IQ VS. Intuition
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):
- 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? - If it takes 5 machines 5 minutes to make 5 widgets, how long would it take
100 machines to make 100 widgets? - 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?
I’ve seen these 3 questions in various forms before so I remember what the trick is for all of them. For example usually the “bat and ball” question is “wine and bottle” and the lily pads in a pond is usually bacteria in a test tube.
I got them all right. Does that make me a genius or someone with a really good memory?
3/3
Princeton
Got all three right. However, the post title tipped me off as to the trick question nature of the questions.
If anyone wants more of these type of questions i recommend playing:
“Professor Layton and the curious village” on the nintendo DS. The game is full of puzzles/enigmas and “mind fucks” .I think that all three of these questions are in the game.
I got them all but it obviously helps to know that they are trick questions in advance. Otherwise I’m pretty sure I would have been fooled by question 1.
3/3
miami dade community college
9/3. I answered all 3 correctly 3 times in a row
No, the ball really costs $.10 because 1.10 is the cost for one bat and ONE ball. The “answer” you gave [.05+(1+.05)=1.1] is for the sum of bat and ball plus another ball, but that is not the what the question specifies. Did you misquote the question?
@ PINhead
The keyword is MORE. 1 dollar MORE than the ball. If the ball costs $.10 then the bat costs 1+.1 or 1.10. 1.10 (bat) plus .10 (ball) is 1.20.
@ bryan
Mkay, I see that now. Damn, I’m not quite smart enough for MIT!
what about sales tax on the bat and ball?
I think the REAL question that these questions are asking is “John answered all three questions correctly in 5 minutes. If John were to ever mention this publicly, how long would it take for some idiot to punch him in the face?”
If it takes 5 machines 5 minutes to make 5 widgets, how long would it take
100 machines to make 100 widgets?
Answer Quote:
“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.”
I got hung up on this one because I didn’t think of the answer the same way.
If 5 machines working in tandem make a rate of 1 widget per minute. Then if you multiplied the number of lines of machines by 20 to accumulate 100 machines as a whole, it would still only take 5 minutes to make 100 widgets because each line would produce their 5 widgets in 5 minutes. I suppose that’s a collaboration between intuition and IQ?
The initial intuitive flaw is assuming the machines work in a forced order and by adding more machines you are adding more time.
for question #1 who says it has to be .05 why can’t the ball cost .06 than the bat would cost 1.04 which is still more than 1.00???
or even the opposite the ball cost .04 and the bat cost 1.06
anything over .05 cents would work in that calc
Hmm…. interesting point Chris. If collaboration is essential to the widget creation, the number would be much different.