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?
Bryan is a jazz and blues guitarist, small-time designer, Python hacker, entrepreneur, and lover of fine whiskeys. He's the man behind such sites as
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.
Gemini:
Your reasoning is wrong, .05 is the correct answer. If the ball costs $.06, then the ball will cost $.98 more, not $1
It has more to do with one, listening and understanding the question being asked than say IQ.
For question #1 the emphasis is on the bat costing £1 more than the cost…… of the ball. Only then did my 12 year old daughter get right.
I approached number 2 differently, and came up with 25 minutes. I thought that it was that 5 machines working on 1 widget could make it in 1 minute, so it took them 5 minutes to make 5. Therefore 100 machines working on 1 widget could make one in 15 seconds. 100 need to be made, so it takes the machines 25 minutes to create 100 widgets.
Can’t question 3 be answered in 2 ways? The first half of the pond would take 47 days, but the last half would only take one day, right? So you could answer 1 day or 47 days since the question didn’t specify the first or second half of the pond.
3/3 for me.
And no, Papi Chulo. Its talking about the magnitude of the spread, not which side its covering.
If you say 1 was your answer, you’re essentially saying that in 1 day, half the pond was covered by the lily pads, and then it took 47 more days to cover the rest, which doesn’t make any sense, since the lily pad patch doubles in size. Why would it take so many more days to cover the other half?
I hope this makes sense to you.
Number one either cannot be answered, or can have any number of answers. It is driving me insane.
“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?”
There is not enough information to form an equation. There is no answer. And it would depend on what state you live in.
You could buy the bat and ball in Delaware tax free, but in Nevada it would be way more expensive. However, if you were in Hawaii there would be no sales tax because they have gross receipts tax, but you’d probably have to pay it just the same. You could go to the airport and get a bat and ball in a duty-free shop, but that seems like an awful lot of trouble, unless you happened to be there anyway, but they jack the prices up so high, I think it would cost way more than $1.10.
Anyway, I would really like to know where this bat and ball come from, because unless it is Dollar Tree, I don’t think you can get a bat and ball for $1.10.
I GOT ALL THREE OF THESE QUESTIONS WRONG LOL. But I think one thing that for sure indicates a higher IQ is being able to understand after the correct answer is given to you. Now I understand on all these and am somewhat humbled.
Ladies and gentlemen, on the ball and bat question: as long as the ball is 5 cents or less, it would work and you could figure it many different ways so that they add up to 1.10 and yet the bat be at least 1.00 more. But thats not what its asking. It says “1.00 more” not “1.00 OR more” there is a difference here. word usage is very important to in these tricky questions
I might have hit a key wrong, but here are my calculations. If a lily pad is about 8 inches in diameter, it covers a surface area of about 50.2655 square inches. By doubling in size every day, after 48 days it will cover 3,524,352 square miles. That is about 111 Lake Superiors.
the solution to question one can be broken down into algebra and therefore can only have one answer.
Bat + Ball = 1.10
Bat = Ball + 1.00
(Ball + 1.00) + Ball = 1.10
(Bat)
Therefore 2Ball + 1.00 = 1.10
2Ball = 1.10 – 1.00
2Ball = 0.10
Ball = 0.10/2 = 0.05
Ball = 0.05
on question #1, the words “more than” mean + 1/2 the price of the ball. Therefore, if the bat costs $1.00 more than the ball, then, the price of the bat is 1 + .05 of .10. So, the price of ball is, indeed, .05.
3/3
Princeton – undergraduate degree
University of Chicago – graduate degree
I got all three right so 3/3 and honestly, I have never seen these questions, does that make me worth MIT
I hignly doubt. It is very situation dependent on how you think about the questions and the time you want to spent thinking to solve the problems.
@Batty.
LOL. just stick to the explanation of comments #9 and #18.
I missed the widget one. I was thinking because 5 machines make 5 widgets in 5 mins, therefore 1 machine makes 1 widget in 1 min.. damn. Thus, 100 machines would make 100 widgets in 1 min… dumb.
DeVry Tech. dropout. Zero correct. Hmm.
Question # 1 is bogus. The term “more” or “more than” is too vague and interchangeable with other terms denoting a quantity or difference to be used in problem solving. An illustration of this would be a statement such as -” I have more than a small lead in the race.” I agree with the fellow above, #6. If these types of questions (#1) tell anything at all about thinking skills, then they indicate only that shiftless nerds can get into MIT.
Wonder what the results of question 1 would be if the person would be asked what is the price of the bat? Then the price of the ball
Because they are only asked the price of the ball, they focus on a solution that works from the perpsective of the ball and because they don’t consider the bat, they end up with the wrong solution. It’s a matter of perspective. You have to realize that the questions are loaded to cause you to look at them from a perspective likely to cause you to not consider the correct solution.
These are akin to the video’s that ask you how many times x happens in the video and then later ask you to remember a detail that didn’t have anything to do with X. (My favorite is the basketball that is passed around and a person in a gorilla costume runs through the video — many people don’t notice) I don’t know that these kind of questions so much measure intelligence as they do ability to discern that your attention has been focused by the wording on the wrong element of the problem. In short: it’s a trick question, designed to distract through slight of mind
2/3!
3/3 University of New Mexico. Never saw these before but fun to do.
3/3 , and i barely finished highschool. Never saw questions before. It helps to have time to think them through, though.