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39 votes
39 votes
Which is the largest three-digit number of the form 9k + 1, where k is any positive integer?​

User Syed Umar Ahmed
by
3.0k points

1 Answer

13 votes
13 votes

Answer:

991

Explanation:

We are looking for a number that is one more than a multiple of 9(denoted by the 9k) and is a three digit number. We can start by looking for 3-digit number divisible by 9 which are close to 1,000, since that is the next number larger than the largest three-digit number. We can tell that 999 is divisible by 9 because when divided it does not leave a remainder(you can also figure this out with divisibility tricks). We add one to get 1,000. This is not a three-digit number, so we need to look for a smaller multiple of 9. Subtracting 9 from 999, we get the next largest multiple of 9. We can add 1, and this time, the number, 991, is a three digit number, and the largest that can be in the form 9k + 1.

User Erick Boshoff
by
3.1k points
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