There is a quick test that can help you determine if you rely on intuition or reflective reasoning (intellect) when making decision. Answer the following question as quickly as possible:
“A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost?”
Do you have your answer? Good. Now I want you to think about it. Commit to it. Say your answer out loud.
If you are an intuitive thinker that relies on your gut feelings, it is highly probable you answered that the ball is 10¢. You would be wrong. If you rely on reflective reasoning, or intellect, to make your decision, you probably got the answer correct.1
Scientists are studying intuition versus reflective reasoning and how a person’s thought patterns influence things such as religious beliefs. They are also looking into whether thought patterns change with education or if it is primarily genetic. Image © iStockphoto/Thinkstock
This was part of a study in the September 19th, online edition of The Journal of Experimental Psychology: General2. As Researcher David Rand of Harvard University said, “It’s not that one way is better than the other. Intuitions are important and reflection is important, and you want some balance of the two.” It’s a spectrum.
Different types of thinking are important in different circumstances. It’s important to be able to tap both. A parent may feel uneasy, for reasons she can’t explain, and not let her children hang around certain people. Likewise, a woman may decide not to walk down an alley alone with someone even though there is no reason for her belief. In many cases, her subconscious may have picked up on something that her intellect hasn’t yet put into concrete form. In other cases, though, those same non-reflective decisions can result in huge financial losses or mistakes.
That is the reason I’m such a fan of a mental framework that requires checklists to help defend against cognition errors. For example, had you worked the question backward, it would have been much easier to solve – as Charlie Munger says always quoting the mathematician Jacobi – “invert, always invert!”. You could have checked the accuracy of your first reaction by asking, “If a bat is $1.00 and a ball is 10¢, is the statement ‘the bat cost $1 more than the ball true?'” You would have had to simply take $1.00 – 10¢ = 90¢ to see that 90¢ is not $1. Therefore, it couldn’t be the correct answer. When in debt, work the problem backward.
1) The correct answer is 5¢. If the bat and ball together cost $1.10, and the bat has to be $1.00 more than the ball, the bat must cost $1.05 and the ball must cost 5¢ for a total of $1.10. Only then is the bat $1.00 more than the ball ($1.05 bat – 5¢ ball = $1.00 differential with the total of the two items still coming to $1.10).
2) The study was designed to test how different types of thinking influences the belief in God. The next steps will be to determine how genes and education influence thinking styles.
Reader Comments (10)
Comments are presented chronologically, with replies indented beneath the comments to which they respond.
bing
September 24, 2011
this is a very nice read. learned from it! 🙂
bing
September 24, 2011
this is a very nice read. learned from it! 🙂
Joshua Kennon
November 20, 2011
Replying to bing
Thank you =) Welcome to the site!
Brian
September 25, 2011
Joshua, I noticed what may be a typo in your last sentence, but it kind of works. "When in debt, work the problem backward." You may have meant "doubt", but after you'd just talked about intuitive thinking costing you money, it made a lot of sense. I wouldn't have pointed out such a trivial thing had it not been so appropriately thought provoking. And funny.
Chris Stuber
October 9, 2012
I swear I looked at this for awhile and still don;t get how the bat cost $1.05. How in the world did they come up with this number.
Joshua Kennon
October 9, 2012
Replying to Chris Stuber
We know two things:
Fact 1: The bat and the ball together must be $1.10.
Fact 2: The price of the bat must be $1.00 more than the price of the ball.
Words are so ... wordy. Let's write it short hand.
Fact 1: bat + ball = $1.10
Fact 2: bat = $1.00 + ball
You follow me? Nothing has happened. We are just restating the basic conditions that must be met. But I hate unnecessary clutter. So let's combine them into one big statement. We know that "bat = $1.00 + ball" because of Fact 2 so whenever we see the word "bat" in Fact 1, let's just cross it out and replace it with $1.00 + ball.
Fact 1: ($1.00 + ball) + ball = $1.10
Perfect. Now we are only dealing with one line. I like one line. It's simple. It's clean. I can focus on it.
But why have the word "ball" written twice? It's messy. Screw that. I am going to change it to say 2 ball.
Fact 1: $1.00 + 2ball = $1.10
That's much better. We've made it even simpler.
But I'm lazy. I am tired of writing "ball". Let me just make an "x" symbol instead. It would save me time.
Fact 1: $1.00 + 2x = $1.10
Crap. That looks like an algebra equation. The "x" is a variable, meaning it can stand for anything (literally, "it varies"). Right now, we are using it to symbolize a bat. We could be talking about Snicker's bars or bottles of dish soap, though.
The other numbers are scared of variables. They hate them. They want to get away from them. So the rule of math is that you need to isolate those suckers. Make them social outcasts. Get them by themselves.
To do that, the other number on the same side of the = sign reverses itself and swings over to the other side. So the equation changes to:
Fact 1: 2x = $1.10 - $1.00
Well ... that looks easy enough. Let's solve that. I know that $1.10 - $1.00 is $0.10 so ...
Fact 1: 2x = $0.10
Hmm ... okay. What does this mean? We know that two balls would cost $0.10. Well, we don't want to know what two balls would cost, we want to know what one ball would cost. So we need to take $0.10 and divided it by 2.
Fact 1: $0.10 ÷ 2x = $0.05
Okay, now we know:
Fact 1: 1x = $0.05
But since "x" stands for ball, we can just change it back now:
Fact 1: ball = $0.05
How can we check our work? If a bat and a ball costs $1.10 together, and the ball costs $0.05, that means the bat must cost $1.05.
Looking at that, we know it is true because:
1. A $1.05 bat plus a $0.05 ball = $1.10 total
2. A $1.05 bat is exactly $1.00 more than a $0.05 ball
jondaw
January 13, 2014
Replying to Joshua Kennon
You make this too difficult. If the ball cost 10 cents and the bat cost a dollar more than the bat, it would mean the bat cost 1.10. Add them up and you get 1.20. So the answer that the ball cost 10 cents is wrong. The idea is to stop and pay close attention to the precise meaning of the sentence. Having understood the precise meaning of the sentence, the right answer is arrived at with simple algebra--or if you are very sharp, after having grasped the sentence correctly, you then note that the answer has to be 5+5 =10. So 1.05 and .05.
Finder Keeper
December 16, 2016
"The correct answer is five cents . . the bat must cost $1.05" - Joshua Kennon
Wrong. Your lecture in the comments section notwithstanding, you haven't thought this through correctly.
There are NINE different configurations that work.
Ball 9 cents + (bat 1 cent + 100 cents) = 110
Ball 8 cents + (bat 2 cents + 100 cents) = 110
Ball 7 cents + (bat 3 cents + 100 cents) = 110
Ball 6 cents + (bat 4 cents + 100 cents) = 110
>>Ball 5 cents + (bat 5 cents + 100 cents) = 110<<
Ball 4 cents + (bat 6 cents + 100 cents) = 110
Ball 3 cents + (bat 7 cents + 100 cents) = 110
Ball 2 cents + (bat 8 cents + 100 cents) = 110
Ball 1 cent + (bat 9 cents + 100 cents) = 110
Finder Keeper
December 16, 2016
No, wait. You're correct, Joshua. Sorry. I just reread the question. Bat has to cost $1 more than ball.
My error.
Thanks for the question anyway. Made me think!
Donna Bayley Lovett
February 1, 2018
I rely on intuition, and my hubby relies on reflective reasoning. Let's just say I drive him nuts sometimes....ha ha.