Question 565182
Modular arithmetic solution:


From (2) we know that the number is even, and it is congruent to -4 mod 6 (which is 2 mod 6 or 2 mod 3). Therefore the sum of the digits is 2 mod 3.


From (3), the sum of the digits is a multiple of 4. Since 8 is the only (small) multiple of 4 congruent to 2 mod 3, the sum of the digits is 8.


From (4), the tens digit is greater than the ones digit. Out of the numbers 17, 26, ..., 62, 71, 80, only the numbers 53, 62, 71, 80 satisfy (4). However we already know the number is even, so 62 and 80 are the only possible numbers.