Mathematical Operations questions in SSC MTS Reasoning are deceptively simple — they look like arithmetic, but the catch is that the symbols mean something different from what they usually mean.
Think of it this way: you walk into a kitchen where the chef has relabelled everything. The jar marked "Sugar" actually contains Salt. The jar marked "Salt" contains Cumin. If you follow the labels literally, your dish is a disaster. But if someone hands you the relabelling key before you cook, you can still make the dish correctly.
That is exactly what Mathematical Operations questions do. They hand you a substitution key like "'+' means '×', '×' means '÷'" and then ask you to evaluate an expression — or identify which of four expressions is correct after substitution.
There are three main question types you will encounter:
Type 1 — Symbol Substitution: A key is given (e.g., '+' means '÷', '−' means '×', etc.). You replace every symbol in the expression with its coded counterpart and then compute using real BODMAS rules.
Type 2 — Sign/Number Interchange: Two specific signs (or two numbers) are swapped, and you must find which swap makes the equation balance. Options are tested one by one.
Type 3 — Coded Symbol Patterns: Custom symbols like # and @ are used. Two example equations reveal what each symbol represents. You decode the pattern and apply it to find the answer.
The common thread across all three types: substitute first, compute later. Students who try to hold the substitution in their head while computing make errors. Students who write it down first and then calculate — get the right answer consistently.
One more thing worth noting: after substitution, BODMAS applies normally. The question paper does not tell you this explicitly, but it is always the case. So if your substituted expression has × and + in it, do the multiplication before the addition — always.
You are given a key like:
× means ++ means ×− means ÷÷ means −The question then shows an expression and asks which option is correct after substitution.
The method:
Step 1 — Write the original expression on your rough sheet.
Step 2 — Under each symbol, write its replacement using the key.
Step 3 — Rewrite the expression with replacements in place.
Step 4 — Apply BODMAS to the new expression.
Step 5 — Check if the result matches the RHS (right-hand side) of the equation.
For option-based questions, test the options one by one — but smartly. Start with the simplest-looking option first. If the numbers are small or the operations look clean, that option is a good candidate. Eliminate heavy decimal-producing options early.
Here, you are told that two signs are swapped (e.g., + and − are interchanged, AND × and ÷ are interchanged simultaneously). One question from SSC MTS 2024 had both pairs swapped at once.
The method:
Step 1 — List all operators in the expression.
Step 2 — Apply both swaps simultaneously (not one at a time — that's a trap).
Step 3 — Compute using BODMAS.
This type frequently appears in SSC MTS 2024 papers — you will see it in the PYQs below. The arithmetic involved is always clean (no ugly fractions), so if you get a messy decimal mid-calculation, you have likely made a substitution error. That is your signal to restart.
A close cousin of sign interchange: two numbers in the equation are swapped, and you must find which swap produces a correct equation. You are given 4 options, each naming a pair of numbers.
The approach: test each option by substituting the swapped pair into the original expression and checking if BODMAS gives the target value.
Do not randomly test all four. Look at the target value on the RHS first. If the target is large, the swap probably brings a large multiplier into a multiplication step. Use that to narrow down options before calculating.
Here, #, @, $ or similar symbols are used. Two example equations are given as a code-breaker.
The method:
Step 1 — Look at the first example: 3 # 9 @ 4 = 3. Observe the numbers — 3 + 9 = 12, 12 ÷ 4 = 3. That works. So # = + and @ = ÷.
Step 2 — Verify with the second example: 4 # 4 @ 4 = 2. Applying: (4 + 4) ÷ 4 = 8 ÷ 4 = 2. Confirmed.
Step 3 — Apply the decoded meaning to the target expression.
For pattern decoding, always verify with both given examples before applying. One example might accidentally work with a wrong assumption — two examples together almost always lock in the correct meaning uniquely.
After substitution, the order of operations is:
Brackets → Orders (powers) → Division → Multiplication → Addition → Subtraction
Division and Multiplication are evaluated left to right. Addition and Subtraction are evaluated left to right. Never add before you multiply just because addition comes first in the written expression.
When the key swaps 4 symbols, write the expression twice on rough paper: once original, once substituted. Never try to hold the swap in your head while computing. Students who skip this step take 90 seconds and often get it wrong. Students who write both lines take 60 seconds and get it right. The extra 5 seconds of writing saves 30 seconds of re-doing.
For # and @ style questions, form a small equation from the first example: does a op1 b op2 c = result suggest addition then division? Test it. Then immediately verify with the second example. If both hold, you have the pattern locked in 2 steps instead of guessing and re-guessing. Standard approach (guessing, re-testing): 5-6 steps. Lock method: 2 steps.
Before computing, estimate the RHS magnitude. If the target answer is large (say, 375), the expression after swap must produce a large number — meaning a multiplication of large numbers must survive the swap. Glance at the swapped expression: if 234 ÷ 6 gives 39, and 6 × 66 gives 396, the sum is already around 375 before subtracting 60. This rough estimate confirms you are on track after just one mental scan, saving a full computation if you were going down the wrong path.
When told + and − are interchanged AND × and ÷ are interchanged, do ALL swaps at once in one pass through the expression. A common error: swap +/− first, then swap ×/÷ in the already-modified expression. That produces a wrong intermediate expression. One pass, all swaps, then compute. This eliminates one complete re-reading of the expression — saves roughly 20 seconds per question.
For number-swap questions, count how many arithmetic steps each option changes. If swapping 2 and 6 affects a multiplication and a division step simultaneously, that option has the highest leverage and is the most likely answer (setters prefer options that meaningfully change the expression). Test the high-leverage option first. On average, this means you find the correct answer in 1-2 tests instead of 3-4 — saving roughly 40 seconds.
Use this decision tree in the exam hall:
Step 1 — Identify the question type.
Is a symbol key given? → Type 1 (Direct Substitution).
Are two signs/numbers being swapped? → Type 2 (Interchange).
Are custom symbols like #, @ used with example equations? → Type 3 (Pattern Decode).
Step 2 — Write the substituted expression on rough paper (never skip this).
Step 3 — Apply BODMAS strictly. If you get a decimal or fraction mid-way and the options are all integers, stop — you have made a substitution error. Re-check.
Step 4 — For option-based questions, test simpler-looking options first. Eliminate options where the LHS cannot possibly match the RHS in magnitude.
Step 5 — For Type 3, verify your decoded meaning against both given examples before computing the answer.
Expected time per question: 60-90 seconds. If you cross 90 seconds on any single question, mark your best guess and move on — these questions are meant to be fast.
Why this question: This is the classic direct substitution format. It tests whether you can apply a four-symbol key correctly and use BODMAS after substitution.
Solving path: The key gives: × → +, + → ×, − → ÷, ÷ → −. For option A: 44 + 4 - 2 = 88. Substitute: 44 × 4 ÷ 2. Apply BODMAS (left to right for same-priority operators): 44 × 4 = 176, then 176 ÷ 2 = 88. LHS = 88 = RHS. Correct.
Why this question: Pattern decoding with two custom symbols. Tests whether you can reverse-engineer the operation from examples.
Solving path: Example 1: 3 # 9 @ 4 = 3. Try (3 + 9) ÷ 4 = 12 ÷ 4 = 3. Works. So # = addition, @ = division. Example 2 verification: (4 + 4) ÷ 4 = 8 ÷ 4 = 2. Confirmed. Now: 6 # 4 @ 5 = (6 + 4) ÷ 5 = 10 ÷ 5 = 2. Answer: 2.
Why this question: Number interchange — tests whether you can identify which pair of swapped numbers balances the equation, a 2024 MTS pattern.
Solving path: Original: (12 ÷ 3) × 18 − 2 × 4 + 42 ÷ 6 = 69. Test option D (swap 2 and 6): (12 ÷ 3) × 18 − 6 × 4 + 42 ÷ 2. BODMAS: 4 × 18 = 72, 6 × 4 = 24, 42 ÷ 2 = 21. Result: 72 − 24 + 21 = 69. Matches. Answer: 2 and 6.
Why this question: Double sign interchange — both +/− and ×/÷ swap simultaneously. A high-frequency 2024 pattern.
Solving path: Original: 29 × 841 ÷ 87 + 37 − 59. After swapping ×↔÷ and +↔−: 29 ÷ 841 × 87 − 37 + 59. BODMAS left to right: 29 ÷ 841 = 29/841. Now (29/841) × 87 = 29 × 87 / 841 = 2523/841 = 3. Then 3 − 37 + 59 = 25. Answer: 25.
Why this question: Sign interchange where you must identify which pair of signs, if swapped, makes the equation true. Tests elimination under time pressure.
Solving path: Original: 8 − 4 + 144 ÷ 16 × 27 = 14. Test option B (swap × and −): rewrite as 8 × 4 + 144 ÷ 16 − 27. BODMAS: 144 ÷ 16 = 9, 8 × 4 = 32. Result: 32 + 9 − 27 = 14. Matches. Answer: × and −.
Applying swaps sequentially instead of simultaneously. When told both +/− and ×/÷ are interchanged, students often swap one pair, rewrite, then swap the second pair in the already-modified expression. This corrupts the expression. Do one clean pass with all swaps applied at once.
Forgetting BODMAS after substitution. After replacing symbols, students sometimes evaluate left to right without priority. If the substituted expression has × ÷ + −, multiplication and division must be done before addition and subtraction regardless of their position in the written expression.
Verifying pattern-decode against only one example. One example can be satisfied by multiple wrong interpretations. Always check both given examples. If your assumed operation satisfies only the first, it is a coincidence — not the pattern.
Treating ÷ and − as interchangeable in number-swap questions. Students sometimes accidentally apply a sign swap while testing a number swap — two different question types, two different procedures. Identify the type before you begin.
Not writing the substituted expression on rough paper. Trying to track a four-symbol key mentally while computing almost always causes at least one substitution error. The 5-second investment of writing the new expression down is non-negotiable.
Ignoring magnitude when choosing which option to test first. If the target RHS is small (say, 2 or 3) and one option produces obviously large numbers after substitution, eliminate that option before computing. Use your eyes before your pencil.