How many positive 5-digit integers have the odd sum R of their digits? Select the correct option:  A) 9*10^2  B) 9*10^3  C) 10^4  D) 45*10^3  E) 9*10^4
We are looking at numbers between 10000 and 99999 both inclusive.   There are 90000 numbers.   Now for   10000 : sum of digits is odd;   10001 :sum of digits is even;   10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.   (Exception for the above statement :   When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd   and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)   This means exactly half of the numbers will have odd sum of their digits. i.e 45000   Answer :45*10^3
<result>D</result>
How many positive 5-digit integers have the odd sum R of their digits?