Mathematical Operations: Definition, Questions, Examples

Mathematical operations is one of the most important topics in Reasoning and the questions from this topic are usually asked in almost every competitive exam. The topic is based on the equations with the set of numbers and the mathematical operations such as addition, subtraction, multiplication, and division. The best approach to tackling questions related to this topic is to improve one's mathematical skills and have a strong grasp of calculations. There are various tricks or methods to solve the questions but the best and the main method to solve these types of questions is the “BODMAS Rule”. BODMAS stands for Brackets, orders, division, multiplication, addition and subtraction. With the help of this rule, a student can easily determine the steps in which to solve a particular equation.

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This Story also Contains

1. Types of questions based on the mathematical operations
2. Recommended books and online resources
3. Question weightage of mathematical operations in competitive exams
4. Practice questions for interchanging symbols-based questions
5. Practice questions for interchanging symbols and numbers-based questions
6. Practice questions for fill in the blanks-based questions
7. Mathematical Operations Questions for SSC/ RRB exams
8. Mathematical Operations Questions for Bank Clerk/ Insurance Assistant exams

Types of questions based on the mathematical operations

There are majorly two types of questions that have been seen from mathematical operations -

1. Interchanging Symbol-Based Question
2. Fill in the blanks Based Question

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

1. Interchanging symbols-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 Symbols-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 BODAMS 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 the set of numbers and the 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 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 online resources

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

2. SSC Reasoning by Rakesh Yadav

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.

Practice questions for interchanging symbols-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.

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.

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.