Here are 8 advanced calculation hacks covering Cubes, Roots, and Approximation techniques essential for Banking Exams (PO/Clerk).
1. Cube Root in 2 Seconds
Look at the Last Digit
| Last Digit | Answer Ends With | Memorize |
|---|---|---|
| 1, 4, 5, 6, 9, 0 | SAME | Easy! |
| 2 | 8 | Flip Pair (2↔8) |
| 8 | 2 | Flip Pair (8↔2) |
| 3 | 7 | Flip Pair (3↔7) |
| 7 | 3 | Flip Pair (7↔3) |
Example: Find ∛12167
1. Last Digit 7 → Answer ends in 3.
2. Ignore last 3 digits (167). Left with 12.
3. Nearest Lower Cube: 2³=8, 3³=27. Take 2.
👉 Answer: 23
2. Cube of 2-Digit Number
Use the Ratio Method (a:b). Example for 12³ (Ratio 1:2).
Example: 12³
1 | 2 | 4 | 8 (Write terms)
+ 0 | 4 | 8 | 0 (Double middles)
-----------------
👉 1 | 7 | 2 | 8
3. Subtraction from 1000/10000
"All from 9, Last from 10"
Example: 1000 - 357
9-3=6, 9-5=4, 10-7=3 → 643
4. Comparing Fractions (Cross Multiply)
Example: 4/7 vs 5/8
4×8 = 32 (Left)
5×7 = 35 (Right)
35 > 32, so 5/8 is larger.
5. Percentage Split Method
Example: 51% of 640
50% = 320, 1% = 6.4
Total: 320 + 6.4 = 326.4
6. Non-Perfect Square Roots (Approximation)
Crucial for "Approximation" questions. Use formula: √A ± B ≈ √A ± B / (2√A)
Example: Find √10
1. Break into Nearest Square: 10 = 9 + 1
2. √9 = 3. Remaining part is 1.
3. Apply Formula: 3 + [1 / (2 × 3)]
4. 3 + 1/6 = 3 + 0.16 → 3.16
Example: Find √29
1. 29 = 25 + 4 (Nearest square is 25)
2. 5 + [4 / (2 × 5)] → 5 + 4/10
👉 Answer: 5.4
7. LCM Shortcut (Time & Work)
Don't draw tables. Check the largest number.
Example: LCM of 4, 6, 8
1. Largest is 8. Is it divisible by 4? Yes. By 6? No.
2. Multiply largest by 2 → 16. Divisible by 6? No.
3. Multiply largest by 3 → 24. Divisible by 6? Yes.
👉 LCM is 24.
8. Multiply by 1.5, 2.5, 3.5
Common in Number Series. Rule: Number × 1 + Half of Number.
Example: 18 × 1.5
1. 18 × 1 = 18
2. Half of 18 = 9
3. Add: 18 + 9 = 27
Example: 12 × 2.5
1. Double of 12 = 24
2. Half of 12 = 6
3. Add: 24 + 6 = 30