Arithmetic and Algebra
This domain tests the algebraic machinery behind business problems: HCF and LCM, indices and surds, logarithms, linear and quadratic equations, arithmetic and geometric progressions, and sets with Venn diagrams. Expect a mix of one-line formula applications and short word problems where the algebra must first be set up from the data.
Core rules
- Indices: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1.
- Logarithms: log(mn) = log m + log n; log(m/n) = log m − log n; log mᵏ = k log m; log_b a = log a / log b.
- Quadratic ax² + bx + c = 0: roots = [−b ± √(b² − 4ac)]/2a; sum = −b/a, product = c/a.
- GP: nth term arⁿ⁻¹; sum = a(rⁿ − 1)/(r − 1) for r > 1, a(1 − rⁿ)/(1 − r) for r < 1.
- Sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
Worked example
A firm's profit in ₹’000 is p(x) = −x² + 12x − 20, where x is units sold in hundreds. Break-even means p(x) = 0, so x² − 12x + 20 = 0. Here a = 1, b = −12, c = 20, discriminant = 144 − 80 = 64, so x = (12 ± 8)/2 = 10 or 2. The firm breaks even at 200 units and again at 1,000 units, and earns positive profit between them.
Traps
Discarding the negative root without checking whether it is meaningful; forgetting to test roots in the original equation when squaring; mixing the GP sum formulas; and double-counting the intersection in Venn problems.