The number 34041 and 32506, when divided by a certain number of three digits, leaves the same remainder. What is the number?

The correct answer is C. If two numbers leave the same remainder when divided by a certain number, then their difference is divisible by that number. Here, 34041 - 32506 = 1535. We need a 3-digit divisor of 1535. 1535 = 5 × 307. The 3-digit divisors are 307 and 5 × 307 = 1535 (not 3-digit). So the only 3-digit divisor is 307.