Question

Let $N=3^n+8^n+{10}^n$. The total number of ways of choosing $n$ from the set $\{1,2,3,....,201\}$, such that $N$ is divisible by $9$ is

• A. $99$
• B. $100$
• C. $101$
• D. $102$

Answer 1

The correct option is B $100$

We know that:
a) Any power of $3$ more than $1$ is divisible by $9$
b) $8^n+{10}^n$ is divisible by 9 when n is odd.
So, we can select any odd number more than $1$ for $n$.
This can be done in $\frac{201+1}{2}-1=101-1=100$ ways.
Hence, (B) is correct.