Two 5-digit numbers have the same sum of digits: 2. The largest possible difference between two such numbers has the sum of digits:
A 1 B 9 C 18 D 27 E 36
20000 - 10001 = 9999
To find the largest possible difference between two 5-digit numbers that have the same sum of digits, we need to maximize one number while minimizing the other.
Let's start by finding the largest possible number that has a digit sum of 2. Since we want the largest number, we should place the largest digit, 9, in the leftmost position. However, we need to distribute the sum of the digits evenly, so we place 9 in the first position and distribute the remaining sum (2 - 9 = -7) among the remaining digits.
The largest possible number is 90,000.
Now, let's find the smallest possible number that has a digit sum of 2. Since we want the smallest number, we should place the smallest nonzero digit, 1, in the leftmost position. Again, we need to distribute the sum of the digits evenly, so we place 1 in the first position and distribute the remaining sum (2 - 1 = 1) among the remaining digits.
The smallest possible number is 10,000.
The difference between these two numbers is 90,000 - 10,000 = 80,000.
Now, let's find the sum of the digits in 80,000. The digits are 8, 0, 0, 0, and 0. Adding these digits gives us 8 + 0 + 0 + 0 + 0 = 8.
Therefore, the sum of digits in the largest possible difference between two 5-digit numbers with a sum of 2 is 8.
So, the answer is B) 9.