Category: Verbal Reasoning

Topic: Mathematical Operations

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Mathematical Operations - Base Level Exercise 1

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Mathematical Operations

✏️ Practice with curated questions covering all difficulty levels. Detailed solutions and expert tips help you master each question type.

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Mathematical Operations – Sample Questions

Mathematical Operations questions evaluate calculation accuracy, symbol substitution ability, logical reasoning, operator interpretation, hidden arithmetic patterns, and analytical thinking skills. These questions are commonly asked in SSC, Banking, Railway, Insurance, Defence, State PSC, and various aptitude examinations.

Regular practice of Mathematical Operations improves calculation speed, operator handling, equation balancing ability, coded inequality solving, and logical analysis skills.

Type #1 : Problem Solving by Substitution

In these questions, mathematical symbols or letters are substituted with different operators. Candidates must first replace the symbols correctly and then solve the expression using VBODMAS rules.

Question 1

If + means ÷, − means ×, × means + and ÷ means −, then find the value of:

45 + 9 − 3 × 15 ÷ 2

(a) 40
(b) 36
(c) 56
(d) 28

Correct Answer: (d) 28

Explanation:

Replace the symbols correctly:

45 ÷ 9 × 3 + 15 − 2

= 5 × 3 + 15 − 2

= 15 + 15 − 2

= 30 − 2 = 28

Question 2

If:

K means minus (−)
L means divided by (÷)
M means plus (+)
D means multiplied by (×)

Then find the value of:

117 L 3 K 5 M 12 D 8

(a) 150
(b) 125
(c) 130
(d) 145

Correct Answer: (c) 130

Explanation:

Replace letters with operators:

117 ÷ 3 − 5 + 12 × 8

= 39 − 5 + 96

= 34 + 96

= 130

Question 3

If '−' stands for '+', '+' stands for '×', and '×' stands for '−', then which equation is NOT correct?

(a) 22 + 7 − 3 × 9 = 148

(b) 33 × 5 − 10 + 20 = 228

(c) 7 + 28 − 3 × 52 = 127

(d) 44 − 9 + 6 × 11 = 87

Correct Answer: (c)

Explanation:

7 × 28 + 3 − 52

= 196 + 3 − 52

= 199 − 52

= 147 ≠ 127

Hence, option (c) is incorrect.

Type #2 : Interchanging Signs and Numbers

In these questions, certain signs or numbers interchange among each other. Candidates must identify the correct interchange and verify which equation becomes mathematically correct.

Question 4

If signs '+' and '−' and numbers 4 and 8 interchange with each other, then which equation becomes correct?

(a) 4 − 8 + 12 = 0

(b) 8 − 4 ÷ 12 = 8

(c) 4 ÷ 8 − 12 = 16

(d) 8 ÷ 4 − 12 = 24

Correct Answer: (a)

Explanation:

Interchange '+' with '−' and 4 with 8:

8 + 4 − 12 = 0

12 − 12 = 0

LHS = RHS

Question 5

Which interchange of signs and numbers will make the equation correct?

6 × 4 + 2 = 16

(a) + and ×, 2 and 4

(b) + and ×, 4 and 6

(c) + and ×, 2 and 6

(d) None of these

Correct Answer: (b)

Explanation:

After interchange:

4 + 6 × 2

= 4 + 12 = 16

Type #3 : Miscellaneous Patterns

These questions are based on hidden arithmetic patterns, equation balancing, operator insertion, and logical numerical tricks.

Question 6

Insert the correct mathematical signs to balance the equation:

24 __ 6 __ 12 __ 16 = 0

(a) ÷, + and −

(b) −, ÷ and +

(c) −, − and −

(d) ÷, + and ÷

Correct Answer: (a)

Explanation:

24 ÷ 6 + 12 − 16

= 4 + 12 − 16

= 16 − 16 = 0

Question 7

If:

5 × 4 = 15

7 × 8 = 49

6 × 5 = 24

Then:

8 × 4 = ?

(a) 24
(b) 26
(c) 28
(d) 30

Correct Answer: (a) 24

Explanation:

5 × 4 = 5 × (4 − 1) = 15

7 × 8 = 7 × (8 − 1) = 49

Similarly:

8 × 4 = 8 × (4 − 1)

= 8 × 3 = 24

Question 8

If:

64 × 52 = 17

48 × 56 = 23

74 × 35 = 19

Then:

84 × 37 = ?

(a) 32
(b) 28
(c) 22
(d) 20

Correct Answer: (c) 22

Explanation:

64 × 52 → (6 + 4) + (5 + 2) = 17

48 × 56 → (4 + 8) + (5 + 6) = 23

Similarly:

84 × 37 → (8 + 4) + (3 + 7)

= 12 + 10 = 22

Type #4 : Simple and Coded Inequalities

These questions test logical comparison, inequality interpretation, conclusion verification, and analytical reasoning using normal or coded symbols.

Directions (Questions 9–11)

Choose the correct answer:

(a) If only conclusion I follows

(b) If only conclusion II follows

(c) If either conclusion I or II follows

(d) If neither conclusion I nor II follows

(e) If both conclusions I and II follow

Question 9

Statements:

P ≥ Q = R

Q > S > T

Conclusions:

I. P ≥ T

II. T < Q

Correct Answer: (b)

Explanation:

P ≥ Q = R > S > T

Conclusion I → Not definite

Conclusion II → True

Question 10

Statements:

A ≤ B = C

D > C = E

Conclusions:

I. E ≥ A

II. A < D

Correct Answer: (e)

Explanation:

A ≤ B = C = E < D

Conclusion I → True

Conclusion II → True

Question 11

Statements:

F ≥ G = H

G > J ≥ K

Conclusions:

I. F ≥ K

II. K < H

Correct Answer: (b)

Explanation:

F ≥ G = H > J ≥ K

Conclusion I → Not definite

Conclusion II → True

Advanced Coded Inequalities

Question 12

Conclusions:

I. R @ D

II. R % D

III. K ★ T

IV. M δ T

(a) Only either I or II is true

(b) III and IV are true

(c) Either I or II and III are true

(d) Either I or II and IV are true

(e) Either I or II and III and IV are true

Correct Answer: (e)

Explanation:

D ≤ T = R ≥ M > K

III → True

IV → True

Only one among I and II can be true.

Question 13

(a) I and II are true

(b) I, II and III are true

(c) I, III and IV are true

(d) All I, II, III and IV are true

(e) None of the above

Correct Answer: (a)

Explanation:

J = F ≤ N > H ≥ G

I → True

II → True

III → False

IV → False

Question 14

Statements:

R ★ K

K % D

D @ V

V δ M

Conclusions:

I. R ★ D

II. V ★ R

III. D @ M

IV. M % D

(a) None is true

(b) Only III is true

(c) Only IV is true

(d) Either III or IV is true

(e) Either III or IV and II are true

Correct Answer: (d)

Explanation:

R < K > D = V ≤ M

III → May be true

IV → May be true

Hence, either III or IV follows.

Quick Tips for Mathematical Operations

Replace symbols carefully before calculation.
Always apply VBODMAS rules correctly.
Rewrite expressions after substitution.
Check hidden numerical patterns carefully.
Use elimination methods in confusing options.
Practice coded inequalities regularly.
Avoid calculation mistakes during operator replacement.
Verify conclusions step-by-step.

Common Mistakes to Avoid

Ignoring operator substitution order.
Violating VBODMAS rules.
Making mistakes during sign interchange.
Ignoring hidden arithmetic patterns.
Assuming conclusions without proper logic.
Misinterpreting coded inequality symbols.

Regular practice of Mathematical Operations questions improves calculation accuracy, logical analysis, operator handling ability, arithmetic speed, and problem-solving confidence. A systematic approach involving substitution, simplification, elimination, and logical comparison helps candidates solve these questions quickly and accurately in competitive examinations.

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