Friday, January 11, 2013

2013 ... 21 & 22

These questions were, for me , quite challenging. I got places with #21, but didn't get close enough to a solution to continue working on it during the test time (I take the test under the same constraints as the students).

Difficulty: Medium - Hard.

Difficulty: Medium. Finding the pattern and breaking the psychological blocks? Yeah, I got this one wrong. I forgot a whole set of numbers. Hope you do better.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 21, answer 22. Published 4/28.


  1. for 21, we can create a relatively easy system (but nothing is easy for me with logs). if logx is a and logy is b, then a + 3b = 2 and 2a - b = 3...

  2. That's it exactly. My error was in trying to get xy^3=1000, etc.

  3. Which method did I stick to until long after the test? Yeah, not the system of equations.