Aptitude & Reasoning · A — Quantitative Aptitude
Speed Toolkit
Recognising a square, a cube, or a fraction on sight is the difference between solving a question and calculating one.
Use: Before every testPays off: Quant & DI sectionsMethod: Memorise, don't compute
Burn these tables into memory before your test. The fastest students never compute 12.5% of a number — they multiply by 1/8. Every fraction below is a shortcut hiding in plain sight; the percentage form is the slow road.
Squares (1–20)
| n | n² | n | n² |
|---|
| 1 | 1 | 11 | 121 |
| 2 | 4 | 12 | 144 |
| 3 | 9 | 13 | 169 |
| 4 | 16 | 14 | 196 |
| 5 | 25 | 15 | 225 |
| 6 | 36 | 16 | 256 |
| 7 | 49 | 17 | 289 |
| 8 | 64 | 18 | 324 |
| 9 | 81 | 19 | 361 |
| 10 | 100 | 20 | 400 |
Cubes (1–12)
Cubes to memorise
1³=1 2³=8 3³=27 4³=64 5³=125 6³=216
7³=343 8³=512 9³=729 10³=1000 11³=1331 12³=1728
Fraction ↔ percentage conversions
| Fraction | Percentage | Fraction | Percentage |
|---|
| 1/2 | 50% | 1/9 | 11.1% |
| 1/3 | 33.3% | 1/10 | 10% |
| 1/4 | 25% | 1/11 | 9.1% |
| 1/5 | 20% | 1/12 | 8.3% |
| 1/6 | 16.6% | 1/16 | 6.25% |
| 1/7 | 14.3% | 2/3 | 66.6% |
| 1/8 | 12.5% | 3/4 | 75% |
The Edge
The fastest students never compute 12.5% of a number — they multiply by 1/8. Every fraction above is a shortcut hiding in plain sight; the percentage form is the slow road.
Formula Vault — every shortcut in one place
Gathered for the night before the test: the formulae and shortcuts that recur across the whole workbook.
| Percentages & Commercial | Rule |
|---|
| Percentage change | (new − old) / old × 100 |
| Successive change a% then b% | a + b + ab/100 |
| Up x% then down x% | net (x²)/100 % decrease |
| Profit / Loss % | (SP − CP) / CP × 100 |
| Selling price | CP × (1 + Profit%/100) |
| Discount | SP = MP × (1 − Discount%/100) |
| Same SP, +x% & −x% | loss = (x/10)² % |
| Numbers, Ratio & Average | Rule |
|---|
| HCF × LCM | = product of the two numbers |
| Unit digit | powers cycle every 4 (use exponent mod 4) |
| Sum of first n naturals | n(n+1)/2 |
| Sum of first n odd numbers | n² |
| Chained ratio | scale the common term to a single value |
| Partnership profit | ratio of (capital × time) |
| Average | total / count |
| Alligation | cheaper:dearer = (dearer−mean):(mean−cheaper) |
| Time, Work, Speed & Interest | Rule |
|---|
| Distance | speed × time |
| km/h to m/s | multiply by 5/18 |
| Average speed (equal distance) | 2ab / (a + b) |
| Relative speed | add (opposite), subtract (same direction) |
| Combined work | 1 / (1/a + 1/b) |
| Men × Days | constant for the same job |
| Simple interest | P × R × T / 100 |
| Compound amount | P × (1 + R/100)^T |
| CI − SI (2 years) | P × (R/100)² |
| Counting, Mensuration & Clocks | Rule |
|---|
| Permutation | nPr = n!/(n−r)! |
| Combination | nCr = n!/(r!(n−r)!) |
| Repeated letters | divide n! by factorial of each repeat |
| Probability | favourable / total |
| Circle area / circumference | pi r² / 2 pi r |
| Cube / cuboid volume | s³ / l × b × h |
| Scaling | area × k², volume × k³ |
| Clock angle | |30H − 5.5M| degrees |
| Hands coincide / 12 h | 11 times (right angle 22 times) |
Takeaways
- Squares to 20 and cubes to 12 should be instant recall — they unlock roots and simplifications.
- Swap percentages for fractions. 12.5% → 1/8, 16.6% → 1/6 turn slow multiplication into cancellation.
- The Formula Vault is your night-before review. Recognising a formula on sight is the whole speed advantage.
Practice this — take a timed mock →
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