posted by tyler on .
Find the mystery number
im a number between 300 and 400
im divisible by 3 and 4 . but not 9
my tens digit is a square number
the sum of the hundreds digit and the tens digit is a prime number.
find the mystery number
we know that the number is 3xx
the tens digit is either 1,4, or 9
4+3 =7 is a prime, so the number is 34x
x cannot be 2 or 5, because 342 and 345 are divisible by 9 (cast out nines)
The number must be even, because it is divisible by 4. So, it is either
340 344 346 348 (but 4 does not divide 346)
Only 348 is divisible by 3 (cast out threes)