A very short quiz

How Many questions did you get correct

  • Zero

    Votes: 4 7.8%
  • One

    Votes: 2 3.9%
  • Two

    Votes: 11 21.6%
  • Three

    Votes: 34 66.7%

  • Total voters
    51

noway2

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Saw this short quiz on MSN today and thought I would share (link: http://www.msn.com/en-us/lifestyle/...0-percent-of-people-can/ar-AAtnwBv?li=BBnb7Kz)

Before you get started, we’ll give you a quick hint: the questions might not be as easy as they first seem. A 2003 study found that students attending some of the nation’s most prestigious universities (including Harvard and Yale) failed to get all three of these questions correct; only 17 percent received a perfect score.

Think you have what it takes? Give it a shot! Here are the three questions:

1. A bat and a ball cost $1.10 in total. The bat costs $1 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?

Answers are below, but have been colored white to hide them. You should be able to select the text with your mouse to read:
1. $0.05. If you guessed 10 cents, you’re not alone. However, if that were the case, the bat would cost $1.20—not $1.10. On the other hand, purchasing a 5 cent ball and a bat priced at $1.05 (which is $1 more expensive than 5 cents) would total $1.10, instead.

2. 5 minutes. Although you might have answered 100 minutes, the actual time is a little less than that. Since the question reveals that it would take 5 minutes for 1 widget machine to make 1 widget, you can determine that it would take 5 minutes for 100 widget machines to make 100 widgets.

3. 47 days. At first, your gut might tell you it would take 24 days. But remember: Since the area of the lake covered in lily pads doubles every day, a patch that covers half the lake would fully cover it in just one day. Subtract one day from 48 days, and what do you get? 47 days.
 
Got them all, but if you’d just asked mo on the street I might have missed #2
 
It's understandable how you could get them wrong if you aren't thinking/paying attention. They aren't really that hard though.
 
It's understandable how you could get them wrong if you aren't thinking/paying attention. They aren't really that hard though.
Bingo. The article that I linked to, has a link in it to a fairly long research paper on this subject and the development of the quiz. The questions are such that they aren't difficult, but the immediately intuitive answer is incorrect. Surprisingly a very small percentage, about 17%, of the overall population gets all three of them correct. Of the subgroups tested students at MIT scored the highest overall typically 48% getting all of them correct. The theory of the quiz is one of testing patience and whether or not you will process information before developing an answer or if you'll intuitively try to solve the problem.

The first quiz I found easy to solve by writing a set of coupled algebraic equations (x+y = 110, x=y+100) and solving. The second one I thought was intuitive. The third one should be intuitively obvious too but I thought too much into it and solved it out the hard way. My first thought on it was that it was a half-life equation, which has an exponential response as it is a linear first order differential equation and I thought that it would be 2^x, I then started writing out (thinking of it doubling in size, 1,2,4,8,16 ... yup 2 to the X). So I wrote the equation 2^48 = 100 for 100% coverage. 2^48 is a very large number but I divided this in two (half coverage) and solved 2^x = this number by taking the log of the half of the number and then dividing by log(2).... Duh, at that point it again should have been obvious and got the correct result of 47.

Another one I like is the Myer's Brigg's (like) personality test: https://www.16personalities.com/personality-types and I recall that one coming up on the old Canook site once and noting that there were a lot of logician's (which I score as too) present on the forum, so I would not be surprised to see a fair number of high scores on this quiz here.
 
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Bingo. The article that I linked to, has a link in it to a fairly long research paper on this subject and the development of the quiz. The questions are such that they aren't difficult, but the immediately intuitive answer is incorrect. Surprisingly a very small percentage, about 17%, of the overall population gets all three of them correct. Of the subgroups tested students at MIT scored the highest overall typically 48% getting all of them correct. The theory of the quiz is one of testing patience and whether or not you will process information before developing an answer or if you'll intuitively try to solve the problem.

The first quiz I found easy to solve by writing a set of coupled algebraic equations (x+y = 110, x=y+100) and solving. The second one I thought was intuitive. The third one should be intuitively obvious too but I thought too much into it and solved it out the hard way. My first thought on it was that it was a half-life equation, which has an exponential response as it is a linear first order differential equation and I thought that it would be 2^x, I then started writing out (thinking of it doubling in size, 1,2,4,8,16 ... yup 2 to the X). So I wrote the equation 2^48 = 100 for 100% coverage. 2^48 is a very large number but I divided this in two (half coverage) and solved 2^x = this number by taking the log of the half of the number and then dividing by log(2).... Duh, at that point it again should have been obvious and got the correct result of 47.

Another one I like is the Myer's Brigg's (like) personality test: https://www.16personalities.com/personality-types and I recall that one coming up on the old Canook site once and noting that there were a lot of logician's (which I score as too) present on the forum, so I would not be surprised to see a fair number of high scores on this quiz here.

You're more thorough than I am. Since I'm not graded for showing work anymore, I just process stuff in my head and live with the errors. I'm not an engineer so I can afford to be wrong. All of the equations you mentioned did come to mind though.
 
It worries me that only 17% of the population get all three correct.

Just saying.....
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Something else people do, besides not thinking it through (e.g., setting up the right equations) before popping off an answer, is to not check it after they come up with an answer (substitute their answer into the original question) to see if it comes out right. Always a good idea...
 
I'm afraid Bernie's answers would have been:

1. Drop the price total to $0.66 by offering a Government subsidy on bats and balls.
2. Do we still manufacture things in this country? I thought we took care of that!
3. Call in the EPA and fine those lily pads for violating the Clean Water Act.
 
someone use common core and explain this to me please.

1. $0.05. If you guessed 10 cents, you’re not alone. However, if that were the case, the bat would cost $1.20—not $1.10. On the other hand, purchasing a 5 cent ball and a bat priced at $1.05 (which is $1 more expensive than 5 cents) would total $1.10, instead.
 
someone use common core and explain this to me please.

1. $0.05. If you guessed 10 cents, you’re not alone. However, if that were the case, the bat would cost $1.20—not $1.10. On the other hand, purchasing a 5 cent ball and a bat priced at $1.05 (which is $1 more expensive than 5 cents) would total $1.10, instead.

Not sure if serious lol.

The bat is $1 dollar more than the ball. So if the ball costs 5 cents and the bat is 1 dollar more than the ball, the bat costs 1 dollar and 5 cents. The 2 add up to 1 dollar and 10 cents.

If the ball was 10 cents and the bat cost 1 dollar more than that then the bat would cost 1 dollar and 10 cents. Add that to the 10 cent ball and you come up with 1 dollar and 20 cents not 1 dollar and 10 cents.

I think the confusion is that it should say the bat and ball would cost $1.20 not the bat by itself.
 
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The Common Core version:

Balls aren't worth much as their high symmetry unfairly competes against and denigrates symmetry-challenged shapes. They should be undervalued in our society. Let's call it a nickel (0.050). Bats, though clearly perpetuating a phallic misogynistic mystery-cult recreational activity, are made from slow-growth, difficult to renew hardwood resources. So, let's say we feel that it is worth a dollar more than the ball (1.05). The total? Like, let's see, my iphone says that 1.05 + 0.05 = 1.10. I feel that's right - for me.
 
I got all three correct "intuitively" - no equations necessary except 10/2 on #1. Saw the trap and ignored it on each.
 
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Not sure if serious lol.

The bat is $1 dollar more than the ball. So if the ball costs 5 cents and the bat is 1 dollar more than the ball, the bat costs 1 dollar and 5 cents. The 2 add up to 1 dollar and 10 cents.

If the ball was 10 cents and the bat cost 1 dollar more than that then the bat would cost 1 dollar and 10 cents. Add that to the 10 cent ball and you come up with 1 dollar and 20 cents not 1 dollar and 10 cents.

I think the confusion is that it should say the bat and ball would cost $1.20 not the bat by itself.

Ok I wasn’t figuring the cost of the ball plus 1 dollar.
 
The first quiz I found easy to solve by writing a set of coupled algebraic equations (x+y = 110, x=y+100) and solving. The second one I thought was intuitive. The third one should be intuitively obvious too but I thought too much into it and solved it out the hard way. My first thought on it was that it was a half-life equation, which has an exponential response as it is a linear first order differential equation and I thought that it would be 2^x, I then started writing out (thinking of it doubling in size, 1,2,4,8,16 ... yup 2 to the X). So I wrote the equation 2^48 = 100 for 100% coverage. 2^48 is a very large number but I divided this in two (half coverage) and solved 2^x = this number by taking the log of the half of the number and then dividing by log(2).... Duh, at that point it again should have been obvious and got the correct result of 47.


I got em all right, but what freakin language is that?!?!


;)
 
One way to view #2 would be:

Given: 5 widgit/5min/5machine = (5*widgit/25*machine*min) = 1*widgit/5*machine*min.

Thus to make 100 widgits: 100*widgit x (5*machine*min/1*widgit) = 500*machine*min (required)

and

500*machine*min x (1/100 machines) = 5 mins.

When put this way, it is actually rather amazing what our minds can do "intuitively."
 
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And, to release my inner geek, #2 is actually problematic as stated in the quiz. The answer given in the quiz (and my post above) assumes a linear relation extrapolated from the single data point given. Were the machines' output to be coupled in some way, such that, say, six machines run more efficiently than two sets of three or six independently, then the answer might well be different. The problem presumes that the machines work independently.

Here's another example.

Consider two points (x, y) as (0, 0) and (2, 12). Two points determine a straight line, in this case, y = 6x + 0. However, those same two points could lie on the parabola, y = 3x^2.

african-or-european-swallow.jpg
 
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I got frustrated halfway through #1 and gave up, called Rev Al to set up a demonstration in front of the offending website and got my Obama phone in the mail a day later.
 
And, to release my inner geek, #2 is actually problematic as stated in the quiz. The answer given in the quiz (and my post above) assumes a linear relation extrapolated from the single data point given. Were the machines' output to be coupled in some way, such that, say, six machines run more efficiently than two sets of three or six independently, then the answer might well be different. The problem presumes that the machines work independently.

Here's another example.

Consider two points (x, y) as (0, 0) and (2, 12). Two points determine a straight line, in this case, y = 6x + 0. However, those same two points could lie on the parabola, y = 3x^2.

african-or-european-swallow.jpg
Are you from Oxford?
 
I actually thought the very short quiz was "how many questions did you get right?" And since that was the only question, the answer was "one".

But now that I think about it, if I said "zero", would it start an endless logical loop and warp the space-time continuum?
 
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Bingo. The article that I linked to, has a link in it to a fairly long research paper on this subject and the development of the quiz. The questions are such that they aren't difficult, but the immediately intuitive answer is incorrect. Surprisingly a very small percentage, about 17%, of the overall population gets all three of them correct. Of the subgroups tested students at MIT scored the highest overall typically 48% getting all of them correct. The theory of the quiz is one of testing patience and whether or not you will process information before developing an answer or if you'll intuitively try to solve the problem.

The first quiz I found easy to solve by writing a set of coupled algebraic equations (x+y = 110, x=y+100) and solving. The second one I thought was intuitive. The third one should be intuitively obvious too but I thought too much into it and solved it out the hard way. My first thought on it was that it was a half-life equation, which has an exponential response as it is a linear first order differential equation and I thought that it would be 2^x, I then started writing out (thinking of it doubling in size, 1,2,4,8,16 ... yup 2 to the X). So I wrote the equation 2^48 = 100 for 100% coverage. 2^48 is a very large number but I divided this in two (half coverage) and solved 2^x = this number by taking the log of the half of the number and then dividing by log(2).... Duh, at that point it again should have been obvious and got the correct result of 47.

Another one I like is the Myer's Brigg's (like) personality test: https://www.16personalities.com/personality-types and I recall that one coming up on the old Canook site once and noting that there were a lot of logician's (which I score as too) present on the forum, so I would not be surprised to see a fair number of high scores on this quiz here.
It says I'm a logician as well, we're on 3% of the population. I'm sure my wife's very thankful for that. *sarc off*
 
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Let x = price of bat; y = price of ball
x + y = 1.10
x = y + 1.0
2y + 1.0 = 1.10
2y = 0.10
y = 0.05
x = 1.05
True, but it takes longer to write "x+y = 1.1" than it takes to solve the problem by simply looking at it.
 
And, to release my inner geek, #2 is actually problematic as stated in the quiz. The answer given in the quiz (and my post above) assumes a linear relation extrapolated from the single data point given. Were the machines' output to be coupled in some way, such that, say, six machines run more efficiently than two sets of three or six independently, then the answer might well be different. The problem presumes that the machines work independently.

Here's another example.

Consider two points (x, y) as (0, 0) and (2, 12). Two points determine a straight line, in this case, y = 6x + 0. However, those same two points could lie on the parabola, y = 3x^2.

african-or-european-swallow.jpg

My daughter asked my wife to help with math worksheet tonight. My daughter said how do you do this, my wife looked at it and said,” Well honey I just used the quadratic equation to get the correct answer but I’m not sure how your teacher is telling how to do it.” Both myself and my daughter just looked at each other and shook our heads.
 
And, to release my inner geek, #2 is actually problematic as stated in the quiz. The answer given in the quiz (and my post above) assumes a linear relation extrapolated from the single data point given. Were the machines' output to be coupled in some way, such that, say, six machines run more efficiently than two sets of three or six independently, then the answer might well be different. The problem presumes that the machines work independently.

Here's another example.

Consider two points (x, y) as (0, 0) and (2, 12). Two points determine a straight line, in this case, y = 6x + 0. However, those same two points could lie on the parabola, y = 3x^2.

african-or-european-swallow.jpg

Making this way too complicated.

9 women have 9 babies in 9 months. How long does it take 100 women to have 100 babies?

Different perspective :)
 
Are you from Oxford?

No. I come from Camelot, and have ridden the length and breath of the land, across the kingdom of Mercia ...

Actually, its been claimed by some over the past 15-20 years or so that I came from Hell or Mordor or some such sulfurous environ.
 
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Making this way too complicated.

9 women have 9 babies in 9 months. How long does it take 100 women to have 100 babies?

Different perspective :)

Different problem. One has implicit additional information in the analogy you suggest to wit: experiential evidence on which to suppose that women do not bear children in coupled or synergistic or non-linear fashion. That is not the case here with this machine problem.

Well, ok, maybe "coupling" does have something to do with bearing children! But ...
 
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Different problem. One has implicit additional information in the analogy you suggest to wit: experiential evidence on which to suppose that women do not bear children in coupled or synergistic or non-linear fashion. That is not the case here with this machine problem.

Well, ok, maybe "coupling" does have something to do with bearing children! But ...

Yes of course, but for the original question to have an answer from the info given, you have to extrapolate linearly, and the point of my exactly parallel restatement of the problem is that it makes answer obvious instead of tricky.
 
I got the last two correct. The first one, I may have to start an expletive laced thread down in Tortuga to explain my thoughts on that one.:D
 
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3/3

Gonna test the wife and son (10) tomorrow. Pretty good chance he scores higher. :D. Math is not her strong suit...
 
Not sure if serious lol.

The bat is $1 dollar more than the ball. So if the ball costs 5 cents and the bat is 1 dollar more than the ball, the bat costs 1 dollar and 5 cents. The 2 add up to 1 dollar and 10 cents.

If the ball was 10 cents and the bat cost 1 dollar more than that then the bat would cost 1 dollar and 10 cents. Add that to the 10 cent ball and you come up with 1 dollar and 20 cents not 1 dollar and 10 cents.

I think the confusion is that it should say the bat and ball would cost $1.20 not the bat by itself.

  • Yeah. I was about to backhand female dog slap the guy at the counter over at Academy this evening. He rung up a bat and ball for me and told me I owed $1.10 total for both. I asked, "Wow! Did Rawlings and Louisville Slugger overproduce a bunch of product, or did they simply forget the economic concept of inflation?" I gave him a dime before I could dig my dollar bill out of my pocket. He said, "You ain't leavin here with both of those with this dime you just gave me. You can have that ball but you still owe me a dollar more if you think you're walking out of here with that bat too.":D
 
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No. I come from Camelot, and have ridden the length and breath of the land, across the kingdom of Mercia ...
Actually, its been claimed by some over the past 15-20 years or so that I came from Hell or Mordor or some such sulfurous environ.
Jerk... You made me spit my coffee this morn. ;)
We've had an interesting time trying to hire people from Oxford, your wit indicates you possibly moved there.
 
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