Final answer:
The three-digit number that is divisible by 6 and includes the numbers 1, 2, 5, and 7 is 257.
Step-by-step explanation:
To find a three-digit number that is divisible by 6 and must use the numbers 1, 2, 5, and 7, we need to check each option.
a) 725 - Not divisible by 6
b) 527 - Not divisible by 6
c) 257 - Divisible by 6, as 2 + 5 + 7 = 14, which is divisible by 3
d) 752 - Not divisible by 6
Therefore, the correct answer is c) 257.