Problem Set #4

What is the largest positive integer n that satisfies n^200 < 3^500?
(A)13 (B)14 (C)15 (D)16 (E)17
This question is asking what n is. n^200 must be less than 3^500.

The first thing that I tried to do to solve this problem was to punch 3^500 into my calculator. I found out that it didn't work. So instead I found out what 3^5 is which is 243. Then instead of trying to figure out what n is by myself, I just tried the numbers given in the multiple choice answers. I knew that I wouldn't be able to type 13^200 into my calculator so I just typed in 13^2. The answer is 169 which is still pretty low so I tried 14^2 which is 196. I tried 15^2 and 16^2. 15^2 is 225 and 16^2 is 256. 256 is greater than 243 so I knew that answer was (C) 15.

I like this question because it was actually really simple to figure out. All I had to do was think about how to solve it for a minute and then punch some numbers in my calculator. This question looks difficult, but it is actually really easy.

By doing this question I learned that you can not always rely on your calculator. When I tried typing in 3^500 it didn't work so I was stuck for a moment. Then I did some thinking and discovered that this problem was quite easy. My caculator helped me do some of the problem, but if I hadn't thought about the question then I wouldn't have been able to solve it. I need to make sure that I understand math principles because my calculator can not do all the work for me.