Michael Michalko, writing for Psychology Today, notes that our habits can often trip us up and cause us to make errors. He offers this exercise as evidence:
[This]must be done in your head only. Do NOT use paper and pencil or a calculator. Try to add up the following numbers as quickly as you can. Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000. Now add 10. What is the total?
Apparently 96% of people asked to perform this simple calculation answered 5,000, which is wrong. Very few answered 4,100 — the correct answer. This is because we the problem is structured to take advantage of how we perform maths in our heads and fool us into coming up with the wrong answer.
The problem isn't so much that we're making the mistake but that we assume we're doing it correctly, then provide a false answer while believing it to be true. The trick to overcoming this is to remember to ask yourself after you solve a problem: "why do I think this is correct?"
One of the more important reasons you needed to show your work when doing a maths problem in school was to make you think about what you were doing. Making assumptions might get you the answer sometimes, but if you spend a few more seconds thinking about the process you can develop the good habit of questioning yourself and catch these little errors. It may take a little more time, but it comes with the added bonus of potentially discovering ineffective methods you regularly use so you can change them for the better.
What Monkeys Can Teach Us About Human Behavior [Psychology Today]