Question

If $4^{25}+5^{15}$ is divided by $10$, then the remainder is :

• A. $4$
• B. $5$
• C. $9$
• D. $0$

Answer 1

The correct option is C

$9$

Step 1: Finding the value of $4^{25}$:

Given: $4^{25}+5^{15}$is divided by $10$.

Taking a natural number in the power of four will always gives $4$ or $6$ at its ones place. If the power is odd, digit at ones place will be $4$ and it will be $6$, if the power is even.

So, here the digit at ones place of $4^{25}$ is $4$ so, $4^{25}=10d+4$

Step 2: Finding the value of $5^{15}$:

Any power on five will always make a number having $5$ at its ones place.

So, $5^{15}=10c+5$.

Step 3: Finding the remainder on dividing $4^{25}+5^{15}$ by $10$:

$4^{25}+5^{15}=10d+4+10c+5=10d+10c+9$.

Thus we can write the sum as $4^{25}+5^{15}=10(d+c)+9$, where $d+c=apositiveinteger$

Then, $\frac{4^{25}+5^{15}}{10}=\frac{10(d+c)}{10}+\frac{9}{10}$.

Therefore, the remainder on dividing $4^{25}+5^{15}$ by $10$ is $9$.

Hence, the correct answer is option (C).