The number $N$ is the product of all positive odd integers from 1 to 99 that do not end in the digit 5. That is, $N=1 \times 3 \times 7 \times 9 \times 11 \times 13 \times 17 \times 19 \times \cdots \times 91 \times 93 \times 97 \times 99$. The units digit of $N$ is
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
The units digit of any product is given by the units digit of the product of the units digits of the numbers being multiplied.

For example, the units digit of the product $12 \times 53$ is given by the product $2 \times 3$, so it is 6 .

Thus to determine the units digit of $N$, we need only consider the product of the units digits of the numbers being multiplied to give $N$.

The units digits of the numbers in the product $N$ are $1,3,7,9,1,3,7,9, \ldots$, and so on.

That is, the units digits $1,3,7,9$ are repeated in each group of four numbers in the product.

There are ten groups of these four numbers, $1,3,7,9$, in the product.

We first determine the units digit of the product $1 \times 3 \times 7 \times 9$.

The units digit of $1 \times 3$ is 3 .

The units digit of the product $3 \times 7$ is 1 (since $3 \times 7=21$ ).

The units digit of $1 \times 9$ is 9 .

Therefore, the units digit of the product $1 \times 3 \times 7 \times 9$ is 9 .

(We could have calculated the product $1 \times 3 \times 7 \times 9=189$ to determine the units digit.)

This digit 9 is the units digits of the product of each group of four successive numbers in $N$.

Thus, to determine the units digit of $N$ we must determine the units digit of

$9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9$.

This product is equal to $81 \times 81 \times 81 \times 81 \times 81$.

Since we are multiplying numbers with units digit 1 , then the units digit of the product is 1 .

ANSWER: (A)