Abe challenges Bee to determine a 3-digit positive integer
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.
Determine the value of N from the above statements and given clues.
2 and 3 cannot both be true. Therefore, 1 must be true. That means that N=1 mod 24. If 2 is true, then N=2 mod 35. Therefore, N=457 mod 840. Since N is a 3-digit number, N=457. If 3 is true, then N=3 mod 55. Therefore, N=553 mod 840. Since N is a 3-digit number, N=553.
We know that N=457 or 553. Now, 57=3 mod 9 and 53=8 mod 9. Therefore, N=457.
Posted by Math Man
on 2016-02-16 17:46:06