions: If × means ÷, – means +, ÷ means × and + means –, then 84 × 7 ÷ 4 – 16 × 8 ÷ 2 + 14 = ?
1) 36

2) 38

3) 44

4) 24

Solution:

After interchanging the given mathematical signs, we get –

⇒ 84 ÷ 7 × 4 + 16 ÷ 8 × 2 – 14

⇒ 12 × 4 + 2 × 2 – 14

⇒ 48 + 4 – 14

⇒ 38

So, 38 is the answer to the given equation. Hence, the second option is correct.

Q-2. Directions: If 617 @ 342 = 572 and 483 @ 342 = 141, then 280 @ 82 = ?

1)632

2)891

3) 188

4) 721

Solution:

Equation I: 617 @ 342 = 572

617 – 342 = 275; On reversing the order of digits of 275, we get 572.

Equation II: 483 @ 342 = 141

483 – 342 = 141; On reversing the order of digits of 141 we get 141.

Similarly, for Equation III: 280 @ 82 = ?

280 – 82 = 198; On reversing the order of digits of 198, we get 891.

Hence, the second option is correct.

Common Mistakes in Solving Mathematical Operations Questions

Many students struggle with mathematical operations reasoning questions because they rush through the process or misinterpret symbols. In exams like SSC, CUET, VITEEE, and Banking, even a small mistake in following the rules or BODMAS order can lead to wrong answers. Below are the most common mistakes you should avoid while solving symbolic operations reasoning questions.

Ignoring the Given Instructions or Rules

One of the most frequent mistakes candidates make in mathematical operations reasoning questions is neglecting the exact instructions. In exams like CUET, SSC, and IPMAT, symbols are often redefined, and missing these small details can lead to completely wrong answers. Always read the directions carefully before attempting symbolic operations.

Confusing Between Symbols and Their Real Meanings

In symbolic operations reasoning questions, students often mix the newly assigned meaning of symbols (+, −, ×, ÷) with their actual values. For example, if “×” is defined as “+”, you must replace it accordingly. Confusing the symbols is one of the biggest errors seen in mathematical operations questions and answers PDF practice sets.

Rushing Without Verifying Each Step

Competitive exams are time-bound, and many candidates try to solve these reasoning questions too quickly. Skipping verification leads to silly mistakes. It’s important to cross-check each step, especially when solving mathematical operations reasoning questions SSC exams.

Overlooking the Order of Operations (BODMAS Rule)

Another common mistake is ignoring the BODMAS rule while solving symbolic problems. Even when symbols are replaced, the order of operations (Bracket, Of, Division, Multiplication, Addition, Subtraction) remains the same. Misapplying BODMAS leads to incorrect answers in reasoning questions for competitive exams.

Tricks and Shortcuts for Mathematical Operations Reasoning

Mathematical operations reasoning questions can be solved faster with simple shortcuts and logical approaches. These tricks help in identifying patterns, reducing errors, and saving time in exams. Below are some of the most effective methods.

Step-by-Step Approach to Solve Symbolic Operations Reasoning Questions

Break the question into smaller steps. Replace each symbol with its new meaning before performing calculations. Following a systematic method ensures accuracy while practicing mathematical operations reasoning questions PDF and mock tests.

Using Elimination Method for Tough Options

When faced with tricky symbolic operations reasoning questions, use the elimination method. Test each option by applying the given rules. This saves time and is particularly helpful in exams like SSC, Banking, CUET, and VITEEE.

Identifying Repeated Patterns in Mathematical Operations

Many mathematical operations reasoning questions follow recurring patterns such as swapped symbols or inverse operations. Identifying these patterns quickly can help in solving questions faster and scoring better in reasoning for all competitive exams.

How to Prepare for Mathematical Operations in Competitive Exams

Preparing for mathematical operations reasoning questions requires consistent practice, strong command over symbolic operations, and smart exam strategies. These questions are commonly asked in CUET, VITEEE, MAH MBA CET, IPMAT, SSC, Banking, and other competitive exams. Below are some effective preparation tips.

Mathematical Operations in CUET, VITEEE, MAH MBA CET, and IPMAT

These exams often include mathematical operations and reasoning questions to test analytical ability. Focus on speed and accuracy by practising symbolic reasoning and pattern-based problems from past papers and PDFs.

Solving Mathematical Operations Reasoning Questions SSC & Banking Exams

In SSC and Banking exams, mathematical operations reasoning questions SSC are designed to check logical interpretation. Practicing previous year questions and mathematical operations questions and answers helps candidates build confidence and reduce errors.

Using Online Quizzes and PDFs for Regular Practice

Free and paid resources like mathematical operations reasoning questions PDF, quizzes, and sectional tests are available online. Regular practice through these platforms helps in mastering shortcuts, avoiding common mistakes, and preparing efficiently for competitive exams like SSC, Banking, CUET, and IPMAT.

Non-Verbal Reasoning Topics

Non-verbal reasoning questions test your ability to analyze patterns, shapes, and figures without using language-based logic. These types of questions are very common in competitive exams like SSC, CUET, Banking, and Railways, making them important for quick problem-solving practice. Below are the key non-verbal reasoning topics you should focus on.

About the Faculty
Tanu Gupta, with over a decade of experience as a reasoning faculty, specializes in preparing students for various entrance examinations and career development. Her extensive work with multiple educational platforms and institutions has honed her expertise in logical and analytical thinking. Her dedication to innovative teaching methods ensures these articles provide practical insights and expert guidance.