What is the unit digit of the number

$$
1 \times 3 \times 5 \times \cdots \times 97 \times 99 ?
$$

(a) 1
(b) 3
(c) 5
(d) 7
(e) 9
The correct option is (c).

The last digit of a multiple of 5 is 0 or 5; those ending in 0 are even and those ending in 5 are odd. Since $1 \times 3 \times 5 \times \cdots \times 97 \times 99$ is odd, being a product of odd numbers, and is a multiple of 5, it follows that its units digit is 5.