GATE | GATE CS 2010 | Question 11

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?

(A)

12

(B)

10

(C)

6

(D)

5

Answer: (C)

Explanation:

Since, 10nlog₁₀n ≤ 0.0001n²

Given n = 10^k records. 

Therefore, 

⟹10×(10^k)log₁₀10^k ≤ 0.0001(10^k)²

 ⟹10^k+1k ≤ 0.0001 × 10^2k

 ⟹k ≤ 10^{2k−k−1−4}

⟹k ≤ 10^k−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.

Quiz of this Question
Please comment below if you find anything wrong in the above post

My Personal Notes arrow_drop_up

Save