When I coach my MathCounts teams, I make sure to remind them to answer the question that is being asked. That is, after all the calculations have been performed and you have a value for x, reread the question, and make sure x is what the problem is asking for. Only when you are sure you have answered the question should you write it down (or bubble it in).
For example, today I’m reviewing materials for my team, and I came across this problem:
“The three-digit integer is a multiple of six. What is the sum of all the possible values for the digit represented by A?”
After some calculations, I found 4 possible values for A: 0, 3, 6, and 9. My first thought was: “The answer is 4! There are four possible values of A.” But then I reread the question, and it asks for the sum of all possible values. The correct answer is
Sometimes you can avoid this error by setting your variable equal to the value the problem is asking for, so that when you do solve for x, you do not need to perform additional calculations to generate the correct answer.
This is a well-known error, and Richard Rusczyk has written about it in the context of developing good problem solving habits. Some people may describe this as a “trick question” but I think it’s just a matter of taking care to reread the question and answer the question that is being asked, not the question that you wish had been asked.