Problem Set #3

Question #11

         Actual Question: Let N=10^3+10^4+10^5+10^6+10^7+10^8+10^9. The sum of the digits of N is
               (A) 12     (B) 1     (C) 6     (D) 9     (E) 7
This question is asking that I figure out the answer to the equation above and then add up all of the digits from the answer that I get.

         To find the solution to this problem first I need to figure out what the answer to the eqation is. This seems quite difficult because there are so many numbers, but actually it is really simple. 10 to the power of any number will always be 1 with however many zeros behind it. So I figured out the answer to each of the exponents so the equation looked like this:
         1,000+10,000+100,000+1,000,000+10,000,000+100,000,000+1,000,000,000=
Now I just added up all of the numbers to solve this equation. The answer I got was 1,111,111,000. Next I added all the digits from my answer and came up with 7. So the answer to question 11 is E) 7.

         I like this problem because at first glance it seems really difficult. There are so many numbers and exponents that it is quite confusing. But after reading through the problem I realized that this question really is not that hard.

         I learned that when I am solving problems I need to read through the question carefully before I decided whether or not this problem is doable. Sometimes when I do math problems I take one look at the question and decide that I can't do it. This problem showed me that I shouldn't do that anymore, but that I should look the question over, analyze it, try and solve it, and then if I still can't get it ask someone for help. I need to make sure that I do not give up too quickly.