Mathematical Operations

Mathematical Operations is a topic where the standard mathematical symbols (+, -, ×, ÷) are replaced by other symbols or the operations are interchanged. You have to decode the correct meaning and solve the equation. It is a quick and scoring topic in SSC CGL Reasoning.

Basic Concept:

In normal mathematics:

• + means addition
• - means subtraction
• × means multiplication
• ÷ means division

But in Mathematical Operations questions, these symbols are either:

1. Replaced by different symbols (like @ means +, # means -)
2. Interchanged with each other (like + means × and × means +)

Types of Mathematical Operations Questions in SSC CGL:

Type 1 - Symbol Substitution Standard symbols are replaced by new symbols. You have to decode and solve.

Example: 

If @ means +, # means -, $ means × and % means ÷ 

Find the value of: 12 @ 8 # 4 $ 2 % 1

Solution: 

Replace symbols: 12 + 8 - 4 × 2 ÷ 1 

Follow BODMAS: 12 + 8 - 8 ÷ 1 = 12 + 8 - 8 = 12

Answer: 12

Type 2 - Interchange of Signs Two mathematical signs are interchanged. You have to find the correct equation.

Example: 

If + and × are interchanged, find the value of: 

4 + 3 × 2

Solution: 

Replace + with × and × with +: 

4 × 3 + 2 = 12 + 2 = 14

Answer: 14

Type 3 - Which Equation is Correct? Four equations are given and you have to find which one is correct after applying the given substitution.

Example: 

If + means -, - means ×, × means ÷, ÷ means + 

Which equation is correct?

a) 4 + 2 - 3 = 10 

b) 8 ÷ 4 - 2 = 16 

c) 6 × 3 + 2 = 0 

d) 5 - 2 × 4 = 7

Solution - 

Check option b: 8 ÷ 4 - 2 = ? 

Replace: 8 + 4 × 2 = 8 + 8 = 16

Answer: b

Type 4 - Balancing the Equation An equation is given with a missing operator and you have to find which operator makes it correct after substitution.

Example: 

If + means ×, what should replace ? to make this correct: 

3 ? 4 + 2 = 14

Replace +: 3 ? 4 × 2 = 14

Try ?: if ? is + (original): 3 + 4 × 2 = 3 + 8 = 11 ✗ 

If ? is - (original): 3 - 4 × 2 = 3 - 8 = -5 ✗ 

If ? is × which means +: 3 + 4 × 2 = same as above 

Hmm - let us try: 3 ? 4 × 2 = 14 

3 × 4 + 2... wait: if ? means × (original) = 3 × 4 × 2 = 24 ✗ 

If ? is ÷ original: 3 ÷ 4 × 2... not integer

Best approach: Substitute all given symbols first, then try options.

BODMAS Rule - Very Important:

After substituting the symbols, always follow BODMAS to solve:

• B - Brackets first
• O - Orders (powers and roots)
• D - Division
• M - Multiplication
• A - Addition
• S - Subtraction

How to Solve Mathematical Operations Questions:

Step 1 - Read the given substitution/interchange carefully. 

Step 2 - Write down what each symbol means after substitution. 

Step 3 - Replace all symbols in the equation with their correct meaning. 

Step 4 - Apply BODMAS to solve the resulting equation. 

Step 5 - Match your answer with the options.

Common Mistakes to Avoid:

Mistake 1 - Not following BODMAS after substitution. Always apply BODMAS - do not solve left to right blindly.

Mistake 2 - Confusing which symbol replaces which. Write down the substitution clearly before solving.

Mistake 3 - In interchange questions, forgetting to replace BOTH symbols. If + and × are interchanged, change ALL + to × AND all × to + in the equation.

Mistake 4 - Not checking all options in Type 3 questions. Sometimes option a seems correct but checking properly shows it is wrong.

Quick Tricks:

Trick 1 - In Type 3 questions, start checking from option b or c - SSC papers often have correct answer in middle options.

Trick 2 - Always write the substitution as a table before solving.

Trick 3 - After substitution, circle the multiplication and division signs first as they are solved before addition and subtraction.

Trick 4 - In interchange questions, the equation value changes significantly - rough estimation can help eliminate wrong options quickly.

Important Tips:

• Always apply BODMAS after substitution - this is where most students make mistakes
• Write the substitution clearly - do not try to solve in your head
• 2 to 3 questions come from this topic in SSC CGL every year
• Practice at least 10 questions daily
• This is one of the easiest topics once BODMAS is clear