- A. 1
- B. 3
- C. 5
- D. 9
Answer: C
Explanation
The given expression is the product of all odd natural numbers from 1 to 999: 1 × 3 × 5 × 7 × 9 × … × 999.
To find the unit digit of a product, we only need to consider the unit digits of the numbers being multiplied.
Key observation:
– The number 5 is present in the multiplication.
– All other numbers in the product (1, 3, 7, 9, 11, 13, …, 999) are odd numbers.
Rule for unit digits involving 5:
– If 5 is multiplied by any odd digit, the unit digit of the product is always 5 (e.g., 5 × 1 = 5, 5 × 3 = 15, 5 × 7 = 35, 5 × 9 = 45).
– If 5 is multiplied by any even digit, the unit digit of the product is always 0 (e.g., 5 × 2 = 10, 5 × 4 = 20).
Since all numbers in the given product are odd, the presence of 5 guarantees that the unit digit of the entire product will be 5. There are no even numbers to turn the unit digit into 0.
Therefore, the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × … × 999 is 5. This question tests basic number properties and the concept of unit digits in multiplication, a fundamental topic in UPSC CSAT quantitative aptitude.