A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first and last digits is greater than the number itself by 198, then the difference between the first and last digits is

Let the three-digit number be represented as 100a + 10b + c, where a, b, and c are the digits. 1. "the middle one is zero": So, b = 0. The number is 100a + c. 2. "their sum is 4": a + b + c = 4. Since b = 0, we have a + c = 4. 3. "interchanging the first and last digits": The new number is 100c + 10b + a. Since b = 0, the new number is 100c + a. 4. "new number is greater than the number itself by 198": (100c + a) - (100a + c) = 198 100c + a - 100a - c = 198 99c - 99a = 198 99(c - a) = 198 c - a = 198 / 99 c - a = 2 The question asks for "the difference between the first and last digits", which is |c - a|. From our calculation, c - a = 2. Therefore, the difference between the first and last digits is 2. The final answer is B.