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Q: How many integers between 10 and 500 begin and end in 3?

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500 of them.

The sum of the first 500 positive integers is: 125,250

There are 11 such numbers.

40 integers (whole numbers), an infinite number of decimal numbers.

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.

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No. The sum of all integers between 1 and 500 is 124,749.

500 of them.

There are infinitely many possible answers.Using only integers, two possibilities are:{3,3,4,9,11} and {-500, -500, 4, 500, 526}There are infinitely many possible answers.Using only integers, two possibilities are:{3,3,4,9,11} and {-500, -500, 4, 500, 526}There are infinitely many possible answers.Using only integers, two possibilities are:{3,3,4,9,11} and {-500, -500, 4, 500, 526}There are infinitely many possible answers.Using only integers, two possibilities are:{3,3,4,9,11} and {-500, -500, 4, 500, 526}

500

-700 is smaller than -500. Integers*

The sum of the first 500 positive integers is: 125,250

There are 11 such numbers.

1,2,3,....500

500 numbers are divisible by 2.

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.

40 integers (whole numbers), an infinite number of decimal numbers.

95