Hi Ndkms -
Thanks for the feedback. Looking at our two solutions, we actually followed a similar path: find the pattern of units digits of 3, and then divide the units digit of 3^24 by 5 to get the answer.
Regarding "eliminating rules" on the GMAT, I have to disagree with your stance. The GMAT is an exam that forces students to answer questions in a limited amount of time. Thus, ANY rule/method that can be easily memorized that will allow students to efficiently and effectively attack a question, without having to create a scenario for its solution, is a valuable rule/method because it will save them valuable time on the GMAT. Does that mean that students should go crazy and memorize every rule/method ever written--no, of course not.
Of course the GMAT is not a number-crunching test; I don’t think you’ll find many people who will disagree with you on that point. The test is clearly a critical-thinking test. However, when you examine the research of those on the forefront of studying rational thought and decision-making, people such as Daniel Kahneman and Keith Stanovich, you see that without rules/methods to follow, critical thinking becomes difficult. Just as we need software on our computers to do spreadsheet analysis, humans require “mindware” in their brains to reason logically. Mindware is simply a term that describes all of the content, facts, and rules that one needs to logically reason through a problem. In general, the more pertinent mindware a person has regarding a certain problem, the better positioned that person will be, all else equal, to begin thinking logically about that problem.
Furthermore, the rule/method that I referenced in my solution simply goes one step further from the rule of units digit patterns, which is a commonly known GMAT rule. Thus, I don't think it would take too much effort to memorize and effectively use it.
But, the beauty of math, and of the GMAT, is that there are many ways to solve most problems. And, one beauty of this forum is that we can all collaborate and help each other, respectfully. So, thank you for the input.
Happy Studying.
Scott
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