Question

What is the remainder when $(1{)}^7+(71{)}^{77}+(771{)}^{777}+(7771{)}^{7777}+(77771{)}^{77777}+(777771{)}^{777777}$ is divided by 50?

• A. 46
• B. 6
• C. 56
• D. 5

Answer 1

The correct option is B

6

To find the remainder when an expression is divided by 50, we need to find the last two digits of that number.

Last two digits of the given expression are 1 + 91 + 91 + 91 + 91 + 91 = 456 (Ten's digit of powers of 71 follow a cycle of 10).
$\therefore \frac{456}{50},remainder=6.$