Question

Two alternative packages A and B are available for processing a database having 10^k records. Package A requires 0.0001n² time units and package B requires 10nlog₁₀n time units to process n records. What is the smallest value of k for which package B will be preferred over A? 
1. 12
2. 10
3. 6
4. 5

Answer 1

Correct Answer - Option 3 : 6

Package B will be preferred over A means A>B

A takes 0.0001n²=10^-4n²

B takes 10nlog₁₀n units of time for k=6

A takes 10^-4 x(10⁶)²=10⁸

B takes 10x10⁶log₁₀10⁶=6x10⁷

Hence the correct answer is 6.