An algorithm takes $0\mathrm{.}5$ ms for input size $100.$ How large a problem can be solved in $1$ min if

the running time is one of the following $($assume low$-$order terms are negligible$)?$

$($a$)$ linear

$($b$)O(NlogN)$

$($c$)$ quadratic

$($d$)$ cubic

Select one or more:

a$.($a$)$ input size $120,000$

b$.($c$)120,{000}^{\frac{1}{2}}$ times as large a problem, or input size $34,641$

c$.($d$)120,{000}^{\frac{1}{3}}$ times as large a problem, or input size $4,933$

d$.($b$)$ N times $($such that NlogN$=120,000)$ as large a problem, or input size $100*N$

e$.($c$)120,{000}^2$ times as large a problem

f$.($d$)120,{000}^3$ times as large a problem

g$.($a$)120,000$ times as large a problem $(1$min$=60,000ms),$ or input size $12,000,000.$