Question

The largest two digit number, which on divided by 6 results a remainder of 4 is .

Answer 1

The number which is divisible by $6$ is a multiple of $6.$

Let $x$ by any integer.
$6x$ is always divisible by $6.$

$\Rightarrow 6x+4$ will result in a remainder of $4.$

The largest two digit number $=99$

$\therefore 6x+4\le 99$
$\Rightarrow 6x\le 99-4$
$\Rightarrow x\le \frac{95}{6}$
$\Rightarrow x\le 15.8\overline{3}$

$\therefore$ The largest possible value of $x$ is $15.$

Hence, the required number is $15\times 6+4=90+4=94.$