What the exam asks
Simplification is the biggest scoring block of SBI Clerk Prelims: usually 7 to 10 questions of the form expression = ? or ? sits inside the expression. Each one should take 15 to 25 seconds. Speed comes from three things: the order of operations, memorised values, and quick answer checks.
Order of operations (BODMAS / VBODMAS)
- Vinculum (bar) first, then Brackets in the order ( ), { }, [ ]
- Of (e.g. 2/5 of 80) is treated like multiplication but done before division
- Division and Multiplication, left to right
- Addition and Subtraction, left to right
Trap: 48 / 4 x 3 = 36 (left to right), not 4. Only "of" jumps ahead of division.
Algebraic identities that save time
| Identity | Use |
|---|---|
| (a + b)² = a² + 2ab + b² | 103² = 10,000 + 600 + 9 = 10,609 |
| (a - b)² = a² - 2ab + b² | 97² = 10,000 - 600 + 9 = 9,409 |
| a² - b² = (a + b)(a - b) | 47² - 43² = 90 x 4 = 360 |
| a³ - b³ = (a - b)(a² + ab + b²) | difference of cubes |
| a³ + b³ = (a + b)(a² - ab + b²) | sum of cubes |
Squares 1 to 30 (memorise)
| n | n² | n | n² | n | n² | n | n² | n | n² |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 4 | 3 | 9 | 4 | 16 | 5 | 25 |
| 6 | 36 | 7 | 49 | 8 | 64 | 9 | 81 | 10 | 100 |
| 11 | 121 | 12 | 144 | 13 | 169 | 14 | 196 | 15 | 225 |
| 16 | 256 | 17 | 289 | 18 | 324 | 19 | 361 | 20 | 400 |
| 21 | 441 | 22 | 484 | 23 | 529 | 24 | 576 | 25 | 625 |
| 26 | 676 | 27 | 729 | 28 | 784 | 29 | 841 | 30 | 900 |
Cubes 1 to 20 (memorise)
| n | n³ | n | n³ | n | n³ | n | n³ |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 8 | 3 | 27 | 4 | 64 |
| 5 | 125 | 6 | 216 | 7 | 343 | 8 | 512 |
| 9 | 729 | 10 | 1,000 | 11 | 1,331 | 12 | 1,728 |
| 13 | 2,197 | 14 | 2,744 | 15 | 3,375 | 16 | 4,096 |
| 17 | 4,913 | 18 | 5,832 | 19 | 6,859 | 20 | 8,000 |
Topper shortcuts
- Digit-sum (casting out nines) check: reduce each number to a single digit, do the same operation, and compare with the option's digit sum. Example: 238 x 47. Digit sums 4 and 2, product 8. Option 11,186 has digit sum 1+1+1+8+6 = 17 = 8. Correct. This kills wrong options in 3 seconds.
- Unit-digit check: 346 x 27 must end in 2 (6 x 7 = 42). Eliminate options that do not end in 2.
- Multiply by 5: multiply by 10 and halve. 864 x 5 = 4,320.
- Multiply by 25: multiply by 100 and divide by 4. 72 x 25 = 1,800.
- Multiply by 11: write the outer digits and put their sum in the middle. 53 x 11 = 583; 78 x 11 = 858 (7, 15, 8 with carry).
- Squares of numbers ending in 5: n5² = n(n + 1) followed by 25. 65² = 6 x 7 = 42, so 4,225.
- Percent as fraction: 12.5% = 1/8, 37.5% = 3/8, 16.67% = 1/6, 66.67% = 2/3. Convert first, then cancel.
- When ? is in the middle: move everything else to the other side with the opposite operation. Do not expand the whole expression.
Worked example
45% of 640 + 3/8 of 1,248 - ? = 250
45% of 640 = 288. 3/8 of 1,248 = 156 x 3 = 468. So 288 + 468 - ? = 250, giving 756 - ? = 250 and ? = 506.
Worked example 2
sqrt(784) x 3 + 15² - 20% of 350 = ?
sqrt(784) = 28, so 84. 15² = 225. 20% of 350 = 70. Total = 84 + 225 - 70 = 239.
Common traps
- Reading "of" late, or doing division before a bracket is closed.
- Mixing up sqrt and cube root of the same number (sqrt 729 = 27, cube root 729 = 9).
- Sign errors when ? is subtracted: 756 - ? = 250 means ? = 756 - 250, not 756 + 250.
Time target: 20 seconds each. If a question needs more than 40 seconds, mark it and move on; come back only if time remains.