CAT 2022 Slot 2 Paper

${\mathit{a}}_1+{\mathit{a}}_2+.....+{\mathit{a}}_{\mathrm{N}}=300\mathrm{N}$
$6{\mathit{a}}_1+{\mathit{a}}_2+.....+{\mathit{a}}_{\mathrm{N}}=400\mathrm{N}$
$5{\mathit{a}}_1=100\mathrm{N}$
${\mathit{a}}_1=20\mathrm{N}$
As the given sequence of numbers is non-decreasing sequence, $\mathrm{N}$ can take values from 2 to 15.
$\mathrm{N}$ is not equal to 1 , if $\mathrm{N}=1$, then average of $\mathrm{N}$ numbers is 300 wouldn't satisfy.
Therefore, $\mathrm{N}$ can take values from 2 to 15 , i.e. 14 values.