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

A. 10,050 B. 5050 C. 5000 D. 50,000 Answer: Option D
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Solution(By Apex Team)

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 $\begin{aligned}&=\left(\frac{n}{2}\right)(a+l)\\ &=\left(\frac{100}{2}\right)(5+995)\\ &=\frac{100\times1000}{2}\\ &=50000\end{aligned}$

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