franz711 wrote:
How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?
a) 9
b) 8
c) 7
d) 6
e) 5
We need to find integers between 200000 and 900000 such that the sum of the digits is 3
For numbers between 200000 and 299999, the first digit is 2. We need one digit to be 1 and the rest to be all 0's
The number will be of the form 2 _ _ _ _ _ where one place is 1 and the rest are all 0's. 1 can take any of the 5 places after 2, so there will be 5 integers
210000, 201000, 200100, 200010, and 200001 => 5 integers
Next for numbers starting with the digit 3, all the places need to be 0 for the sum to be 3
Hence only one number is possible
300000 => 1 Integer
For any numbers after 300000, the sum of the digits will be greater than 3.
Hence a total of 6 integers are possible. Answer D