Question

Let m, n be two distinct integers chosen randomly from the set $\{0,1,2,....99\}$. Then the probability that $4^m+4^n+3$ is divisible by $5$ lies in the interval.

• A. $(0,0.25]$
• B. $(0.25,0.5]$
• C. $(0.5,0.75]$
• D. $(0.75,1)$

Answer 1

The correct option is A $(0,0.25]$

If $4^m+4^n+3$ is divisible by $5$, then

$n$ and $m$ must be the multiple of $2$, so the unit's place digit of $4^n$ and $4^m$ is $6$.

Thus, probability $=\frac{50}{100}\times \frac{50}{100}=0.25$