What is the sum of all positive integers up to 1000, which are divisible by 5 and are not divisible by 2?

Answer: Option D

The positive integers, which are divisible by 5 are 5, 10, 15, ....., 1000
Out of these 10, 20, 30, ......, 1000 are divisible by 2
Thus, we have to find the sum of the positive integers 5, 15, 25, ......, 995
If n is the number of terms in it the sequence then
995 = 5 + 10(n - 1)
⇒ 1000 = 10n
∴ n = 100
Thus the sum of the series
$$\begin{array}{rl}& =\left(\frac{n}{2}\right)\left(a+l\right)\\ & =\left(\frac{100}{2}\right)\left(5+995\right)\\ & =\frac{100\times 1000}{2}\\ & =50000\end{array}$$