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

[_TKO_]

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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.

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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.

[hmkpoker]

1. $.05

2. five minutes

3. 47

..right?

[etgryphon]

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(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?


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

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

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


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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.

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(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?


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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

[Bork]

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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.


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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

[ScottieK]

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

ScottieK

[etgryphon]

[ 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

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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

[tolbiny]

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.

[Charon]

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)

[Borodog]

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)

[Charon]

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