How many positive four-digit integers are multiples of 5 and less than 4,000

  Number of positive four-digit integers which are multiples of 5 and less than 4,000 = 600

Explanation:

 Lowest four digit positive integer = 1000

 Highest four digit positive integer less than 4000 = 3999

 We know that multiples of 5 end with 0 or 5 in their last digit.

 So, lowest four digit positive integer which is a multiple of 5 = 1000

 Highest four digit positive integer less than 4000 which is a multiple of 5  = 3995.

 So, the numbers goes like,

       1000, 1005, 1010 3990, 3995

 These numbers are in arithmetic progression, so we have first term = 1000 and common difference = 5 and nth term(An) = 3995, we need to find n.

          An = a + (n-1)d  

           3995 = 1000 + (n-1)x 5

           (n-1) x 5 = 2995

           (n-1) = 599

            n = 600

 So, number of positive four-digit integers which are multiples of 5 and less than 4,000 = 600