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.
(In reply to d3 answer
by Steve Herman)
3) If statement 3 is true, then (100y + 9z +3) mod 11 = 3 = (100y + 9z + 3) mod 5
Then 9z = 0 mod 5 and y = 2z mod 11. wrong
But 9z = 0 mod 5 implies z = 0 or 5, and this fails if y = 2z mod 11.
So statement 3 is false.
that's why you lost 993