The interesting concept of intuition can be best understood, when studied alongside the concept of IQ. In order to highlight the fallibility of trusting your intuition over cold hard logic, here are the three questions of interest (try to answer each rather quickly):
1. A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball costs. How much does the ball cost?
2. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
3. 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?
A little background: These three questions were first proposed by Shane Frederick of MIT and are commonly referred to as the “Cognitive Reflection Test” or the CRT. The questions basically test your reliance on logic vs. intuition and are supposedly correlated with one’s IQ and their willingness to wait for good things.
1. A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball costs. How much does the ball cost?
2. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
3. 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?
A little background: These three questions were first proposed by Shane Frederick of MIT and are commonly referred to as the “Cognitive Reflection Test” or the CRT. The questions basically test your reliance on logic vs. intuition and are supposedly correlated with one’s IQ and their willingness to wait for good things.
Each question presents an easy “intuitive” answer which is actually incorrect. However, it is assumed that those with a higher IQ will notice that the intuitive answer contains inconsistencies that deserve a further (and more time consuming) examination. You might take it with a grain of salt, but it is interesting.
Solutions below:
For question #1, one might intuitively say, “$1.00 plus $0.10 is $1.10, therefore a ball costs $0.10“. While this is quite intuitive, it is also incorrect. A person who is more thorough might respond that the ball actually costs $0.05 (.05+(1+.05)=1.1). The correct answer is the ball costs $0.05.
For question #2, an intuitive response would be that “5=5=5 so 100=100=100“. However, if it takes a single machine 5 minutes to make a single widget, even a million machines can make a million widgets in 5 minutes. The correct answer is therefore 5 minutes.
For question #3, the common intuitive response would be, “half the pond would be covered in half the time, so 48/2=24 days“. However, this ignores the exponential growth of the lily pads. Try working it backwards, if the pond is covered after 48 days, and they double in size every day, then day 47 would be half covered. The correct answer is 47 days.
How do you compare?
How many did you get right? Compare your score to the below averages for various colleges.
Massachusetts Institute of Technology: 2.18
Princeton University: 1.63
Harvard University: 1.43
Web-based studies: 1.10
Michigan State University: 0.79
Please note that even if you missed them all, don’t fret, it’s obviously not a full IQ test.
This is to understand the difference between Intuition and Intelligence quotient!
Author and Credits: Bryan Helmig