Three easy math problems. Can SMP do better than MIT?
 

Take this quiz

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

Did you get them all right?

Undergrads at elite universities really struggled with them. The percentage of students quizzed at each university who got all three answers right were as follows:

MIT: 48%
Princeton: 26%
Carnegie Mellon: 25%
Harvard: 20%
U.Michigan (Ann Arbor): 14%
Bowling Green: 13%
U.Michigan (Dearborn): 6%
Michigan State: 6%
U.Toledo: 5%

LINK

Re: Three easy math problems. Can SMP do better than MIT?
 

My answers:

<font color="white">1 - 0.05
2 - 5 minutes
3 - 47 days</font>

How did I do?

Re: Three easy math problems. Can SMP do better than MIT?
 

<font color="white">1. $0.05
2. 5 minutes
3. 47 days
</font>

Re: Three easy math problems. Can SMP do better than MIT?
 

Grunch

1, ball cost $0.05
2, 100 machines takes 5 minutes to make 100 widgets.
3, 47 days

Now to check the answers!

Edit - I'm an undergrad at Loughborough uni England

Re: Three easy math problems. Can SMP do better than MIT?
 

By the way, this quiz was not the point of the paper I got it from. The actual point was much more interesting.

The quiz was given so the correctness of those answers could be correlated with the answers to questions about risk-aversion and discount rates.

Would you rather have a) $1000 for sure, or b) a 90% chance of $5000?

The people who got 3 out of 3 correct on the quiz were much more likely to take the 90% chance of $5000 than were the people who got 0 out of 3 correct on the quiz.

In general, the paper concludes that intelligence of the sort required to do well on the quiz is positively correlated with a willingness to take +EV gambles, and also with lower future discount rates (e.g., people who aced the quiz were more likely to take $140 next year instead of $100 now).

That's kind of interesting.

Re: Three easy math problems. Can SMP do better than MIT?
 

<font color="white">

(1) A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost?

x + y = 1.1
y = x + 1
x + x + 1 = 1.1
2x + 1 = .1
2x = .1
x = .05

.05 + y = 1.1
y = 1.05

(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

5 machines / 5 minutes = 5 widgets

1 machine / 5 minutes = 1 widget

1 machine / 1 widget = 5 minutes

1 machine 100 widgets
--------- * ------------ = 1 * X = X
1 widget 100 machines

X = 5 minutes

(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?

On the 48th day, the patch covers the entire lake. Since the previous day has half as much covered as the current (problem posed in reverse), the 47th day has half the lake covered.

</font>

Edit: Math Major, Undergrad Liberal Arts College

Also, I gamble it up for 5k since the expected EV's are $4,500 vs. $1,000 - that's too big a differential to ignore.

Re: Three easy math problems. Can SMP do better than MIT?
 

My answers: <font color="white">
1) The bat costs $1.05
2) 5 min
3) 47 days
</font>

Seemed easy enough, hopefully I'm not stupid.

Edit: GDI I am stupid ... I checked the first one twice and still put the wrong one.

Re: Three easy math problems. Can SMP do better than MIT?
 

<font color="white"> 5 cents
5 minutes
47 days </font>

Re: Three easy math problems. Can SMP do better than MIT?
 

<font color="white">
1).05
2)5 min
3)47
</font>

did we at least beat Toledo?

Re: Three easy math problems. Can SMP do better than MIT?
 

(not reading the rest of the thread, just responding the original test)

(1) The ball costs $0.05

(2) What the hell is a widget?! j/k [img]/images/graemlins/smile.gif[/img]. 5 minutes is the answer.

(3) 47 days.



It's really amazing that these people couldn't get at least 99% on these easy questions

Re: Three easy math problems. Can SMP do better than MIT?
 

1 - .05
2 - 5 min
3 - 47 days

Simple enough. #1 was the easiest.

EDIT: SMP seems to be making a strong showing.

Re: Three easy math problems. Can SMP do better than MIT?
 

it seems absurd that anyone would get any of these questions wrong. I would guess that the figures for the various schools are bs.

Re: Three easy math problems. Can SMP do better than MIT?
 

I taught physics and astronomy at a public university and I have no doubt that the vast majority of the students I taught would not be able ot answer these questions. Admittedly these were non-major, elective courses, but still.

Re: Three easy math problems. Can SMP do better than MIT?
 

Here's what I think the people who got them wrong would have said:

1) 0.1$
2) 100 minutes
3) 24 days

But, IMO, anybody who graduated from high school math should get

1) 0.05$
2) 5 minutes
3) 47 days

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
I taught physics and astronomy at a public university

[/ QUOTE ]
No wonder all you guys think circles around me. I do love this forum though. Say, I found this math quiz to be extremely easy. I think I could have tackled it in the 6th grade, and I don't consider myself all that smart. Is this dumbness a recent phenomenon? Could entry level college students have done better on it 30 years ago? 50? If so, what has changed?

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
Could entry level college students have done better on it 30 years ago? 50? If so, what has changed?


[/ QUOTE ]
I remember reading a newspaper article from 1900 bemoaning the sorry state of higher education. X percentage of Harvard freshmen couldn't identify such and such country. Nothing has changed, we're still as dumb as we used to be ;0)

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
Here's what I think the people who got them wrong would have said:

1) 0.1$
2) 100 minutes
3) 24 days

But, IMO, anybody who graduated from high school math should get

1) 0.05$
2) 5 minutes
3) 47 days

[/ QUOTE ]

I dont think its the math that is hanging anyone up. Majority of people are just poor critical thinkers. The math required to do these is probably on a 2nd grade level. I cant believe that schools dont make logic/problem solving/critical thinking type classes mandatory. That said those stats are still surprising.

Re: Three easy math problems. Can SMP do better than MIT?
 

Off the top of my head and quickly...

A1) $0.05

A2) 5 minutes

A3) 24 hours &lt;&lt;edit: i obviously completely misread that problem

Re: Three easy math problems. Can SMP do better than MIT?
 

These were extremely easy. It's very shocking how bad these students from top tier schools did. And I got my degree at a 4-year state school. It doesn't surprise me that we all got the questions right. We got a pretty well educated, smart group of people here.

edit&gt;&gt;I didn't even click the link yet. Just noticed that this article is about much more than these 3 questions. Going to read it now.

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
U.Michigan (Ann Arbor): 14%
Bowling Green: 13%
U.Michigan (Dearborn): 6%
Michigan State: 6%
U.Toledo: 5%


[/ QUOTE ]

Are these really ELITE universities, deserving of being on the same list as MIT, Princeton, Carnegie Mellon, and Harvard?

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
I dont think its the math that is hanging anyone up. Majority of people are just poor critical thinkers. The math required to do these is probably on a 2nd grade level. I cant believe that schools dont make logic/problem solving/critical thinking type classes mandatory. That said those stats are still surprising.

[/ QUOTE ]

The math is closer to a 5th grade level. I think the ability to find the correct answer is determined by your ability to spot trick questions. In order to get the correct answers, you would likely first have to think to yourself, "These seem to obvious; there must be something more." And from that point, whether you know how to do the math or not, you will not pick the obviously incorrect answers.

It's not incredibly surprising that the overall population at some elite schools score so low. Consider the fact that most programs do not require excellent math skills. My girlfriend is very good at writing essays (she's in a Media Studies program) but she could not answer these questions. Perhaps if she actually took the time to think about it, she could work through it, but most people don't see that kind of waste of time as worthwhile.

Re: Three easy math problems. Can SMP do better than MIT?
 

1. $.05

2. five minutes

3. 47

..right?

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]

(1) A bat and a ball cost $1.10 in total. The bat costs a dollar more than the ball. How much does the ball cost?


[/ QUOTE ]

This is the easy one using straight alegebra with no ambiguity.

x + (x + 1) = 1.10
x = 0.5

[ QUOTE ]

(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?


[/ QUOTE ]

The true answer to this is a system of solutions because there is ambiguity introduced with the terms "5 machines" it does not explicitly state that these are "identical" machines with the same production rate so there is techinically an infinite number of solutions.

[ QUOTE ]

(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?


[/ QUOTE ]

This is easy if we use day unit measurements because when the "exact" time that the lily pads cover half the lake is dependent on the initial size of the lily patch at the exponentally preportional size of the lake to that initial size of the lily patch.

But it will always cross the "half lake threshold" T-1 in unit days where T = the whole lake being covered.

-Gryph

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
The true answer to this is a system of solutions because there is ambiguity introduced with the terms "5 machines" it does not explicitly state that these are "identical" machines with the same production rate so there is techinically an infinite number of solutions.


[/ QUOTE ]

Lets disambiguate:
uniform machines- problem makes sense, has one clear answer

the 100 machines are different types of machines- makes the correct answer: it is impossible to know from this information

The implication is that the machines are identical or at least average out to some production rate. Technically the words on the paper don't mean this, but it is implied by the context and the fact that the 5 machines would be irrelevant if they did not relate in some important way to the 100 machines.

http://www.sil.org/linguistics/Gloss...Implicatur.htm

Re: Three easy math problems. Can SMP do better than MIT?
 

I'm going to MIT, baby! SHIP IT.

ScottieK

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
[ QUOTE ]
The true answer to this is a system of solutions because there is ambiguity introduced with the terms "5 machines" it does not explicitly state that these are "identical" machines with the same production rate so there is techinically an infinite number of solutions.


[/ QUOTE ]

Lets disambiguate:
uniform machines- problem makes sense, has one clear answer

the 100 machines are different types of machines- makes the correct answer: it is impossible to know from this information

The implication is that the machines are identical or at least average out to the some production rate. Technically the words on the paper don't mean this, but it is implied by the context and the fact that the 5 machines would be irrelevant if they did not relate in some important way to the 100 machines.

http://www.sil.org/linguistics/Gloss...Implicatur.htm

[/ QUOTE ]

100% Agreed...I was just nit-ing the words because question (2) is technically more ambiguous than questions (1) and (3). It is a matter of function...I could argue any number of answers are the solution to question (2) within the realm of the literal context of the word problem.

I still stand by the premise that the question is ambiguous to the point of forcing assumptions which is the basis of the discrepency that the study was suppposed to quantify.

A more properly worded question would induce less error into the answers and be of greater scientific value. It would be interesting to study in isolation the shift in wording and whether it has bearing on the outcome.

-Gryph

Re: Three easy math problems. Can SMP do better than MIT?
 

1. Ball costs $0.05
2. 1 min
3. 47 days (but i cheated i already heard this one many times before)

Bah- i'm a retard on question 2- saw the trick but put down 1 min anyway, because i'm a tard who doesn't double check his answers.

Re: Three easy math problems. Can SMP do better than MIT?
 

Might be fun:

Can everybody still calculate question 3 if we say for instance 3,15% of the lake covered? (it shouldnt be too hard, but notice I just made this percentage up so you probably need a calculator to get the decimal answer)

Re: Three easy math problems. Can SMP do better than MIT?
 

ln(0.15)/ln(2) + 48 ~ 45.263 (days)

Unless you meant 3.15%, in which case it would be:

ln(0.0315)/ln(2) + 48 ~ 43.011 (days)

Re: Three easy math problems. Can SMP do better than MIT?
 

Correct, but you taught a physics class, right? Was mainly wondering if people without too much mathematical background know this stuff.

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
Correct, but you taught a physics class, right? Was mainly wondering if people without too much mathematical background know this stuff.

[/ QUOTE ]

I doubt it.

Re: Three easy math problems. Can SMP do better than MIT?
 

[ QUOTE ]
Correct, but you taught a physics class, right? Was mainly wondering if people without too much mathematical background know this stuff.

[/ QUOTE ].

Not a chance in hell.