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sat prep question
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Jason11
science forum beginner


Joined: 25 Mar 2006
Posts: 10

PostPosted: Thu Jul 13, 2006 7:49 pm    Post subject: Re: sat prep question Reply with quote

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.
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Pubkeybreaker
science forum Guru


Joined: 24 Mar 2005
Posts: 333

PostPosted: Thu Jul 13, 2006 9:00 pm    Post subject: Re: sat prep question Reply with quote

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?
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Darrell
science forum addict


Joined: 04 Jun 2005
Posts: 78

PostPosted: Fri Jul 14, 2006 6:40 am    Post subject: Re: sat prep question Reply with quote

"Pubkeybreaker" <Robert_silverman@raytheon.com> wrote in message
news:1152816961.422609.263620@p79g2000cwp.googlegroups.com...
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
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G.E. Ivey
science forum Guru


Joined: 29 Apr 2005
Posts: 308

PostPosted: Sat Jul 15, 2006 11:48 am    Post subject: Re: sat prep question Reply with quote

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
includes addition and subtraction."
It does not say "includes ONLY addition and subtraction".
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