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

1. Identify the core structure: We have a 3-digit number and its reverse (interchanging first and last digits). \n2. Recall the 'Difference of Reverses' concept seen in 2017 PYQs [12, 83]: The difference between a 3-digit number and its reverse is always $99 \\times (\\text{difference of first and last digits})$.\n3. The question states the difference is 198. \n4. Set up the simple equation: $99 \\times D = 198$, where $D$ is the difference we are looking for.\n5. Solve mentally: $D = 198 / 99 = 2$.\n6. The condition 'sum of digits is 4' and 'middle digit is 0' are just scaffolding to define a valid number (e.g., 103 and 301), but we don't even need to find the number to answer the question.\n7. Final check: Difference is 2.