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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".
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
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?
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 6:56 pm    Post subject: Re: sat prep question

Darrell wrote:
 Quote: "Pubkeybreaker" 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
matt271829-news@yahoo.co.
science forum Guru

Joined: 11 Sep 2005
Posts: 846

Posted: Thu Jul 13, 2006 5:31 pm    Post subject: Re: sat prep question

Darrell wrote:
 Quote: "Pubkeybreaker" 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.
Darrell

Joined: 04 Jun 2005
Posts: 78

Posted: Thu Jul 13, 2006 4:00 pm    Post subject: Re: sat prep question

"Pubkeybreaker" <Robert_silverman@raytheon.com> wrote in message
 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"

--
Darrell
Pubkeybreaker
science forum Guru

Joined: 24 Mar 2005
Posts: 333

Posted: Thu Jul 13, 2006 2:28 pm    Post subject: Re: sat prep question

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.
Jason11
science forum beginner

Joined: 25 Mar 2006
Posts: 10

Posted: Thu Jul 13, 2006 12:09 pm    Post subject: Re: sat prep question

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

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
Travis
science forum beginner

Joined: 05 Feb 2005
Posts: 7

Posted: Wed Jul 12, 2006 12:45 am    Post subject: Re: sat prep question

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" 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
matt271829-news@yahoo.co.
science forum Guru

Joined: 11 Sep 2005
Posts: 846

Posted: Tue Jul 11, 2006 12:53 pm    Post subject: Re: sat prep question

Travis wrote:
 Quote: On 10 Jul 2006 13:06:16 -0700, matt271829-news@yahoo.co.uk wrote: W H G wrote: "Travis" 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...
Travis
science forum beginner

Joined: 05 Feb 2005
Posts: 7

Posted: Tue Jul 11, 2006 12:59 am    Post subject: Re: sat prep question

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

 Quote: W H G wrote: "Travis" 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.
matt271829-news@yahoo.co.
science forum Guru

Joined: 11 Sep 2005
Posts: 846

Posted: Mon Jul 10, 2006 8:06 pm    Post subject: Re: sat prep question

W H G wrote:
 Quote: "Travis" 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.
W H G
science forum beginner

Joined: 03 Aug 2005
Posts: 11

Posted: Mon Jul 10, 2006 2:52 pm    Post subject: Re: sat prep question

"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
William Elliot
science forum Guru

Joined: 24 Mar 2005
Posts: 1906

Posted: Mon Jul 10, 2006 11:33 am    Post subject: Re: sat prep question

On Mon, 10 Jul 2006, David C. Ullrich wrote:
 Quote: Travis 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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