Explanation:

Let's examine the series: 648, 448, 294, 180, 100, ?

- Observe the pattern in the series:

- 648 to 448: Subtracted 200

- 448 to 294: Subtracted 154

- 294 to 180: Subtracted 114

- 180 to 100: Subtracted 80

- Notice the pattern in the subtractions:

- These are decreasing by subtracting successive perfect square numbers: 200 (14² + 4), 154 (12² + 10), 114 (10² + 14), 80 (8² + 16).

- Continuing this pattern:

- Subtract (6² + 18) = 54 from 100, we should get 46.

Thus, the number that should replace the question mark is 46.

Based on the given options, none of them match 46. Therefore, re-evaluating the pattern isn't completely fitting as expected, but based on traditional checks, the logic suggests the next in the series should be 46. However, considering your options:

- Option 1: 42

- Option 2: 48

- Option 3: 64

- Option 4: 56

Since none of the logical calculations perfectly align with the options given, but considering the options and your calculation regarding 48, your choice feels relatively reasonable.

, based on the expected calculations not aligning with the exact numbers given. Also, check calculations and patterns for accuracy once more to determine precise proper match.