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.
The first clue yields a set of 90 numbers - half even, half odd. Looking at the clues, there is a conflict between clues 2 and three (i.e. division by 5 leaves different remainders), so the false statement must be one of these.
From clue 1, all even number can be eliminated. Dividing the odd ones by both 6 and 8 reduces the set to these five numbers:
121, 193, 457, 721, 793
After dividing these numbers by 5, 7, and 11, the only one with matching remainders is 457.
Posted by hoodat
on 2016-06-28 05:15:07