Watch out, it might be a trap
March 23, 2011 11:18 AM Subscribe
A baseball and bat together cost $11. The bat costs $10 more than the ball. How much does the ball cost?
Apparently 50% of people get this wrong! I'd be interested to hear your a) answers and b) your theories of why the different answers are given. Or, better still, what is your thought process when you work this out.
Thanks,
Apparently 50% of people get this wrong! I'd be interested to hear your a) answers and b) your theories of why the different answers are given. Or, better still, what is your thought process when you work this out.
Thanks,
This post was deleted for the following reason: This is kind of chatty for askme. -- cortex
I am terrified to be one of the people who gets this wrong, but doesn't the ball cost $0.50? Because $10 more is $10.50, and that together equals $11?
If you want to deal with tax, BOGO offers, etc., I can't help you.
posted by moviehawk at 11:21 AM on March 23, 2011 [1 favorite]
If you want to deal with tax, BOGO offers, etc., I can't help you.
posted by moviehawk at 11:21 AM on March 23, 2011 [1 favorite]
My answer is $0.50. I instantly wanted to say $10 and $11 because it's so simple to read it just as the bat costing $10 which would leave $1 for the ball.
posted by theichibun at 11:21 AM on March 23, 2011
posted by theichibun at 11:21 AM on March 23, 2011
The answer is
posted by muddgirl at 11:22 AM on March 23, 2011 [1 favorite]
Bat+Ball=$11 Bat=$10+Ball $10+2*Ball=$11 Ball=$1/2=$0.50 Bat=$10.50People get this wrong, probably by answering "Ball=$1, Bat=$10", because they don't do the math in their head and use a heuristic "$11-$10=$1." In the end it's really not too far off.
posted by muddgirl at 11:22 AM on March 23, 2011 [1 favorite]
Unless there's a trick I'm not seeing, this is basic algebra.
x + y = 11
x = y + 10
Replace x in the first equation with the second equation: y + 10 + y = 11
Then simplify:
2y + 10 = 11
2y = 1
y = 1/2
posted by valeries at 11:22 AM on March 23, 2011 [2 favorites]
x + y = 11
x = y + 10
Replace x in the first equation with the second equation: y + 10 + y = 11
Then simplify:
2y + 10 = 11
2y = 1
y = 1/2
posted by valeries at 11:22 AM on March 23, 2011 [2 favorites]
I clearly do too many of these puzzles since I just said 50 cents immediately.
posted by Obscure Reference at 11:22 AM on March 23, 2011 [1 favorite]
posted by Obscure Reference at 11:22 AM on March 23, 2011 [1 favorite]
My first thought - that looks like the simultaneous equation problems I had to solve in high school... x+y=11; y+10=x. x=ball, y=bat. Solve for both.
posted by cgg at 11:23 AM on March 23, 2011
posted by cgg at 11:23 AM on March 23, 2011
One of my dad's favorite "brainteasers" is:
If a hog and a half costs a dollar and a half, how much to three hogs cost?
Another one people get wrong all the time.
Why do people get these problems wrong? They just don't think about them long enough, 1, and 2, people are used to dealing in whole numbers. Fractions and decimals can confuse the crap out of folks, are "scary", and therefore aren't the first thing to jump to mind when trying to solve a simple math problem.
posted by phunniemee at 11:24 AM on March 23, 2011
If a hog and a half costs a dollar and a half, how much to three hogs cost?
Another one people get wrong all the time.
Why do people get these problems wrong? They just don't think about them long enough, 1, and 2, people are used to dealing in whole numbers. Fractions and decimals can confuse the crap out of folks, are "scary", and therefore aren't the first thing to jump to mind when trying to solve a simple math problem.
posted by phunniemee at 11:24 AM on March 23, 2011
Here was my thought process:
If x is the value of the ball, then x+10 is the value of the bat. So...
(x+10) + x = 11
2x + 10 = 11
2x = 1
x = 1/2
posted by keep it under cover at 11:27 AM on March 23, 2011
If x is the value of the ball, then x+10 is the value of the bat. So...
(x+10) + x = 11
2x + 10 = 11
2x = 1
x = 1/2
posted by keep it under cover at 11:27 AM on March 23, 2011
Here's my thought process. First, set out what you know from the question:
Divide both sides by 2: $x = $0.50. You have the ball cost.
Add back the $10 to get the bat cost: $10.50.
posted by daisyk at 11:27 AM on March 23, 2011
- Ball cost = $x.
- Bat cost = $(x + 10).
- Total cost = $(x + x + 10) = $11.
Divide both sides by 2: $x = $0.50. You have the ball cost.
Add back the $10 to get the bat cost: $10.50.
posted by daisyk at 11:27 AM on March 23, 2011
If a hog and a half costs a dollar and a half, how much to three hogs cost?
Another one people get wrong all the time.
I must be missing something, but it seems obvious that it's either three dollars, or $2.25, if you assume that buying half a hog is the same price as buying the whole hog, because then the hog seller is left with a half a hog he can't use.
posted by iknowizbirfmark at 11:31 AM on March 23, 2011
Another one people get wrong all the time.
I must be missing something, but it seems obvious that it's either three dollars, or $2.25, if you assume that buying half a hog is the same price as buying the whole hog, because then the hog seller is left with a half a hog he can't use.
posted by iknowizbirfmark at 11:31 AM on March 23, 2011
I think people get this wrong for a couple reasons: first, because we're not really used to thinking about shopping this way - in a real life situation, if you're trying to figure out how much something cost without knowing its price, you just do simple subtraction from the total, not the comparison of two prices. Second, because there's only two numbers in the problem (11 and 10) and the most immediately visceral solution to any problem involving two numbers is either their sum or difference. Basically my brain is going "math problem.. 11.. 10.. answer is probably 1 or 21, even though I don't know what the question is. time for lunch"
posted by theodolite at 11:31 AM on March 23, 2011 [3 favorites]
posted by theodolite at 11:31 AM on March 23, 2011 [3 favorites]
It's because people are lazy morans who don't bother to do math. I knew it was 50 cents right away, but then again, I've been grading grade 5 math assignments for a few weeks now.
posted by GuyZero at 11:31 AM on March 23, 2011 [1 favorite]
posted by GuyZero at 11:31 AM on March 23, 2011 [1 favorite]
My thought process was this:
- of course the ball is going to be cheap. So let's say it costs $0.
- Then the bat would cost $10.
- but we're a dollar short! oh noez!
- we need to keep the difference between the two prices the same. So add the same amount to each price, which is half a dollar.
and I have a PhD in math. So presumably I could do this the writing-out-the-algebra way.
posted by madcaptenor at 11:32 AM on March 23, 2011 [1 favorite]
- of course the ball is going to be cheap. So let's say it costs $0.
- Then the bat would cost $10.
- but we're a dollar short! oh noez!
- we need to keep the difference between the two prices the same. So add the same amount to each price, which is half a dollar.
and I have a PhD in math. So presumably I could do this the writing-out-the-algebra way.
posted by madcaptenor at 11:32 AM on March 23, 2011 [1 favorite]
I'm not sure my thought process is helpful to you, but FWIW it's something like this: "I've heard this puzzle, or ones similar to it, a dozen times before. And the answer is that the less expensive item is half the difference of the two numbers given."
I'm also capable of formally deriving that answer for those who need to see it, but the formal derivation does not consciously enter into my thought process if I just want to give the answer.
Assuming that $1 is the most common wrong answer, my theory about why people give that is that the problem does not conform to real-world situations: If you buy two items at a store, the receipt will show the price of each individual item, and the total price. The difference between the prices is not given. People aren't in the habit of thinking about the difference between two prices, except when comparing two similar items and deciding to buy one or the other. If you're buying ingredients for a peanut butter and jelly sandwich, do you stop and think about the fact that the peanut butter costs $1.50 more than the jelly? Only if you realize that you don't have enough to buy both and can only buy one or the other; if you're going to buy both anyway, you only care what the total price is, not the difference. So "The bat costs $10 more than the ball" doesn't register the way it's written, because who would care what the difference between the two prices is? Even though it's incorrect, it's somewhat understandable that someone not reading closely would parse that sentence simply as "The bat costs $10."
posted by DevilsAdvocate at 11:32 AM on March 23, 2011 [3 favorites]
I'm also capable of formally deriving that answer for those who need to see it, but the formal derivation does not consciously enter into my thought process if I just want to give the answer.
Assuming that $1 is the most common wrong answer, my theory about why people give that is that the problem does not conform to real-world situations: If you buy two items at a store, the receipt will show the price of each individual item, and the total price. The difference between the prices is not given. People aren't in the habit of thinking about the difference between two prices, except when comparing two similar items and deciding to buy one or the other. If you're buying ingredients for a peanut butter and jelly sandwich, do you stop and think about the fact that the peanut butter costs $1.50 more than the jelly? Only if you realize that you don't have enough to buy both and can only buy one or the other; if you're going to buy both anyway, you only care what the total price is, not the difference. So "The bat costs $10 more than the ball" doesn't register the way it's written, because who would care what the difference between the two prices is? Even though it's incorrect, it's somewhat understandable that someone not reading closely would parse that sentence simply as "The bat costs $10."
posted by DevilsAdvocate at 11:32 AM on March 23, 2011 [3 favorites]
Another thought -- this one might look a little more tricky for people who don't have a lot of experience or confidence manipulating numbers because the answer is not a whole number.
The prices given are both in whole dollars, why complicate matters by making the answer require another level of granularity? It could feel almost like a cheat on the part of the question-asker. Fractions and decimals don't feel as friendly as round figures, and if you're bringing pennies into it, that opens up a hundred times more ways to get the wrong answer!
posted by daisyk at 11:32 AM on March 23, 2011
The prices given are both in whole dollars, why complicate matters by making the answer require another level of granularity? It could feel almost like a cheat on the part of the question-asker. Fractions and decimals don't feel as friendly as round figures, and if you're bringing pennies into it, that opens up a hundred times more ways to get the wrong answer!
posted by daisyk at 11:32 AM on March 23, 2011
Fractions and decimals don't feel as friendly as round figures
Again back to the theory that people are stupid or at least that otherwise smart people treat basic math like nuclear waste for some reason.
posted by GuyZero at 11:34 AM on March 23, 2011 [1 favorite]
Again back to the theory that people are stupid or at least that otherwise smart people treat basic math like nuclear waste for some reason.
posted by GuyZero at 11:34 AM on March 23, 2011 [1 favorite]
God forbid we overestimate the cost of a baseball by 50 cents!
posted by muddgirl at 11:36 AM on March 23, 2011 [2 favorites]
posted by muddgirl at 11:36 AM on March 23, 2011 [2 favorites]
My thought process was: is this question chatfilter? If not, why not? I'll go first...
posted by mattbucher at 11:37 AM on March 23, 2011 [2 favorites]
posted by mattbucher at 11:37 AM on March 23, 2011 [2 favorites]
I must be missing something...
You're not missing anything, there's no trick. The answer is that three hogs cost three dollars.
I simply point it out as another illustration of people getting tripped up on simple, straightforward math problems primarily (I assume) because it requires thinking about fractions of numbers rather than whole numbers.
Maybe you guys all went to school with mini math geniuses, but any time fractions came up in class (and I was in the advanced group!) the whole class would groan, "noooo, fractions are haaaard!!!" For some reason, there's just a disconnect there for a lot of people, and folks tend to gloss over fractions to keep things "easy".
posted by phunniemee at 11:37 AM on March 23, 2011
You're not missing anything, there's no trick. The answer is that three hogs cost three dollars.
I simply point it out as another illustration of people getting tripped up on simple, straightforward math problems primarily (I assume) because it requires thinking about fractions of numbers rather than whole numbers.
Maybe you guys all went to school with mini math geniuses, but any time fractions came up in class (and I was in the advanced group!) the whole class would groan, "noooo, fractions are haaaard!!!" For some reason, there's just a disconnect there for a lot of people, and folks tend to gloss over fractions to keep things "easy".
posted by phunniemee at 11:37 AM on March 23, 2011
Again back to the theory that people are stupid or at least that otherwise smart people treat basic math like nuclear waste for some reason.
Cannot favorite that hard enough.
I, like madcaptenor, don't do the "algebra". I just think about it for a bit. "Well, if the ball is a dollar, then the bat is 11 dollars, that's a total of 12 dollars, that's just too much. The ball must be cheaper, how about 50 cents?" Then it works.
posted by King Bee at 11:37 AM on March 23, 2011
Cannot favorite that hard enough.
I, like madcaptenor, don't do the "algebra". I just think about it for a bit. "Well, if the ball is a dollar, then the bat is 11 dollars, that's a total of 12 dollars, that's just too much. The ball must be cheaper, how about 50 cents?" Then it works.
posted by King Bee at 11:37 AM on March 23, 2011
Hmm. Actually, although I wrote out the algebra for solving this problem, and I guess that was the way I solved the first few puzzles of this sort that I saw, I now no longer need to think it through to work them out. Now I either get them immediately (I'm sure the same logic or similar is happening in my head but it's not processed consciously) or after watching a little animation in my mind's eye, with blocks of different length joining and splitting up -- something like 23skidoo's comment.
posted by daisyk at 11:38 AM on March 23, 2011
posted by daisyk at 11:38 AM on March 23, 2011
I think theodolite's explanation of why people get it wrong sounds right.
In the versions I've heard, it's not $11. It's $1.10. (see: http://mitsloan.mit.edu/newsroom/newsbriefs-0605-frederick.php )
I wonder if people are more likely to get it wrong in that version. Especially if you say it out loud "a bat and a ball cost a dollar and ten cents". In that case you think of two things (a bat and a ball, and two amounts of money (A dollar and ten cents), so it's easy for your brain to just go: Bat=Dollar Ball=dime. It'd be a neat experiment to see how the amount affects people's inclination to get it wrong.
posted by ManInSuit at 11:38 AM on March 23, 2011
In the versions I've heard, it's not $11. It's $1.10. (see: http://mitsloan.mit.edu/newsroom/newsbriefs-0605-frederick.php )
I wonder if people are more likely to get it wrong in that version. Especially if you say it out loud "a bat and a ball cost a dollar and ten cents". In that case you think of two things (a bat and a ball, and two amounts of money (A dollar and ten cents), so it's easy for your brain to just go: Bat=Dollar Ball=dime. It'd be a neat experiment to see how the amount affects people's inclination to get it wrong.
posted by ManInSuit at 11:38 AM on March 23, 2011
The OP's question is one of the standard Cognitive Reflection Test questions, which is used to assess how well people can suppress instinctual answers in favor of more reflective answers (this process can be seen in many of the responses above).
The other two questions:
posted by jasonhong at 11:40 AM on March 23, 2011 [1 favorite]
The other two questions:
- 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?
posted by jasonhong at 11:40 AM on March 23, 2011 [1 favorite]
I don't think it has anything to with math, rather that it posits a situation that would probably never occur in real life, ie where you know the total of the transaction and how much the cost one item exceeds the other. A more common situation is where you know the total cost and the cost of one item but not the other so you intuitively think it is going to be that sort of a problem.
posted by canoehead at 11:40 AM on March 23, 2011 [3 favorites]
posted by canoehead at 11:40 AM on March 23, 2011 [3 favorites]
Also, if fractions are scary: what happens when we replace (11, 10) with (22, 20) or (12, 10)?
posted by madcaptenor at 11:40 AM on March 23, 2011
posted by madcaptenor at 11:40 AM on March 23, 2011
If you just asked me this question on the street I'd have just said $1. Because its a bit strangely worded and my default would be to just subtract the 10 from the 11 and be done with it. I don't think I'm stupid or treat math as nuclear waste as GuyZero would have you believe. I just think its a strange question that takes advantage of how our minds generally parse these types of questions combined with the fact that generally, in real life, we don't tend to "check our work" on seemingly simple questions.
posted by bitdamaged at 11:41 AM on March 23, 2011 [3 favorites]
posted by bitdamaged at 11:41 AM on March 23, 2011 [3 favorites]
I guess I'd fail Jason's Cognitive Reflection Test ;-)
posted by bitdamaged at 11:42 AM on March 23, 2011
posted by bitdamaged at 11:42 AM on March 23, 2011
I would say one buck. If you told me I was wrong, i would hit you with the ten buck bat.
posted by Postroad at 11:44 AM on March 23, 2011 [1 favorite]
posted by Postroad at 11:44 AM on March 23, 2011 [1 favorite]
Here's my thought process:
1) Hey, baseball gear is pretty cheap.
2) If the bat costs $10 more, how much does that leave for the ball? $1? No, probably less.
3) Argh, it's one of those trick questions - I need to actually solve the equation.
4) x + x + 10 = 11, 2x = 1, x =0.5
So I guess I'm naturally stupid but have trained myself to avoid embarrassment.
posted by Dr Dracator at 11:47 AM on March 23, 2011 [1 favorite]
1) Hey, baseball gear is pretty cheap.
2) If the bat costs $10 more, how much does that leave for the ball? $1? No, probably less.
3) Argh, it's one of those trick questions - I need to actually solve the equation.
4) x + x + 10 = 11, 2x = 1, x =0.5
So I guess I'm naturally stupid but have trained myself to avoid embarrassment.
posted by Dr Dracator at 11:47 AM on March 23, 2011 [1 favorite]
I heard they asked 110 people this question. 100 more people got it right than got it wrong. The rest couldn't figure out how many people got it wrong...
posted by NoDef at 11:49 AM on March 23, 2011
posted by NoDef at 11:49 AM on March 23, 2011
I don't think I'm stupid or treat math as nuclear waste as GuyZero would have you believe. I just think its a strange question that takes advantage of how our minds generally parse these types of questions
So, no offense, you're treating math as nuclear waste here.
How you mind works or how you add up your grocery bill has nothing to do with math questions. You treat them as math questions. They have their own rules.
Also, I tend to remember these tricks where I guess most people forget them. But halving the difference is the basic trick for this type of question. Most math problems have a trick. Math is as much a trivia contest for recognizing common problem structures as it is about doing computation.
posted by GuyZero at 11:51 AM on March 23, 2011
So, no offense, you're treating math as nuclear waste here.
How you mind works or how you add up your grocery bill has nothing to do with math questions. You treat them as math questions. They have their own rules.
Also, I tend to remember these tricks where I guess most people forget them. But halving the difference is the basic trick for this type of question. Most math problems have a trick. Math is as much a trivia contest for recognizing common problem structures as it is about doing computation.
posted by GuyZero at 11:51 AM on March 23, 2011
A baseball and bat together cost $11. The bat costs $10 more than the ball.
So, I would roughly think: the $10 is part of the $11. It's "how much more the bat costs than the ball." So, the $10 takes up space in the exact middle of the $11, and the remaining amount has to be the same on both ends. (You could visualize it as a classic magic wand.) Add the thing on one end to that $10, and you have the cost of the bat. The thing at the other end is the whole cost of the ball. Now, what can you multiply by 2 and add to $10 to get $11? 50 cents. So, the $11 consists of 50 cents, then $10, then another 50 cents. One of those 50 cents is the whole cost of the ball, and that's the answer. (Thus, the bat is $10.50).
To translate this into algebra (though this is all an attempt to formalize my rough thinking after the fact):
11 = cost of bat + ball
x = cost of ball
x + (x+10) = 11
We can tidy that up: 2x + 10 = 11
After subtracting 10 from both sides of the equation, then canceling out the "minus 10" from both sides, we get: 2x = 11 - 10 = 1
Divide both sides by 2 to isolate x, and you get: (2x)/x = x = 1/2
The numbers have represented dollars all along, so 1/2 = half a dollar = 50 cents.
posted by John Cohen at 11:54 AM on March 23, 2011
So, I would roughly think: the $10 is part of the $11. It's "how much more the bat costs than the ball." So, the $10 takes up space in the exact middle of the $11, and the remaining amount has to be the same on both ends. (You could visualize it as a classic magic wand.) Add the thing on one end to that $10, and you have the cost of the bat. The thing at the other end is the whole cost of the ball. Now, what can you multiply by 2 and add to $10 to get $11? 50 cents. So, the $11 consists of 50 cents, then $10, then another 50 cents. One of those 50 cents is the whole cost of the ball, and that's the answer. (Thus, the bat is $10.50).
To translate this into algebra (though this is all an attempt to formalize my rough thinking after the fact):
11 = cost of bat + ball
x = cost of ball
x + (x+10) = 11
We can tidy that up: 2x + 10 = 11
After subtracting 10 from both sides of the equation, then canceling out the "minus 10" from both sides, we get: 2x = 11 - 10 = 1
Divide both sides by 2 to isolate x, and you get: (2x)/x = x = 1/2
The numbers have represented dollars all along, so 1/2 = half a dollar = 50 cents.
posted by John Cohen at 11:54 AM on March 23, 2011
My thought process:
1. I hate math and word problems.
2. Well, obviously the answer isn't $10 because that would be too obvious.
3. I don't know. I'm stupid and treat math as nuclear waste.
4. Wow. People think they're pretty awesome in these comments.
posted by KogeLiz at 11:56 AM on March 23, 2011 [2 favorites]
1. I hate math and word problems.
2. Well, obviously the answer isn't $10 because that would be too obvious.
3. I don't know. I'm stupid and treat math as nuclear waste.
4. Wow. People think they're pretty awesome in these comments.
posted by KogeLiz at 11:56 AM on March 23, 2011 [2 favorites]
4. Wow. People think they're pretty awesome in these comments.
Kids get good at baseball because of social pressure. So I'm assuming the same thing works for math.
posted by GuyZero at 11:59 AM on March 23, 2011 [1 favorite]
Kids get good at baseball because of social pressure. So I'm assuming the same thing works for math.
posted by GuyZero at 11:59 AM on March 23, 2011 [1 favorite]
I don't think the reason people get it wrong is because it involves fractions; I'm pretty sure some set of people would still get the wrong answer if the numbers were doubled in the original question and the whole problem could be solved with whole numbers.
It's easy to skim the question, see the phrase "bat costs $10" and immediately jump to, well, together they're $11, therefore the ball must be $1. Which is exactly what I did at first, and I lurves me the mathiness of math.
The error is obvious if you then plug those numbers into either equation to check whether you're correct, which is the next thing I did because it's obviously a trick question. But it looks correct enough on the surface that many people won't bother to do that, and in all honesty if it hadn't been presented as "hey! This is a trick question that a lot of people get wrong!" I'd have easily fallen for it too.
Algebraically I ended up working it slightly differently than others seem to have done:
X+Y=11; X+10=Y
so
X=11-Y; X=Y-10
therefore
11-Y=Y-10
21-Y=Y
21=2Y
10.50 = Y
posted by ook at 12:03 PM on March 23, 2011 [1 favorite]
It's easy to skim the question, see the phrase "bat costs $10" and immediately jump to, well, together they're $11, therefore the ball must be $1. Which is exactly what I did at first, and I lurves me the mathiness of math.
The error is obvious if you then plug those numbers into either equation to check whether you're correct, which is the next thing I did because it's obviously a trick question. But it looks correct enough on the surface that many people won't bother to do that, and in all honesty if it hadn't been presented as "hey! This is a trick question that a lot of people get wrong!" I'd have easily fallen for it too.
Algebraically I ended up working it slightly differently than others seem to have done:
X+Y=11; X+10=Y
so
X=11-Y; X=Y-10
therefore
11-Y=Y-10
21-Y=Y
21=2Y
10.50 = Y
posted by ook at 12:03 PM on March 23, 2011 [1 favorite]
X + Y = $11 X - Y = $10 --------------- 2X = $21 X = $10.50 Y = $ 0.50
posted by misterbrandt at 12:04 PM on March 23, 2011 [1 favorite]
This thread is closed to new comments.
posted by theodolite at 11:20 AM on March 23, 2011 [9 favorites]