Why Smart People Are Stupid

I am not a psychiatrist nor a psychologist. I do, however, have an explanation I find logical for why both of these questions would get wrong answers.

A bat and ball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost?

The reason this "problem" will yield a common answer of 1 dollar is because so many of us have seen the same thing over and over in school. It has been over the course of 5+ years engraved into our thought process to separate pieces of the sentence into logical portions and stop as soon as we have enough information (ie: to assume most of it is useless information). So as soon as the reader sees the intentionally deceptively worded sentence, it's effectively an expected response from this programmed behavior: most people stop where I'm about to show you:

A bat and a ball cost a dollar and ten cents. The bat costs a dollar --

Immediately, we have a situation: a + b = 110, a = 100. We immediately deduce that b = 10, and have a solution instantaneously without completing the thought. This is what standardized testing and predictable word problems with extraneous information teaches people. This isn't a result of their intelligence, this is a result of cognitive process sculpted by years of stupid, pointless exercises. You'd have to be outrageously stupid to think this is somehow unexpected. The people who we classify as "smart" are people who perform well at these tasks (high score on standardized test, breezed through courses with similar problems). This is causation -- people who make this mental leap are considered "smart." So you ask "why are all these smart people making this stupid mistake!?" The answer is clear -- your fundamental measure of intelligence is wrong. The solution is that these so-called "smart" people aren't very smart at all. They're just good at solving tricky word problems as quickly as possible, primarily by ignoring information. In my experience, this methodology is often the inverse of an intelligent process.

Now for the second problem:

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

What most people will do, because this is how they've been taught, is to read sentence one. Note it as an interesting fact, then proceed. Upon finishing the second sentence, we realize we didn't come up with an answer yet, so we refer to only the information in the latter part of the question. What most people just read is:

If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

We aren't used to thinking in terms of exponentiation, so it's natural to assume a linear growth rate when you completely discard the first sentence.

While I agree, these are both absurd questions, they have something in common: people tend to ignore part of the question and answer the question with incomplete information. This is not something I do very often, intentionally. This is something, though, that I recall being the fundamental "trick" to answering 99.99999999999% of questions on standardized tests. They gave you extraneous information. When literally every problem exposed to you has extraneous information, of 2 forms: A, B or B, A, where B = worthless information, it becomes habitual to process information in this manner, especially when the problem is worded like a problem you'd find on a high-school level standardized test (you know, you never really forget how to ride a bike, like you never forget how to solve very badly designed problems that don't test intelligence in any way).

I don't know, maybe I'm too smart for this researcher. But the answer seems obvious: years and yea

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