Chapter 10 of 14

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SSC CGL General Intelligence & Reasoning★ Tier 1: 1–2 Q (2–4 marks) · Tier 2: 1–2 Q (3–6 marks)

Mathematical Operations

1–2 questions per tier where symbols are swapped for arithmetic signs and you compute under BODMAS, or where you pick the sign interchange that balances an equation. The whole skill is: substitute exactly as told, then obey the order of operations — never the visual sign on the page.

⏱ 13 min readEasy difficulty✓ Free · exam-pattern aligned

Timed practiceMCQs from this chapter with instant scoring

FlashcardsFormulas & traps on spaced repetition

SSC CGL PYQsSolved previous-year questions

By the end of this chapter you'll be able to…

1Substitute swapped symbols correctly before evaluating an expression
2Apply BODMAS to the substituted expression, respecting ÷/× precedence
3Solve letter-coded operation problems fluently
4Find the sign interchange that balances a given equation
5Identify the number interchange that corrects an equation

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Why this chapter matters in SSC CGL

Mathematical operations are quick, near-guaranteed marks that test one disciplined habit — substitute the symbols, then obey BODMAS. Candidates lose them only by computing in the order the visible signs suggest instead of the substituted ones. The BODMAS discipline reinforced here also carries into simplification and every arithmetic topic, so the practice compounds.

Before you start — revise these

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Simplification, Surds and Indices

The BODMAS order applied here is the same as in arithmetic simplification.

Mathematical Operations — SSC CGL Reasoning

These questions disguise ordinary arithmetic behind swapped symbols: "+ means ×, ÷ means −", and so on. The rule is simple but strict — substitute every symbol first, then apply BODMAS. The one habit that guarantees the mark is refusing to trust the sign you see on the page; only the substituted meaning counts, and division/multiplication still come before addition/subtraction.

1. What SSC actually asks

Tier 1: 1–2 Q · Tier 2: 1–2 Q. Types: symbol substitution (compute an expression after replacing signs), letter-coded operations (P means ÷, Q means ×…), sign interchange to make an equation true, and "which combination of signs balances the equation" or "interchange these two numbers to correct it".

2. Symbol substitution — the core method

Write the substituted expression, replacing each given symbol with its real operation.
Apply BODMAS to the substituted expression — brackets, then ÷ and × (left to right), then + and −.

If '+' means '−', '−' means '×', '×' means '÷', '÷' means '+', evaluate $18 \times 6 \div 3 - 2 + 4$ . Substitute: $18 \div 6 + 3 \times 2 - 4$ . BODMAS: $3 + 6 - 4 =$ 5.

The trap is doing the arithmetic in the order the original signs suggest — always re-read the substituted line.

3. Letter-coded operations

Same idea, letters instead of new symbols:

If P = ÷, Q = ×, R = +, S = −, then $18 Q 12 P 4 R 5 S 6$ becomes $18 \times 12 \div 4 + 5 - 6$ . Left to right for ×/÷: $18 \times 12 = 216$ , $\div 4 = 54$ ; then $54 + 5 - 6 =$ 53.

4. Sign interchange to balance

To make a false equation true, find the swap that fixes it. Test each candidate quickly:

Make $5 + 3 - 2 = 4$ true. Currently it equals 6. Interchange + and −: $5 - 3 + 2 = 4$ ✓.
"Which signs make $6_3_2_4 = 8$ ?" Try $6 \div 3 \times 2 + 4 = 2 \times 2 + 4 =$ 8 ✓.

Plug in the option and compute under BODMAS; the right one lands on the target.

5. Interchange numbers to correct

Sometimes you swap two numbers, not signs:

Make $4 \times 6 + 2 = 16$ correct. As written it's 26. Interchanging 2 and 4 gives $2 \times 6 + 4 = 16$ ✓.

Scan for the swap that shrinks or grows the value to the target — usually only one pair works.

6. Solved PYQ-style examples

Q1. If '+' means '−', '−' means '×', '×' means '÷', '÷' means '+', find $15 - 3 + 10 \times 5 \div 5$ . Solution. Substitute: $15 \times 3 - 10 \div 5 + 5 = 45 - 2 + 5 =$ 48.

Q2. If A = +, B = −, C = ×, D = ÷, then $8 C 2 A 4 B 6 =$ ? Solution. $8 \times 2 + 4 - 6 = 16 + 4 - 6 =$ 14.

Q3. Which two signs, interchanged, make $5 + 3 - 2 = 4$ true? Solution. Swap + and −: $5 - 3 + 2 =$ 4 ✓.

Q4. If '>' means +, '<' means −, '=' means ×, find $5 > 2 = 3 < 4$ . Solution. $5 + 2 \times 3 - 4 = 5 + 6 - 4 =$ 7.

Q5. If '−' and '÷' are interchanged and '+' and '×' are interchanged, evaluate $20 - 4 \div 5 + 2 \times 10$ . Solution. $20 \div 4 - 5 \times 2 + 10 = 5 - 10 + 10 =$ 5.

7. Exam protocol

Rewrite the whole expression with substituted operations before computing anything.
Apply BODMAS to the substituted line; ÷ and × outrank + and −.
For ÷ and × together, work left to right.
Balancing an equation? Plug each option in and compute — the target picks the answer.
Number-interchange: find the single pair that moves the value onto the target.

Key formulas & results

Everything to memorise for the exam hall, in one card. Screenshot this for revision.

Method

substitute symbols \to apply BODMAS

Never compute in the order of the visible signs.

Operation precedence

Brackets \to \div, \times (left to right) \to +, -

Division and multiplication outrank addition and subtraction.

Balance an equation

test each sign combination under BODMAS until it equals the target

Plug and check — the correct swap hits the required value.

Number interchange

find the single pair whose swap moves the value to the target

Usually exactly one pair works.

SSC CGL test series

Ready to be tested on this?

Mathematical Operations shows up in every SSC CGL paper — sit a timed one and find out where you actually stand.

1–2Qs in Tier 1

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Full SSC CGL mocks, real clock
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Traps SSC CGL sets — and how to dodge them

These are the exact option-traps and misreads that cost marks under negative marking.

WATCH OUT

✗ Computing in the order suggested by the printed signs.

✓ First rewrite the whole expression with the substituted operations, then evaluate. The visible '+' may actually mean '×'.

WATCH OUT

✗ Ignoring BODMAS after substitution.

✓ The substituted line still follows order of operations. In 18 ÷ 6 + 3 × 2 − 4, do 18÷6 and 3×2 first, giving 3 + 6 − 4 = 5.

WATCH OUT

✗ Doing ÷ and × in the wrong order when both appear.

✓ They share a rank — work left to right. 18 × 12 ÷ 4 = (18 × 12) ÷ 4 = 54, not 18 × (12 ÷ 4) unless that's the left-to-right order.

WATCH OUT

✗ Guessing the balancing swap instead of testing.

✓ Substitute each option into the equation and compute under BODMAS. Only the correct interchange lands on the stated result.

WATCH OUT

✗ Swapping the wrong numbers in a correction problem.

✓ Estimate whether the value needs to rise or fall, then pick the pair whose interchange moves it that way. Interchanging 2 and 4 turns 4×6+2 = 26 into 2×6+4 = 16.

Exam-pattern practice

PYQ-style questions with full solutions. Work through them as a readiness check — mark yourself honestly and get your gap report at the end.

Readiness check

Are you exam-ready for Mathematical Operations?

9 problems from this chapter. Try each one, reveal the worked solution, mark yourself honestly — get your gap report at the end.

9 questions~6 min

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Substitute every symbol first, then apply BODMAS
•Never compute in the order the printed signs suggest
•÷ and × outrank + and −; among themselves, go left to right
•Letter-coded operations work exactly like symbol swaps
•Balance an equation by testing each option under BODMAS
•Number-interchange: pick the single pair that hits the target
•Re-read the substituted line before doing any arithmetic
•Estimate whether the value must rise or fall to choose a swap

SSC CGL question blueprint

How this topic is asked, tier by tier — so you can prep to the pattern.

Typical weightage: 8

Question style	Marks each	Typical count	What it tests
Tier 1 — symbol/letter substitution	2–4 (1–2 Q × 2 marks)
Tier 2 — sign/number interchange and balancing	3–6 (1–2 Q × 3 marks)

Prep strategy

Drill 15 substitution problems, always writing the substituted line first
Practise balancing and interchange questions to speed up option testing
Reinforce BODMAS with mixed ÷/× expressions
Timed set: 10 questions in 7 minutes

Exam-hall strategy

Battle-tested tips from mentors and toppers for this topic under the sectional clock.

Rewrite the full expression with substituted operations before computing.
Apply BODMAS to the substituted line; ÷/× before +/−.
Handle consecutive ÷ and × left to right.
For balancing questions, test each option to the target value.
For number swaps, pick the single pair that lands on the target.

Beyond the exam

Where this skill shows up in the job you're competing for — and in life.

Formula debugging

Tracing how an expression evaluates under strict operator precedence is exactly what fixing a spreadsheet or code formula requires.

Cipher-style puzzles

Substituting one set of symbols for another and re-evaluating is a lightweight version of decoding and encoding.

Careful reading

Following redefined rules precisely — not what a symbol usually means — is a transferable discipline for contracts and instructions.

Where else this topic is tested

Prepare once, score in every exam that asks it.

SSC CHSL1–2 Q — symbol substitution

SSC MTS1–2 Q — sign interchange

IBPS / RRB Clerk1 Q — coded operations

RRB NTPC1–2 Q — balancing equations

📝 My notes

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Questions aspirants ask

Pulled from the Q&A community and mentor sessions.

Usually 1–2 per tier. They are fast marks once the substitute-then-BODMAS habit is fixed.

Computing in the order the visible signs imply. Always rewrite the expression with the real operations first, then evaluate that new line under BODMAS.

Yes — completely. The substitution changes which operation each symbol means, but the order of operations on the resulting expression is unchanged.

Plug each option's signs into the blanks and compute under BODMAS. The combination that equals the stated result is the answer; usually only one does.

Some questions ask you to swap two numbers to correct an equation. Judge whether the value needs to increase or decrease, then find the pair whose swap achieves it.

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Mathematical Operations

By the end of this chapter you'll be able to…

Before you start — revise these

Mathematical Operations — SSC CGL Reasoning

1. What SSC actually asks

2. Symbol substitution — the core method

3. Letter-coded operations

4. Sign interchange to balance

5. Interchange numbers to correct

6. Solved PYQ-style examples

7. Exam protocol

Key formulas & results

Traps SSC CGL sets — and how to dodge them

Exam-pattern practice

Are you exam-ready for Mathematical Operations?

5-minute revision

SSC CGL question blueprint

Exam-hall strategy

Beyond the exam