⚡ Cheatsheet: General Aptitude
Quantitative Aptitude
| Topic | Formula |
|---|---|
| Series | AP Sum: \(\frac{n}{2}(2a + (n-1)d)\). GP Sum: \(a\frac{r^n-1}{r-1}\). |
| Sum of N | Natural: \(\frac{n(n+1)}{2}\). Squares: \(\frac{n(n+1)(2n+1)}{6}\). Cubes: \((\frac{n(n+1)}{2})^2\). |
| Time & Work | If A takes \(x\) days, B takes \(y\) days: Together \(\frac{xy}{x+y}\). |
| Speed | \(S = D/T\). Avg Speed (2 speeds): \(\frac{2xy}{x+y}\). |
| Interest | SI: \(P \times R \times T / 100\). CI: \(P(1 + R/100)^n - P\). |
| Logarithms | \(\log_a(mn) = \log_a m + \log_a n\). \(\log_a(x) = \frac{\ln x}{\ln a}\). |
Geometry / Mensuration
| Shape | Area | Circumference / Perimeter | Volume (if 3D) |
|---|---|---|---|
| Triangle | \(\frac{1}{2} b h\), \(\sqrt{s(s-a)(s-b)(s-c)}\) (Heron's) | \(a + b + c\) | — |
| Rectangle | \(l \times w\) | \(2(l + w)\) | — |
| Square | \(a^2\) | \(4a\) | — |
| Parallelogram | \(b \times h\) | \(2(a + b)\) | — |
| Trapezium | \(\frac{1}{2}(a + b)h\) | \(a + b + c + d\) | — |
| Circle | \(\pi r^2\) | \(2\pi r\) | — |
| Ellipse | \(\pi a b\) | \(\approx \pi [3(a+b) - \sqrt{(3a+b)(a+3b)}]\) | — |
| Cube | \(6a^2\) | — | \(a^3\) |
| Cuboid | \(2(lw + lh + wh)\) | — | \(lwh\) |
| Cylinder | \(2\pi r h\) (CSA), \(2\pi r(r+h)\) (TSA) | — | \(\pi r^2 h\) |
| Cone | \(\pi r l\) (CSA), \(\pi r (l + r)\) (TSA) | — | \(\frac{1}{3}\pi r^2 h\) |
| Sphere | \(4\pi r^2\) | — | \(\frac{4}{3}\pi r^3\) |
| Hemisphere | \(2\pi r^2\) (CSA), \(3\pi r^2\) (TSA) | — | \(\frac{2}{3}\pi r^3\) |
Abbreviations: \(a, b, c, d\) = sides, \(l\) = length, \(w\) = width, \(h\) = height, \(r\) = radius, \(s\) = semi-perimeter, \(l\) (in cone) = slant height, \(a, b\) (ellipse) = semi-axes, CSA = Curved Surface Area, TSA = Total Surface Area.
Combinatorics (Basics)
- Handshakes: In a room of \(n\) people, total handshakes = \(\binom{n}{2} = \frac{n(n-1)}{2}\).
- Letters: Arrangements of \(N\) letters with \(r\) repetitions = \(N!/r!\).
Clocks & Calendars
- Angle: \(|\frac{11}{2}M - 30H|\).
- Overlap: Hands coincide every \(65 \frac{5}{11}\) minutes.
- Odd Days: Year (1), Leap Year (2). Century (100y=5, 200y=3, 300y=1, 400y=0).