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
-
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 Operators -
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 Operations -
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 Equations -
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 Coding -
If 4 ∇ 3 = 25 and 5 ∇ 2 = 29, then 6 ∇ 4 = ? Answer: ∇ = a² + b² → 36 + 16 = 52
Shortcut: Spot square sum pattern.
Tag: Dummy Operations -
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 Operators -
If 9 © 7 = 63, 6 © 8 = 48, then 5 © 12 = ? Answer: © means simple product → 5 × 12 = 60
Tag: Dummy Operations -
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 Equations -
If ‘←’ means ‘+’, ‘→’ means ‘–’, ‘↑’ means ‘×’, ‘↓’ means ‘÷’, then 12 ↑ 3 ↓ 4 ← 5 → 2 = ? Answer: 12 × 3 ÷ 4 + 5 – 2 = 9 + 5 – 2 = 12
Tag: Interchange of Operators -
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 Operations -
Interchange + & ÷ and 8 & 9. Evaluate: 9 + 8 ÷ 2 Answer: 8 ÷ 9 + 2 = 0.88 + 2 ≈ 2.88 (closest integer option 3)
Tag: Interchange of Operators -
If 6 π 4 = 10 and 7 π 5 = 12, then 9 π 3 = ? Answer: π = a + b – 0 → 9 + 3 = 12
Tag: Dummy Operations -
Which sign makes 15 _ 3 _ 5 = 10 true? Answer: 15 ÷ 3 + 5 = 5 + 5 = 10 → ÷, +
Tag: Balancing Equations -
If 5 ◆ 2 = 17 and 4 ◆ 3 = 13, then 6 ◆ 1 = ? Answer: ◆ = 3a – b → 18 – 1 = 17
Tag: Dummy Operations -
If % means ‘square first number then add second’, then 3 % 4 = ? Answer: 3² + 4 = 9 + 4 = 13
Tag: Dummy Operations
Speed 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
