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How many even integers are between 100 and 1000?
To find the number of even integers between 100 and 1000, we first determine the number of even integers between 1 and 1000, which is half of the total integers (since every other integer is even). So, 1000/2 = 500 even integers between 1 and 1000. Next, we subtract the number of even integers between 1 and 100, which is 50 (since every other integer is even in this range as well). Therefore, there are 500 - 50 = 450 even integers between 100 and 1000.
What is the sum of the first 500 positive integers?
The sum of the first 500 positive integers is: 125,250
How many integers between 200 and 500 inclusive leave a remainder of 1 when divided 7 and a remainder of 3 when divided by 4?
There are 11 such numbers.
How many integers between 100 and 500 are divisible by 6 but not 8?
There are (500-100)/2 = 200 numbers divisible by 2 between 100 and 500 counting 100 but not 500. Of these (500-100)/8 = 50 are divisible by 8. So there are 150 numbers between 100 and 500 divisible by two but not by 8. By relative primeness exactly 50 out of these 150 are divisible by 3 and therefore these 50 are exactly the ones divisible by 6 but not by 8.
What are all the numbers that can be rounded to 500?
Any of the integers from 450 to 499 can be rounded to the nearest 100 as 500
