the smallest value of kk for which package BB will be preferred over A
B\leqslantA
$10nlog_{10}(n) ≤ 0.0001n^{2}$
Given$ n = 10^{k }$records. Therefore,
$10*10^{k}log_{10}(10^{k}) ≤ 0.0001(10^{k})^{2}$
$10^{k+1}*k ≤ 0.0001 × 10^{2k}$
$k ≤ 10^{2k−k−1−4}$
$k ≤ 10^{k−5}->(1)$
if $k=12$ put in equation 1
$12\leqslant10^{12-5}$
$12\leqslant10^{7}$ IT IS true
if $k=10$ put in equation 1
$10\leqslant10^{10-5}$
$10\leqslant10^{5}$ IT IS true
if $k=6$ put in equation 1
$6\leqslant10^{6-5}$
$6\leqslant10$ it is true
if $k=5$ put in equation 1
$5\leqslant10^{5-5}$
$5\leqslant1$ it is not true
here K=12,10,6 satisfied but in question asking minimum value which satisfied equation 1
MINIMUM VALUE IS 6
Option C