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Two alternative package $A$ and $B$ are available for processing a database having $10^{k}$ records. Package $A$ requires $0.0001 n^{2}$ time units and package $B$ requires $10n\log _{10}n$ 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. $5$
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This can be solved using substitution.

Substituting the value of 6 in k we get that A takes more time (10^8) than B (6 * 10^7). making B more preferable than A.
Answer:

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