Abe challenges Bee to determine a
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.
Determine the value of N from the above statements and given clues.
Just looking at the problem on the board perceived that the last two digits must be 21+18k i.e 21,39,57,75 and 93.
Looking at the last digit mod 5 only 57 and 93 remained.
checking for hundreds:
457 and 993 both qualify
The statement "Abe makes the following statements, precisely one of which is false:" is a false statement.
my way - final answers
