Consider two natural numbers, each with three different digits. The larger one only has even digits, and the smaller one only has odd digits. If the difference between them is as large as possible, what is this difference?
(a) 997
(b) 777
(c) 507
(d) 531
(e) 729
The correct option is (e).

To make the difference as large as possible, we should choose the largest number with three different even digits and the smallest number with three different odd digits. The largest number with three different even digits is 864 and the smallest number with three different odd digits is 135. The difference between them is $864-135=729$.