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I know you could find the number of even numbers (since they are a multiple of two). For example the number of even numbers between $11$ and $30$ will be $$n= \frac{28-12}{2} + 1 = 9 $$

I wanted to know is there a similar way to find the number of odd numbers b/w two extremes?

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3 Answers 3

up vote 3 down vote accepted

You can use the exact formula. What is number of odd numbers between 11 and 30? n = (29-13)/2 + 1 = 16/2 + 1 = 9. Let's list them out to make sure: 13, 15, 17, 19, 21, 23, 25, 27, 29. There are 9 of them, so that is correct

By the way, your formula was calculated wrong. n = (28-12)/2 + 1 = 16/2 + 1 = 8 + 1 = 9 (12, 14,16,18,20,22,24,26,28)

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2  
Sidd's answer certainly gives you what you want, and if you understand the reasoning behind the formula for evens then you should be able to see why it works for odds too. But here's another way of thinking about it: Counting the number of odd numbers between 11 and 30 is the same as counting the number of even numbers between 12 and 31. –  Brett Frankel Aug 6 '12 at 5:40

If you can find the number of numbers, and you can find the number of even numbers, ....

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use the A.P formula for finding the number of terms...say for no. of odd numbers between 1 and 11.... nth term= first term+(n-1)(common difference)......(*),where n=no. of terms,which we have set out to find in this case.

from (*) we have n= {(nth term-first term)/common difference}+1.....

For our problem, n= {(11-1)}/2}+1 =6

here common difference is 2 as an odd number occurs by adding 2 to the previous odd number etc.,

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