Simple problems

There's an amusing article in The Wall Street Journal [display] about a Nobel Laureate in economics, Daniel Kahneman, who's a professor of psychology at Princeton.

Apparently Kahneman is intrigued by the fact that many people are surprisingly irrational… which would seem to be a polite way of saying that they often react in a foolish manner, as if they were incapable of reasoning correctly. Kahneman has the habit of asking allegedly smart individuals to answer extremely simple questions. Here's a specimen:

A bat and ball cost $1.10.
The bat costs $1 more than the ball.
How much does the ball cost?

According to the article, about half the students of Harvard, Princeton and the Massachusetts Institute of Technology give the wrong answer. That's amazing! Personally, although I'm not particularly bright (as friends and members of my family know), it took me no more than a dozen seconds of mental arithmetic to obtain the right answer.

How about you?

I'm a little troubled, though, by the fact that, in handling questions of this kind, I immediately resort to basic algebra, rather than trying to find a solution intuitively, using so-called common sense. I'm disturbed because I have the impression that I'm cheating. I know beforehand that, as soon as I say "Let's refer to the unknown as x", I'm absolutely certain to find a solution, rapidly. Funnily, I would feel more like an honest citizen if I were to force myself to stagger around in the sludge of common sense for a while, waiting for a solution to drop down upon me like the gentle rain from heaven. In using mental algebra, I feel like an exam student who's exploiting stealthily his iPhone to obtain vital data.

Am I an abnormal cheat?

CORRECT ANSWER: The ball costs 5 cents and the bat, $1.05.