Speed is everything in aptitude tests. The difference between solving 25 questions and 35 questions is often just mental math speed. These tricks won’t make us smarter — but they’ll make us faster. And in a timed exam, faster IS smarter.
Every trick here can be learned in 5 minutes and mastered with 10 minutes of practice. Let’s go.
Fraction-Percentage Equivalents
Memorize these. Seriously. This single table saves more time in exams than any other trick.
| Fraction | % | Fraction | % | Fraction | % |
| 1/2 | 50% | 1/6 | 16.67% | 1/12 | 8.33% |
| 1/3 | 33.33% | 1/7 | 14.28% | 1/15 | 6.67% |
| 1/4 | 25% | 1/8 | 12.5% | 1/20 | 5% |
| 1/5 | 20% | 1/9 | 11.11% | 1/25 | 4% |
How this helps: Instead of computing “What is 12.5% of 480?” we think “1/8 of 480 = 60.” Instead of “What is 33.33% of 270?” we think “1/3 of 270 = 90.” Instant answers.
Multiplying by 11
This is the coolest trick. To multiply any two-digit number by 11, we “split and add.”
Practice: 45 × 11 = 4(4+5)5 = 495. 63 × 11 = 6(6+3)3 = 693. 78 × 11 = 7(15)8 → carry → 858.
Multiplying by 5, 25, 50, 99, 101
These are faster than regular multiplication.
Worked examples:
48 × 5 = 48/2 × 10 = 24 × 10 = 240
36 × 25 = 36/4 × 100 = 9 × 100 = 900
68 × 50 = 68/2 × 100 = 34 × 100 = 3400
73 × 99 = 73 × 100 - 73 = 7300 - 73 = 7227
43 × 101 = 43 × 100 + 43 = 4300 + 43 = 4343 (just write the number twice!)
56 × 125 = 56/8 × 1000 = 7 × 1000 = 7000
Squaring Numbers Ending in 5
This is a fan favorite. To square any number ending in 5:
Why does this work? (n×10 + 5)² = n²×100 + 100n + 25 = n(n+1)×100 + 25. The “n(n+1)” part goes in front, and “25” goes at the end.
Squaring Numbers Near 50
For numbers close to 50, we use 50 as the base.
Method: For (50 ± d)², the answer is (25 ± d) followed by d².
47² = (50 - 3)². Take 25 - 3 = 22. Then d² = 9. Append with two digits: 2209.
53² = (50 + 3)². Take 25 + 3 = 28. Then d² = 9. Answer: 2809.
46² = (50 - 4)². Take 25 - 4 = 21. Then d² = 16. Answer: 2116.
56² = (50 + 6)². Take 25 + 6 = 31. Then d² = 36. Answer: 3136.
Check: 56² = 3136. ✓ (56 × 56 = 56 × 50 + 56 × 6 = 2800 + 336 = 3136)
Squaring Numbers Near 100
For numbers close to 100, we use the “base 100” method.
Method: For a number like 96 (which is 100 - 4):
- Deficit from 100 = 4
- First part: 96 - 4 = 92 (or equivalently, 100 - 2×4 = 92)
- Second part: 4² = 16
- Answer: 9216
96²: Deficit = 4. First part = 96 - 4 = 92. Second part = 16. Answer: 9216 ✓
97²: Deficit = 3. First part = 97 - 3 = 94. Second part = 09. Answer: 9409 ✓
103²: Surplus = 3. First part = 103 + 3 = 106. Second part = 09. Answer: 10609 ✓
108²: Surplus = 8. First part = 108 + 8 = 116. Second part = 64. Answer: 11664 ✓
Complementary Multiplication (Near 100)
This extends the squaring trick to multiplying two different numbers near 100.
96 × 97:
- Deficits: 4 and 3
- First part: 96 - 3 = 93 (or 97 - 4 = 93)
- Second part: 4 × 3 = 12
- Answer: 9312 ✓
104 × 107:
- Surpluses: 4 and 7
- First part: 104 + 7 = 111 (or 107 + 4 = 111)
- Second part: 4 × 7 = 28
- Answer: 11128 ✓
98 × 103:
- 98 has deficit 2, 103 has surplus 3
- First part: 98 + 3 = 101 (or 103 - 2 = 101)
- Second part: (-2) × 3 = -6. Since it’s negative: 101 - 1 = 100, and 100 - 6 = we get first part 100 and second part 94.
- Easier: just compute 98 × 103 = 98 × 100 + 98 × 3 = 9800 + 294 = 10094
The complementary method works cleanest when both numbers are on the same side of 100 (both below or both above).
Digit Sum (Casting Out 9s) for Verification
This is our checking tool. It tells us if our answer is WRONG (but can’t guarantee it’s right). Still incredibly useful for catching silly mistakes.
Example: Verify 347 × 56 = 19432
Digit sum of 347: 3+4+7 = 14 → 1+4 = 5 Digit sum of 56: 5+6 = 11 → 1+1 = 2 Product of digit sums: 5 × 2 = 10 → 1+0 = 1
Digit sum of 19432: 1+9+4+3+2 = 19 → 1+9 = 10 → 1+0 = 1
Both give 1. ✓ The answer is likely correct.
Example: Is 123 × 45 = 5525?
Digit sum of 123: 1+2+3 = 6 Digit sum of 45: 4+5 = 9 → treat as 0 (casting out 9) Product: 6 × 0 = 0
Digit sum of 5525: 5+5+2+5 = 17 → 1+7 = 8
0 ≠ 8. The answer is DEFINITELY wrong. (Correct answer: 123 × 45 = 5535)
Quick Squares and Cubes to Memorize
These come up so frequently that memorizing them saves us from computing every time.
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| n² | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 | 121 | 144 |
| n³ | 1 | 8 | 27 | 64 | 125 | 216 | 343 | 512 | 729 | 1000 | 1331 | 1728 |
A General Squaring Shortcut
For any number: a² = (a+b)(a-b) + b², where b is chosen to make the multiplication easy.
43²: Choose b=3, so 43² = (43+3)(43-3) + 9 = 46 × 40 + 9 = 1840 + 9 = 1849
67²: Choose b=3, so 67² = 70 × 64 + 9 = 4480 + 9 = 4489
38²: Choose b=2, so 38² = 40 × 36 + 4 = 1440 + 4 = 1444
The idea is to choose b so that one of (a+b) or (a-b) is a round number (multiple of 10).
Division Tricks
Dividing by 5: Multiply by 2, then divide by 10 (just move decimal).
- 345 ÷ 5 = 345 × 2 / 10 = 690/10 = 69
Dividing by 25: Multiply by 4, then divide by 100.
- 625 ÷ 25 = 625 × 4 / 100 = 2500/100 = 25
Dividing by 50: Multiply by 2, then divide by 100.
- 4350 ÷ 50 = 4350 × 2 / 100 = 8700/100 = 87
Practice Problems
Problem 1: Calculate mentally: 45 × 11, 76 × 5, 85², 97 × 103
Problem 2: Using digit sum, verify if 234 × 67 = 15678 is correct.
Problem 3: What is 16.67% of 540? (Use the fraction table.)
Answers
Problem 1:
- 45 × 11: 4(4+5)5 = 4(9)5 = 495
- 76 × 5: 76/2 × 10 = 38 × 10 = 380
- 85²: 8 × 9 = 72, append 25 → 7225
- 97 × 103: (100-3)(100+3) = 10000 - 9 = 9991 (difference of squares!)
Problem 2: Digit sum of 234: 2+3+4 = 9 → 0. Digit sum of 67: 6+7 = 13 → 4. Product: 0 × 4 = 0. Digit sum of 15678: 1+5+6+7+8 = 27 → 2+7 = 9 → 0. Match! ✓ (It’s likely correct. Actual: 234 × 67 = 15678 ✓)
Problem 3: 16.67% = 1/6. So 1/6 of 540 = 90