Mathematical Operations
Subject: Mental Ability | Frequency: 1-2 questions per APPSC paper | Time: 30-45 sec/question
Introduction
Symbols or words replace mathematical operators. You must substitute correctly and solve using BODMAS. The trap is always in operator precedence, not the substitution itself.
Core Method
- Read the substitution rules carefully
- Replace ALL symbols with actual operators — rewrite the full expression
- Apply BODMAS strictly: Brackets → Orders → Division → Multiplication → Addition → Subtraction
- Solve step by step — do NOT evaluate left-to-right
- Key: Division and Multiplication have equal priority (L→R). Addition and Subtraction have equal priority (L→R).
Types
- Symbol substitution: +,−,×,÷ interchanged
- Statement substitution: "add means multiply" etc.
- Number and sign interchange: Both numbers AND operations swap
- Balancing equations: Choose correct signs to make equation true
- Relationship detection: 5 @ 3 = 34 → find the hidden operation (5²+3²=34)
Worked Examples — Easy
Q1: If + means ÷, − means ×, × means +, ÷ means −: 12 + 4 − 3 × 8 ÷ 2 Replace: 12 ÷ 4 × 3 + 8 − 2 = 3 × 3 + 8 − 2 = 9 + 8 − 2 = 15
Q2: If × means +, + means −, − means ÷, ÷ means ×: 6 × 4 ÷ 3 − 6 + 2 Replace: 6 + 4 × 3 ÷ 6 − 2 = 6 + 2 − 2 = 6
Worked Examples — Medium
Q3: If P=+, Q=−, R=×, S=÷: 18 S 6 R 4 P 5 Q 3 Replace: 18 ÷ 6 × 4 + 5 − 3 = 3 × 4 + 5 − 3 = 12 + 5 − 3 = 14
Q4: 5 * 3 * 8 * 4 = 19 → signs: 5 × 3 + 8 − 4 = 15 + 8 − 4 = 19 ✓ → ×, +, −
Q5: If 5 @ 3 = 34, 7 @ 2 = 53 → a² + b² → 9 @ 1 = 81 + 1 = 82
Worked Examples — Hard
Q6: 4 # (3 # 2) where A # B = A² − B → Inner: 9−2=7 → Outer: 16−7 = 9
Shortcuts & Tricks
| Shortcut | Details |
|---|---|
| Substitute first, BODMAS second | Never compute while substituting |
| Write it out fully | Rewrite before solving |
| For balancing: try ÷ first | Most restrictive operation |
| Equal priority = left to right | × and ÷ are L→R; + and − are L→R |
Common Mistakes
- Forgetting BODMAS after substitution — #1 error
- Double substitution — replacing already-replaced symbols
- Ignoring brackets
- Doing addition before multiplication (3+4×2 = 11, NOT 14)
- Sign confusion with negatives
Practice Questions
- If + means ×, × means −: 5 + 4 × 2 = 5×4 − 2 = 18
- If A=÷, B=×, C=+, D=−: 20 A 4 B 3 C 2 D 1 = 20÷4×3+2−1 = 5×3+2−1 = 16
- Which signs: 6 * 2 * 3 * 5 = 10? → 6 × 2 + 3 − 5 = 10 (×,+,−)
- If 3 # 4 = 25, 5 # 12 = 169 → a²+b² → 6 # 8 = 100
- P means +, Q means ×: 8 Q 3 P 4 = 8×3+4 = 28