SOF IMO · Bite-size lessons

Mathematical Operations

About 7 min · Logical Reasoning · English

Time worked out from the lesson's 483 words at 150 words a minute, plus a minute for each question.

Mathematical Operations is a logical reasoning topic in the SOF IMO. Questions test whether you can follow unusual rules, substitute symbols correctly and apply BODMAS when operators are shuffled. Unlike standard arithmetic, the challenge lies in changing how you think about familiar symbols — a "+" might mean "×" and a "÷" might mean "−". Once you learn the given rule, you apply it step by step, carefully avoiding the trap of reverting to normal meanings.

Key ideas

• Symbol substitution: Familiar operators (+, −, ×, ÷) are redefined. Always use the new meanings given in the question; ignore what the symbol normally means.
• BODMAS priority: Even when symbols are swapped, BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) usually still applies unless the question explicitly says otherwise. Apply the substituted operation in BODMAS order.
• Operator-based logic problems: Some questions define new symbols (e.g. a @ b = 2a + b). You must compute by plugging values into the defined formula.
• "Which statement is correct?" questions: Test each answer choice by substituting and computing. Only one will satisfy the equation.
• Nested operations: When expressions have multiple operations, work inside-out (brackets first) and left-to-right for equal-precedence operations after substitution.

Watch out for

• Reverting to normal operations by habit: Students write down the substitution rule but halfway through the calculation forget and use + to mean addition again. Fix: After substituting, rewrite the entire expression with standard operators before calculating.
• Ignoring BODMAS after substitution: You substitute symbols correctly but then compute left to right without respecting multiplication/division priority. Fix: After substitution, treat the new expression as a normal BODMAS problem. Underline or bracket the multiplication/division parts first.
• Misreading the operator mapping: Confusing "× means ÷" with "÷ means ×". The wording is "old symbol means new operation". Fix: Write a clear mini-table (e.g. + → ×, − → ÷, × → +, ÷ → −) on scrap paper before starting.

Quick reference

• Symbol swap: Always use the new meaning given; never the old one.
• BODMAS still rules: After substitution, apply standard order of operations.
• Custom operation a @ b: Plug values into the given formula; treat @ as a recipe.
• Verification questions: Test each answer choice by substituting and computing LHS vs RHS.
• Write it down: Rewrite the expression with substituted operations before calculating — it prevents confusion.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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