Question

Let \( n \) be a 5-digit number and let \( q \) and \( r \) be the quotient and remainder respectively, when \( n \) is divided by 100. For how many values of \( n \) is \( q + r \) divisible by 11?

• A. 8180
• B. 8181
• C. 8182
• D. 9000

Hint:

When solving divisibility problems, use the properties of division and remainders to set up equations that help find the number of solutions.

Answer 1

The Correct Option is B

To solve for the number of values of \( n \) where \( q + r \) is divisible by 11, you analyze the behavior of the division of \( n \) by 100 and count the instances when \( q + r \) is divisible by 11. The correct answer is 8181.