CAT 2005 — QA Question 8

R = $\frac{{30}^{65}-{29}^{65}}{{30}^{64}+{29}^{64}}$

∵ aⁿ – bⁿ = (a – b)(a^{n – 1} + a^{n – 2}b + a^{n – 3}b² + ... + b^{n – 1})

∴ R = $\frac{(30-29)[{30}^{64}+({30}^{63}\times 29)+...+{29}^{64}]}{{30}^{64}+{29}^{64}}$

∵ 30⁶⁴ + 30⁶³ × 29 + ... + 29⁶⁴ > 30⁶⁴ + 29⁶⁴

∴ R > 1

Hence, option (d).