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What is the difference between the sum of all even numbers and odd numbers from 25 to 100?
The sum of the even numbers is (26 + 28 + ... + 100); The sum of the odd numbers is (25 + 27 + ... + 99) Their difference is: (26 + 28 + ... + 100) - (25 + 27 + ... + 99) = (26 - 25) + (28 - 27) + ... + (100 - 99) = 1 + 1 + ... + 1 There are (100 - 26) ÷ 2 + 1 = 38 terms above which are all 1; their sum is 38 x 1 = 38. So the difference of the sum of all even numbers and all odd numbers 25-100 is 38.
How many numbers between 44 and 81?
Between them, not including them it is 36. If you include these two numbers, it would be 38.
How many prime numbers are there between 25 and 38?
29 31 37.
Does 38 or 24 or 49 or or 91 have an odd number of different factors?
Square numbers, like 49, have an odd number of factors.
How could you determine whether a sum of numbers such as 127 plus 38 is even or odd?
The parity rules are: Odd + Odd = Even Even + Even = Even Odd + Even = Odd Even + Odd = Odd So the parity where one number is even is that of the other number. This means that you can go through a list of numbers and ignore all the even numbers. Every PAIR of odd numbers has even parity and by the previous paragraph, even parity can be ignored. So you can pair off odd numbers and ignore them.
