Simplification Tricks
Simplification Tricks – Railway Exams
Must-Know Facts & Formulas
- BODMAS → Bracket, Of, Division, Multiplication, Addition, Subtraction
Mnemonic: Big Old Dogs Munch All Sausages - VBODMAS → Vinculum (bar), Bracket, Of, Division, Multiplication, Addition, Subtraction
- Fraction ↔ Percentage ↔ Decimal
½ = 50 % = 0.5 ⅓ ≈ 33.33 % ≈ 0.333 ¼ = 25 % = 0.25
⅕ = 20 % = 0.2 ⅛ = 12.5 % = 0.125 1/16 = 6.25 % = 0.0625 - Squares 1-30 – cram; Cubes 1-15 – cram
Last-digit trick: 24² → 4² last digit 6 → 576 ✔ - (a+b)² = a²+2ab+b² (a−b)² = a²−2ab+b² a²−b² = (a+b)(a−b)
- Sum of 1st n odd nos. = n²
- Sum of 1st n even nos. = n(n+1)
- Sum of 1st n natural nos. = n(n+1)/2
- Cross-multiplication for fractions: a/b ÷ c/d = a×d / b×c
- Decimal shift trick: 0.008×25 = 8×25×10⁻³ = 200×10⁻³ = 0.2
- Digit-sum check (mod 9) → quick option elimination
Memory Tables
| Fraction | % | Decimal | Square Root ≈ |
|---|---|---|---|
| 1/1.44 | 69.44 | 0.6944 | 0.833 |
| 1/2.25 | 44.44 | 0.4444 | 0.666 |
| 1/3.24 | 30.86 | 0.3086 | 0.555 |
| Powers of 2 | 2¹=2 | 2²=4 | 2³=8 | 2⁴=16 | 2⁵=32 | 2⁶=64 | 2⁷=128 | 2⁸=256 | 2⁹=512 | 2¹⁰=1024 |
|---|
Rapid-Fire MCQs
Click to expand 10 MCQs with answers
-
48÷6×(2+3)−7 = ?
A) 33 B) 40 C) 27 D) 35
Ans: A) 33 -
0.625 as fraction in lowest terms
A) 5/8 B) 3/5 C) 7/11 D) 2/3
Ans: A) 5/8 -
(0.2)³ = ?
A) 0.008 B) 0.08 C) 0.8 D) 0.0008
Ans: A) 0.008 -
12.5 % of 800 = ?
A) 100 B) 96 C) 104 D) 110
Ans: A) 100 -
√(2.56) = ?
A) 1.6 B) 1.4 C) 1.8 D) 1.2
Ans: A) 1.6 -
1/3 + 1/4 − 1/6 = ?
A) 5/12 B) 7/12 C) 1/2 D) 1/3
Ans: A) 5/12 -
(64)^½ × (27)^⅓ = ?
A) 12 B) 14 C) 16 D) 18
Ans: A) 12 -
333×999 = ?
A) 332667 B) 333667 C) 333000 D) 333333
Ans: A) 332667 -
7² + 24² = ?
A) 625 B) 600 C) 650 D) 725
Ans: A) 625 -
0.004×0.5÷0.002 = ?
A) 1 B) 0.1 C) 10 D) 100
Ans: A) 1
BETA
