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Jason11
science forum beginner

Joined: 25 Mar 2006
Posts: 10

Posted: Thu Jul 13, 2006 7:49 pm    Post subject: Re: sat prep question

Pubkeybreaker wrote:
 Quote: Jason wrote: I have to disagree with the people who think this is a stupid question. You need to learn some more linear algebra. I think it is quite interesting. What is being tested here is the ability to use the properties of linear funtions (without knowing the term linear functions -- but people should know the properties of addition and subtraction). It is possible to derive a linear function that gives ANY value as the correct answer. This is what makes the problem ridiculous.

Give an example then of a linear function that meets both givens and
gives an answer other than 6.
Pubkeybreaker
science forum Guru

Joined: 24 Mar 2005
Posts: 333

Posted: Thu Jul 13, 2006 9:00 pm    Post subject: Re: sat prep question

Jason wrote:
 Quote: Pubkeybreaker wrote: Jason wrote: I have to disagree with the people who think this is a stupid question. You need to learn some more linear algebra. I think it is quite interesting. What is being tested here is the ability to use the properties of linear funtions (without knowing the term linear functions -- but people should know the properties of addition and subtraction). It is possible to derive a linear function that gives ANY value as the correct answer. This is what makes the problem ridiculous. Give an example then of a linear function that meets both givens and gives an answer other than 6.

Moron. I gave a hint when I said to study linear algebra, but you
did not listen.

Let T(x,y) = ax + by - c, for some a,b,c to be chosen.

We have T(5,3) = 6
T(4,1) = 2

Whence 5a + 3b - c = 6
4a + b - c = 2

This is a system of 2 equations in 3 unknowns and has INFINITELY
many solutions. It even has infinitely many integral solutions.
For example, a = 2, b = 1, c = 7

Whence T(x,y) = 2x + y - 7 Or, if you prefer the original notation:
x T y = 2x + y - 7.

T is a function that has both addition and subtraction.

T(5,3) = 6, T(4,1) = 2 and we get T(7, 3) = 10

What is it that compels you to argue with people who know more about
this subject than you do?
Darrell

Joined: 04 Jun 2005
Posts: 78

Posted: Fri Jul 14, 2006 6:40 am    Post subject: Re: sat prep question

"Pubkeybreaker" <Robert_silverman@raytheon.com> wrote in message
 Quote: Yet more nonsense. There is no such thing as the 'best' answer.

For multiple choice, there is indeed.

 Quote: If you think there is such a thing, please specify how you measure whether one answer is better than another. Specify your metric.

By what the grading key says the best answer is. What else.

--
Darrell
G.E. Ivey
science forum Guru

Joined: 29 Apr 2005
Posts: 308

Posted: Sat Jul 15, 2006 11:48 am    Post subject: Re: sat prep question

 Quote: Pubkeybreaker wrote: Jason wrote: I have to disagree with the people who think this is a stupid question. You need to learn some more linear algebra. I think it is quite interesting. What is being tested here is the ability to use the properties of linear funtions (without knowing the term linear functions -- but people should know the properties of addition and subtraction). It is possible to derive a linear function that gives ANY value as the correct answer. This is what makes the problem ridiculous. Give an example then of a linear function that meets both givens and gives an answer other than 6. To find five different linear functions that meet both conditions and give each of the five answers is a trivial exercise in linear algebra.

Notice, by the way, that the problem, as originally posted (which may NOT be the way it was actually given, especially since this is not grammatically correct) was
"If T represents an operation that
It does not say "includes ONLY addition and subtraction".

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