If '502x62y' is a seven-digit number which is divisible by 72, then find the least possible value of (x -
y).

Since the given number is divisible by 72, it must also be divisible by both 9 and 8. We know that for a number to be divisible by '8', the number formed by last three digits of the number must also be divisible by '8'. So, '62y' must be divisible by 8. Only value of 'y' that makes '62y' divisible by '8' is '4'. So, y = 4 Now, for the number to be divisible by 9, the sum of digits of the number must be divisible by 9. Sum of digits of the given number = 5 + 0 + 2 + x + 6 + 2 + 4 = (19 + x) So, possible value of 'x' = 27 - 19 = 8 So, required value = 8 - 4 = 4