The interesting concept of intuition was brought up the other day in one of my classes. In order to highlight the fallibility of trusting your intuition over cold hard logic, they proposed to us a slew of questions (although only three were really important). We were simply told to answer each question the best we could. Without further ado, 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.
   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 (according the original study).

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.

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The Solutions.

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. I would imagine that getting each question is a bit like adding a few more points to an average IQ score. Besides, how much credence can you give some odd paper?

Regardless, I am pretty sure I cheated and saw these all before the test. But I feel like I can be pretty impatient at times. Isn’t knowing half the batttle?