Mathematical Operations
Key Concepts
| # | Concept | Explanation |
|---|---|---|
| 1 | Interchange of Operators | The usual symbols (+, –, ×, ÷) are swapped with new ones; solve exactly as the new definitions say. |
| 2 | BODMAS Rule (Modified) | Brackets → New ‘Order’ → Division → Multiplication → Addition → Subtraction with new operator meanings. |
| 3 | Dummy Operations | A meaningless symbol (★, ∇, ©) is defined for one question only; never carry its meaning forward. |
| 4 | Balancing Equations | Find the pair of signs/numbers that make LHS = RHS after the given interchange. |
| 5 | Inequality Coding | <, >, =, ≤, ≥ are disguised as letters/shapes; decode first, then solve. |
| 6 | Reverse Operations | After every step, the result is reversed digit-wise (18 → 81) before feeding into next step. |
| 7 | Priority Swap | Inside brackets, priority of + and × is swapped; + is done before ×. |
15 Practice MCQs
1. If ‘+’ means ‘÷’, ‘–’ means ‘×’, ‘×’ means ‘+’, ‘÷’ means ‘–’, then 18 + 6 × 4 – 2 ÷ 5 = ?
**Answer:** 18 ÷ 6 + 4 × 2 – 5 = 3 + 8 – 5 = **6** **Shortcut:** Rewrite the whole expression with new symbols first, then apply BODMAS. **Tag:** Interchange of Operators2. If 3 ★ 5 = 16 and 7 ★ 2 = 23, then 4 ★ 9 = ?
**Answer:** Pattern is a★b = 2a + b → 2×4 + 9 = **17** **Shortcut:** Check linear relation 2a + b fits both samples. **Tag:** Dummy Operations3. Select the correct interchange: 8 _ 4 _ 2 = 4 (make equation true).
**Answer:** Replace first ‘_’ with ‘÷’, second with ‘×’ → 8 ÷ 4 × 2 = 4 → **A (÷, ×)** **Shortcut:** Plug options quickly; only one satisfies. **Tag:** Balancing Equations4. If P > Q means P is father of Q, P @ Q means P is sister of Q, then which means A is grandfather of B?
**Answer:** A > C @ B implies A is father of C and C is sister of B ⇒ A is grandfather. **Option C** **Tag:** Inequality Coding5. If 4 ∇ 3 = 25 and 5 ∇ 2 = 29, then 6 ∇ 4 = ?
**Answer:** ∇ = a² + b² → 36 + 16 = **52** **Shortcut:** Spot square sum pattern. **Tag:** Dummy Operations6. After interchanging ‘×’ and ‘+’ and 4 and 5, the value of 4 × 5 + 6 is
**Answer:** 5 + 4 × 6 = 5 + 24 = **29** **Shortcut:** Swap digits & operators first, then compute. **Tag:** Interchange of Operators7. If 9 © 7 = 63, 6 © 8 = 48, then 5 © 12 = ?
**Answer:** © means simple product → 5 × 12 = **60** **Tag:** Dummy Operations8. Which pair of signs fits 7 _ 5 _ 3 = 26?
**Answer:** 7 × 5 – 3 = 32 – 3 = 29 (no); 7 + 5 × 3 = 22 (no); 7 × 5 – 9 (invalid); 7 + 5 × 3 – 2 (extra); correct pair is **×, –** → 7 × 5 – 3 = 32 – 3 = 29 (still no); retry: 7 × (5 – 3) = 14; finally 7 + 5 × 3 = 22; none given; hence **None of these** **Answer:** **D (None of these)** **Shortcut:** Bracket trial saves time. **Tag:** Balancing Equations9. If ‘←’ means ‘+’, ‘→’ means ‘–’, ‘↑’ means ‘×’, ‘↓’ means ‘÷’, then 12 ↑ 3 ↓ 4 ← 5 → 2 = ?
**Answer:** 12 × 3 ÷ 4 + 5 – 2 = 9 + 5 – 2 = **12** **Tag:** Interchange of Operators10. If 2 ▲ 3 = 11, 3 ▲ 4 = 19, then 5 ▲ 6 = ?
**Answer:** ▲ = a² + a×b – b → 25 + 30 – 6 = **49** **Shortcut:** Quadratic fit in 5 s. **Tag:** Dummy Operations11. Interchange + & ÷ and 8 & 9. Evaluate: 9 + 8 ÷ 2
**Answer:** 8 ÷ 9 + 2 = 0.88 + 2 ≈ **2.88** (closest integer option **3**) **Tag:** Interchange of Operators12. If 6 π 4 = 10 and 7 π 5 = 12, then 9 π 3 = ?
**Answer:** π = a + b – 0 → 9 + 3 = **12** **Tag:** Dummy Operations13. Which sign makes 15 _ 3 _ 5 = 10 true?
**Answer:** 15 ÷ 3 + 5 = 5 + 5 = 10 → **÷, +** **Tag:** Balancing Equations14. If 5 ◆ 2 = 17 and 4 ◆ 3 = 13, then 6 ◆ 1 = ?
**Answer:** ◆ = 3a – b → 18 – 1 = **17** **Tag:** Dummy Operations15. If % means ‘square first number then add second’, then 3 % 4 = ?
**Answer:** 3² + 4 = 9 + 4 = **13** **Tag:** Dummy OperationsSpeed Tricks
| Situation | Shortcut | Example |
|---|---|---|
| 1 | Swap & Write | Before solving, rewrite entire expression with new symbols in one pass to avoid confusion. |
| 2 | Two-Point Formula | For dummy ops, plug two given pairs into linear model y = mx + c in 5 s. |
| 3 | Balancing by 10-sec plug | Try each option mentally; stop when LHS = RHS. |
| 4 | Digit Reversal Last | Leave reversal to the final numeric answer to cut intermediate mistakes. |
| 5 | BODMAS Tattoo | Never start calculation without marking brackets order with pencil dots (1-2-3). |
Quick Revision
| Point | Detail |
|---|---|
| 1 | Always decode symbols before numbers. |
| 2 | Brackets enjoy top priority even after interchange. |
| 3 | Check linear relation first for dummy ops (faster than quadratic). |
| 4 | If no option satisfies, mark “None of these” boldly. |
| 5 | Write new operator map on rough sheet: +→÷, –→× etc. |
| 6 | Reverse digit rule applies only when explicitly stated. |
| 7 | Inequality coding questions test blood/relational logic, not math. |
| 8 | Two-operator balancing: try ×,+ first; they give big numbers quickly. |
| 9 | Keep calculator finger off; RRB is calculation-light, logic-heavy. |
| 10 | Finish 15 Q in ≤ 10 min → target <40 s per Q using swap-&-write trick. |
BETA
