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sat prep question
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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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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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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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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 6:56 pm    Post subject: Re: sat prep question Reply with quote

Darrell wrote:
Quote:
"Pubkeybreaker" <Robert_silverman@raytheon.com> wrote in message
news:1152800910.927778.46290@h48g2000cwc.googlegroups.com...

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.

The objective is not to find "the" correct answer but to find the "best"
answer of those listed.


Yet more nonsense. There is no such thing as the 'best' answer.
If you think there is such a thing, please specify how you measure
whether one answer is better than another. Specify your metric.
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matt271829-news@yahoo.co.
science forum Guru


Joined: 11 Sep 2005
Posts: 846

PostPosted: Thu Jul 13, 2006 5:31 pm    Post subject: Re: sat prep question Reply with quote

Darrell wrote:
Quote:
"Pubkeybreaker" <Robert_silverman@raytheon.com> wrote in message
news:1152800910.927778.46290@h48g2000cwc.googlegroups.com...

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.

The objective is not to find "the" correct answer but to find the "best"
answer of those listed.


With vaguely-worded questions like this, I think the correct answer
needs to be very obviously correct once you've discovered it (as with
those much-derided next-number-in-the-sequence questions). It needs to
"leap out at you". The possibility that x T y = 2*y, so 7 T 3 = 6, was
actually the first pattern I noticed (like many others I guess), but I
dismissed it straight away as being obviously *not* what was intended.
If there's no more information or context than is given in the original
post then I do think it's a very poor question.
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Darrell
science forum addict


Joined: 04 Jun 2005
Posts: 78

PostPosted: Thu Jul 13, 2006 4:00 pm    Post subject: Re: sat prep question Reply with quote

"Pubkeybreaker" <Robert_silverman@raytheon.com> wrote in message
news:1152800910.927778.46290@h48g2000cwc.googlegroups.com...
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.

The objective is not to find "the" correct answer but to find the "best"
answer of those listed.

--
Darrell
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Pubkeybreaker
science forum Guru


Joined: 24 Mar 2005
Posts: 333

PostPosted: Thu Jul 13, 2006 2:28 pm    Post subject: Re: sat prep question Reply with quote

Jason wrote:
Quote:
I have to disagree with the people who think this is a stupid question.

You need to learn some more linear algebra.


Quote:
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.
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Jason11
science forum beginner


Joined: 25 Mar 2006
Posts: 10

PostPosted: Thu Jul 13, 2006 12:09 pm    Post subject: Re: sat prep question Reply with quote

I have to disagree with the people who think this is a stupid question.
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). 4T1 = 2 multiplied throughout by 3 implies
12T3 = 6. Subtracting the first "equation" from this gives 7T0 = 0.
Which implies that the answer depends only on the second number and the
answer is 6. Quite cool.

Travis wrote:
Quote:
If T represents an operation that
includes addition and subtraction.
Ex) 5 T 3 = 6, 4 T 1 = 2.
What is the value of 7 T 3?
A. 5
B. 6
C. 7
D. 8
E. 9


I want to say the answer is 6 but I dont know why
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Travis
science forum beginner


Joined: 05 Feb 2005
Posts: 7

PostPosted: Wed Jul 12, 2006 12:45 am    Post subject: Re: sat prep question Reply with quote

On 11 Jul 2006 05:53:35 -0700, matt271829-news@yahoo.co.uk wrote:

Quote:
Travis wrote:
On 10 Jul 2006 13:06:16 -0700, matt271829-news@yahoo.co.uk wrote:

W H G wrote:
"Travis" <notgonatellyou@mail.com> wrote in message
news:76o3b2tfcksuirpg7ffhm9vib3928rp4ij@4ax.com...
If T represents an operation that
includes addition and subtraction.
Ex) 5 T 3 = 6, 4 T 1 = 2.
What is the value of 7 T 3?
A. 5
B. 6
C. 7
D. 8
E. 9


I want to say the answer is 6 but I dont know why

So we see that 5 and 3 wind up at 6 and we can use + and -
5+3=8 3-3=2

Do you mean 5 - 3 = 2?

combine the 8 and 2: 8-2=6 ---ok, does this work
with the next example:
4 and 1 get to 2: (4+1) - (4-1) = 2 Bingo! it worked.
Try it on 7 T 3 and get 6.

So you're suggesting that x T y = (x + y) - (x - y) = 2*y?

That doesn't look at all likely to me.


why is that unlikely?? (x + y) - (x - y) becomes x +y -x +y and can be
reduced to y + y which does appear to be 2y thanks W H G.

It's unlikely because the first operand, x, is irrelevant to the
answer. I have absolutely no idea what answer is expected, but if the
answer depends only on the second operand then it's a pretty stoopid
question...


agreed but it was from a sat prep book
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matt271829-news@yahoo.co.
science forum Guru


Joined: 11 Sep 2005
Posts: 846

PostPosted: Tue Jul 11, 2006 12:53 pm    Post subject: Re: sat prep question Reply with quote

Travis wrote:
Quote:
On 10 Jul 2006 13:06:16 -0700, matt271829-news@yahoo.co.uk wrote:

W H G wrote:
"Travis" <notgonatellyou@mail.com> wrote in message
news:76o3b2tfcksuirpg7ffhm9vib3928rp4ij@4ax.com...
If T represents an operation that
includes addition and subtraction.
Ex) 5 T 3 = 6, 4 T 1 = 2.
What is the value of 7 T 3?
A. 5
B. 6
C. 7
D. 8
E. 9


I want to say the answer is 6 but I dont know why

So we see that 5 and 3 wind up at 6 and we can use + and -
5+3=8 3-3=2

Do you mean 5 - 3 = 2?

combine the 8 and 2: 8-2=6 ---ok, does this work
with the next example:
4 and 1 get to 2: (4+1) - (4-1) = 2 Bingo! it worked.
Try it on 7 T 3 and get 6.

So you're suggesting that x T y = (x + y) - (x - y) = 2*y?

That doesn't look at all likely to me.


why is that unlikely?? (x + y) - (x - y) becomes x +y -x +y and can be
reduced to y + y which does appear to be 2y thanks W H G.

It's unlikely because the first operand, x, is irrelevant to the
answer. I have absolutely no idea what answer is expected, but if the
answer depends only on the second operand then it's a pretty stoopid
question...
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Travis
science forum beginner


Joined: 05 Feb 2005
Posts: 7

PostPosted: Tue Jul 11, 2006 12:59 am    Post subject: Re: sat prep question Reply with quote

On 10 Jul 2006 13:06:16 -0700, matt271829-news@yahoo.co.uk wrote:

Quote:
W H G wrote:
"Travis" <notgonatellyou@mail.com> wrote in message
news:76o3b2tfcksuirpg7ffhm9vib3928rp4ij@4ax.com...
If T represents an operation that
includes addition and subtraction.
Ex) 5 T 3 = 6, 4 T 1 = 2.
What is the value of 7 T 3?
A. 5
B. 6
C. 7
D. 8
E. 9


I want to say the answer is 6 but I dont know why

So we see that 5 and 3 wind up at 6 and we can use + and -
5+3=8 3-3=2

Do you mean 5 - 3 = 2?

combine the 8 and 2: 8-2=6 ---ok, does this work
with the next example:
4 and 1 get to 2: (4+1) - (4-1) = 2 Bingo! it worked.
Try it on 7 T 3 and get 6.

So you're suggesting that x T y = (x + y) - (x - y) = 2*y?

That doesn't look at all likely to me.


why is that unlikely?? (x + y) - (x - y) becomes x +y -x +y and can be
reduced to y + y which does appear to be 2y thanks W H G.
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matt271829-news@yahoo.co.
science forum Guru


Joined: 11 Sep 2005
Posts: 846

PostPosted: Mon Jul 10, 2006 8:06 pm    Post subject: Re: sat prep question Reply with quote

W H G wrote:
Quote:
"Travis" <notgonatellyou@mail.com> wrote in message
news:76o3b2tfcksuirpg7ffhm9vib3928rp4ij@4ax.com...
If T represents an operation that
includes addition and subtraction.
Ex) 5 T 3 = 6, 4 T 1 = 2.
What is the value of 7 T 3?
A. 5
B. 6
C. 7
D. 8
E. 9


I want to say the answer is 6 but I dont know why

So we see that 5 and 3 wind up at 6 and we can use + and -
5+3=8 3-3=2

Do you mean 5 - 3 = 2?

Quote:
combine the 8 and 2: 8-2=6 ---ok, does this work
with the next example:
4 and 1 get to 2: (4+1) - (4-1) = 2 Bingo! it worked.
Try it on 7 T 3 and get 6.

So you're suggesting that x T y = (x + y) - (x - y) = 2*y?

That doesn't look at all likely to me.
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W H G
science forum beginner


Joined: 03 Aug 2005
Posts: 11

PostPosted: Mon Jul 10, 2006 2:52 pm    Post subject: Re: sat prep question Reply with quote

"Travis" <notgonatellyou@mail.com> wrote in message
news:76o3b2tfcksuirpg7ffhm9vib3928rp4ij@4ax.com...
Quote:
If T represents an operation that
includes addition and subtraction.
Ex) 5 T 3 = 6, 4 T 1 = 2.
What is the value of 7 T 3?
A. 5
B. 6
C. 7
D. 8
E. 9


I want to say the answer is 6 but I dont know why

So we see that 5 and 3 wind up at 6 and we can use + and -
5+3=8 3-3=2 combine the 8 and 2: 8-2=6 ---ok, does this work
with the next example:
4 and 1 get to 2: (4+1) - (4-1) = 2 Bingo! it worked.
Try it on 7 T 3 and get 6.

(I will agree with the comment about why have such a question)

------- W H G
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William Elliot
science forum Guru


Joined: 24 Mar 2005
Posts: 1906

PostPosted: Mon Jul 10, 2006 11:33 am    Post subject: Re: sat prep question Reply with quote

On Mon, 10 Jul 2006, David C. Ullrich wrote:
Quote:
Travis <notgonatellyou@mail.com> wrote:

If T represents an operation that
includes addition and subtraction.
Ex) 5 T 3 = 6, 4 T 1 = 2.
What is the value of 7 T 3?

If this is an actual question it's an extremely
_bad_ question, unless they clarify what the heck
"an operation that includes addition and subtraction"
means. Do they explain that?

Why bother? Take a course on how to be a psychic.

I just finished that course some timeless time ago,
and have subsequently divined the one and only true answer.

(5 + 3) - (5 - 3) 3(5 - 3) + 0 (3 - 1)(5 - 2) + 0
(4 + 1) - (4 - 1) 2(4 - 3) + 0 (2 - 1)(4 - 2) + 0
(7 + 3) - (7 - 3) 3(7 - 3) + 0 (3 - 1)(7 - 2) + 0

3 + 3 - 0 (3 - 1)(5 - 3) + (5 - 3)
1 + 1 - 0 (2 - 1)(4 - 3) + (4 - 3)
3 + 3 - 0 (3 - 1)(7 - 3) + (7 - 3)

3 + 3 + 3 - 3 Which the psychic reader will clearly see.
1 + 1 + 1 - 1
3 + 3 + 3 - 3


Quote:
A. 5
B. 6
C. 7
D. 8
E. 9

I want to say the answer is 6 but I dont know why

Naw, by my divinations, it is

F. 10
G. 12
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