Correct Option (C)
The given expression represents the product of all odd integers from 1 to 999: 1 × 3 × 5 × 7 × 9 × … × 999.
To determine the unit digit of this product, consider the properties of multiplication involving the digit 5:
- The number 5 is a constituent factor within this product series.
- When the digit 5 is multiplied by any odd digit (1, 3, 7, 9), the unit digit of the resulting product is consistently 5.
- For instance:
- Unit digit of (5 × 1) is 5.
- Unit digit of (5 × 3) is 5 (from 15).
- Unit digit of (5 × 7) is 5 (from 35).
- Unit digit of (5 × 9) is 5 (from 45).
- Since all numbers in the sequence (1, 3, 5, 7, ..., 999) are odd, and 5 is present as a factor, the unit digit of the entire product must be 5.
Incorrect Options:
Options A (1), B (3), and D (9) are incorrect. The fundamental property that the product of 5 and any odd number yields a unit digit of 5 renders these alternatives invalid. A unit digit other than 5 would necessitate the absence of 5 in the product or the inclusion of an even number, neither of which applies to the given series.
