Review question

# What is this multiple of $13$'s final digit? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6962

## Solution

The four digit number $2652$ is such that any two consecutive digits from it make a multiple of $13$. Another number $N$ has this same property, is $100$ digits long and begins in a $9$. What is the last digit of $N$?

1. 2

2. 3

3. 6

4. 9

The two-digit multiples of $13$ are $13,\ 26,\ 39,\ 52,\ 65,\ 78,\ 91.$

$N$ starts with a $9$, so the first two digits must be $91$. Then the second and third must be $13$, and the third and fourth $39$.

Then the sequence repeats, so $N$ is $913913913...913$ up to the $99$th digit, with $9$ as its $100$th digit.

Hence the answer is (d).