Question

The greatest possible divisor of $3^{2n+3}$ - 24n - 27 for every n $ϵ$ N, which necessarily divides is:

• A. 64
• B. 24
• C. 96
• D. None of these

Answer 1

The correct option is D None of these

Let's check for n = 1
$3^{2\times 1+3}-24\times 1-27=3^5-51=192$
For n=2, we get $\Rightarrow 3^{2\times 2+3}-24\times 2-27=3^7-75=2112$
$2112=192\times 11$
For n=3, we get $\Rightarrow 3^{2\times 3+3}-24\times 3-27=3^9-72-27=19584$
$19584=192\times 102$
Similarly, we can see for $n=4,5,\dots$ so on & so forth. Hence, the greatest possible divisor is 192