A positive two digit number is divided by the sum of its digits. What is the smallest and largest the result can be?
max=10 for 10,20,...,90
min: 19/10 = 1.9
To find the smallest and largest possible results, we need to consider the two extreme cases.
Let's start with the smallest possible result:
The smallest positive two-digit number is 10. If we divide 10 by the sum of its digits, which is 1+0=1, we get 10/1 = 10. Therefore, the smallest possible result is 10.
Now, let's move on to the largest possible result:
The largest positive two-digit number is 99. If we divide 99 by the sum of its digits, which is 9+9=18, we get 99/18 = 5.5. Since we're dealing with a positive two-digit number, we can't have a result that is a decimal. Thus, rounding up to the next whole number, the largest possible result is 6.
Therefore, the smallest possible result is 10, and the largest possible result is 6.