Mathematical Signs and Operations Test: IQ and Logical Reasoning Questions, Tricks, and Practice

The Mathematical Signs and Operations Test is an important topic in Numerical Reasoning that evaluates your ability to manipulate mathematical symbols, decode coded operations, and solve equations by inserting or interchanging operators. These questions test your understanding of arithmetic operations, your ability to apply the BODMAS rule, and your logical reasoning skills in a structured, rule-based format. The key skill is to accurately interpret symbols, substitute operations correctly, and solve expressions using the standard order of operations.

In this guide, we’ll explore what mathematical signs and operations problems involve, the rules you need, the common question types you’ll encounter, proven methods to solve them, and practical tricks to boost your speed and accuracy.

What are Mathematical Signs and Operations in Numerical Reasoning?

Mathematical Signs and Operations problems involve operators such as +, −, ×, ÷, and = and their relationships within an equation. You’ll typically be asked to insert the correct signs to balance an equation, interchange signs to correct one, or decode symbols that have been reassigned new meanings.

Example: If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’, and ‘÷’ means ‘+’, what is the value of 15 × 3 ÷ 15 + 5 − 2? Substituting each symbol with its new meaning turns the expression into 15 ÷ 3 + 15 − 5 × 2, and applying BODMAS to that rewritten expression gives the final value. Answer: 10

These problems appear as logical puzzles in competitive exams and aptitude tests, coding-and-decoding sections, and general brain-teaser style reasoning assessments.

What Skills Do These Questions Measure?

Mathematical signs and operations questions test your ability in:

• Understanding of basic arithmetic operations – knowing what each operator does
• Knowledge of the BODMAS rule – applying the correct order of operations
• Substituting and decoding symbols – correctly translating coded operators into real ones
• Logical reasoning and analytical thinking – testing combinations systematically rather than guessing
• Speed and accuracy – solving symbol-heavy expressions quickly under exam pressure

This topic is listed in the Officer Cadet syllabus under Numerical Reasoning as “Inserting Correct Mathematical Signs,” and it’s a high-scoring area because questions follow predictable patterns that can be solved quickly with the right approach.

Important Terms and Definitions

• BODMAS rule – the standard order of operations: Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right)
• Symbol substitution – replacing given symbols with their assigned mathematical operations before solving
• Operator precedence – the priority order operations are performed in, with multiplication and division coming before addition and subtraction
• Interchange – swapping two operators (or an operator and a number) in an equation to make it correct
• Coded operations – symbols that don’t carry their usual meaning and have instead been assigned new operations

Fundamental Rules

The BODMAS Rule

1. Brackets ( ) are resolved first
2. Orders (powers, roots) come next
3. Division (÷) and Multiplication (×) are performed left to right
4. Addition (+) and Subtraction (−) are performed left to right

Always apply BODMAS after substituting any coded symbols — never before.

Common Arithmetic Operations

Quick References

Always perform × and ÷ before + and − unless brackets say otherwise, and when two operations share the same priority (× and ÷, or + and −), work through them strictly left to right.

How to Solve These Questions

Follow this step-by-step method during your exam.

Step 1: Read the Question Carefully

Identify the type of question — symbol substitution, inserting missing signs, interchanging signs, or coded symbols with new meanings.

Step 2: For Symbol Substitution

Note the new meaning of each symbol, replace every symbol in the expression with its actual operation, apply BODMAS to evaluate the rewritten expression, and compare the result with the given options.

Step 3: For Inserting Missing Signs

Look at the numbers and the target result, try different combinations of +, −, ×, and ÷ in the blanks, apply BODMAS while testing each combination, and confirm which one makes the equation true.

Step 4: For Interchanging Signs

Identify the two signs being swapped, replace them in the equation, evaluate the result using BODMAS, and check whether the equation now balances correctly.

Step 5: Verify Your Answer

Substitute your answer back into the original equation and confirm it balances. For substitution problems, re-evaluate the full expression one more time after substitution.

Step 6: Manage Your Time

If a question is taking too long, mark it, move on, and return later if time allows: Solve → Mark if necessary → Move on → Return later.

Types of Mathematical Signs and Operations Questions

For Officer Cadet preparation, these questions may involve:

• Symbol substitution – mathematical operators are coded as different symbols or operators
• Inserting missing mathematical signs – filling blanks with +, −, ×, ÷, or = to make an equation true
• Interchanging signs – swapping two signs in an equation to correct it
• Coded operations – symbols like @, #, $, and others assigned specific operations
• Interchanging signs and numbers – both operators and numbers may need to be swapped together

Symbol Substitution

Example: If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’, and ‘÷’ means ‘+’, what is the value of 15 × 3 ÷ 15 + 5 − 2? Replacing each symbol gives the rewritten expression 15 ÷ 3 + 15 − 5 × 2. Applying BODMAS, 15 ÷ 3 = 5 and 5 × 2 = 10, so the expression becomes 5 + 15 − 10. Answer: 10

Inserting Correct Mathematical Signs

Example: Which signs should be inserted in the blanks to make the equation correct? 8 _ 6 _ 2 _ 4 _ 8 = 28 Testing combinations with BODMAS in mind, using ×, ÷, −, and + in that order works: 8 × 6 = 48, 48 ÷ 2 = 24, 24 − 4 = 20, 20 + 8 = 28. Answer: 8 × 6 ÷ 2 − 4 + 8 = 28

Interchanging Signs

Example: Which two signs should be interchanged to make the following equation correct? 15 × 12 + 40 ÷ 40 − 6 = 21 Interchanging the × and + signs turns the expression into 15 + 12 × 40 ÷ 40 − 6. Applying BODMAS, 40 ÷ 40 = 1, 12 × 1 = 12, and 15 + 12 − 6 = 21. Answer: Interchange ‘×’ and ‘+’ to get 15 + 12 × 40 ÷ 40 − 6 = 21

Coded Operations

Example: If ‘P’ denotes ‘×’, ‘Q’ denotes ‘+’, ‘R’ denotes ‘÷’, and ‘S’ denotes ‘−’, what is the value of 8 P 4 Q 6 R 3 S 2? Substituting gives 8 × 4 + 6 ÷ 3 − 2. Applying BODMAS, 6 ÷ 3 = 2 and 8 × 4 = 32, so the expression becomes 32 + 2 − 2. Answer: 32

Interchanging Signs and Numbers

Example: If the given interchanges are made in signs and numbers, which equation would be correct? Interchanges: signs ‘+’ and ‘−’, numbers ‘4’ and ‘8’. Replace every ‘+’ with ‘−’ and every ‘−’ with ‘+’, and every ‘4’ with ‘8’ and every ‘8’ with ‘4’ in each option, then evaluate each rewritten equation with BODMAS to see which one balances correctly.

Complex Coded Operations with Multiple Symbols

Example: If ‘<‘ means ‘minus’, ‘>’ means ‘plus’, ‘=’ means ‘multiplied by’, and ‘#’ means ‘divided by’, evaluate: 12 > 4 # 2 = 3 < 1 Substituting gives 12 + 4 ÷ 2 × 3 − 1. Applying BODMAS, 4 ÷ 2 = 2 and 2 × 3 = 6, so the expression becomes 12 + 6 − 1. Answer: 17

Important Tricks

Trick 1: Always Rewrite the Expression First

Solving directly without substitution invites errors — always rewrite the full expression after replacing every coded symbol.

Trick 2: Apply BODMAS After Substitution, Never Before

First apply the new symbol definitions, rewrite the expression, and only then use BODMAS to evaluate it.

Trick 3: Decode All Symbols Before Calculating

Before doing any arithmetic, make sure you’ve decoded what every symbol in the expression actually means.

Trick 4: Work Backwards from the Options

If the expression is long or complex, it’s often faster to test the given answer options directly.

Trick 5: Watch for Repeated Symbols

If a symbol appears more than once, the same mapping applies every time it appears — this consistency can save you time.

Trick 6: Apply BODMAS Strictly Once Operations Are Known

Once every symbol has been decoded into its real operation, follow BODMAS exactly — don’t skip steps.

Trick 7: Test Each Option Systematically

For insertion and interchange questions, work through each candidate combination one at a time using BODMAS rather than guessing.

Trick 8: Remember Operator Precedence

Multiplication and division always come before addition and subtraction unless brackets say otherwise.

Trick 9: Evaluate Left to Right for Equal-Priority Operations

When two operations share the same priority level, work through them strictly from left to right.

Trick 10: Avoid Confusing Similar-Looking Patterns

Be careful not to mix up + and × substitutions, or to accidentally apply the old meaning of a symbol out of habit.

Common Mistakes to Avoid

• Ignoring BODMAS after substitution — always apply BODMAS to the rewritten expression, not the original
• Assuming symbols keep their normal meaning — coded questions specifically reassign meanings; decode first
• Evaluating strictly left to right regardless of precedence — this violates the actual order of operations and gives wrong answers
• Forgetting that ‘=’ can also be a candidate sign — some insertion questions include equality as an option to test
• Overriding precedence by habit — doing addition before multiplication out of instinct is a common, avoidable error

Quick Solving Checklist

Before selecting your answer, use this checklist:

• Read the question carefully
• Identified the type of question (substitution, insertion, interchange, or coding)
• Decoded all symbols before starting any calculation
• Rewrote the expression after substitution
• Applied BODMAS strictly
• Tested each option systematically for insertion/interchange questions
• Verified the answer makes logical sense
• Avoided spending too much time on one question

Practice Questions

Conclusion

Mastering the Mathematical Signs and Operations Test is essential for the Nepal Army Officer Cadet Entrance Examination. Success requires systematic application of substitution rules and the BODMAS principle — not guesswork — across scenarios involving symbol substitution, missing signs, interchanging signs, and coded operations.

Follow this disciplined approach:

Read → Decode → Substitute → Apply BODMAS → Verify → Answer

Regular practice enhances pattern recognition, speed, logic, and accuracy. With the right approach and consistent practice, these questions can become some of the highest-scoring in the Numerical Reasoning section.

This resource is part of the IQ and Logical Reasoning preparation series for the Nepal Army Officer Cadet exam. For structured lessons, practice banks, and mock tests, access the Numerical Reasoning course on the Pratima Academy LMS.

This resource is part of the Officer Cadet Entrance Exam Preparation series, focusing on IQ and Logical Reasoning for the Nepal Army Officer Cadet Entrance Exam. For structured lessons, comprehensive practice banks, and mock tests, explore the Mathematical Signs and Operations Test course on the Pratima Academy LMS.