*3-digit positive integer*N.

It is known that the

*number formed by the last two digits of N*when divided by 9, yields a remainder of 3.

Abe makes the following statements, precisely one of which is false:

- N divided separately by each of 2, 4, 6, and 8 yields a remainder of 1.
- N divided separately by each of 5 and 7 yields a remainder of 2.
- N divided separately by each of 5 and 11 yields a remainder of 3.