GATE | GATE CS 2010 | Question 11

Two alternative packages A and B are available for processing a database having 10k 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?
(A) 12
(B) 10
(C) 6
(D) 5


Answer: (C)

Explanation: Since,
10nlog10n ≤ 0.0001n2

Given n = 10k records. Therefore,

⟹10×(10k)log1010k ≤ 0.0001(10k)2
⟹10k+1k ≤ 0.0001 × 102k
⟹k ≤ 102k−k−1−4
⟹k ≤ 10k−5

Hence, value 5 does not satisfy but value 6 satisfies.
6 is the smallest value of k for which package B will be preferred over A.

Option (C) is correct.

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