SAT question of the day
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To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what is the proportion of yellow dye in the new mixture? a. 3/16 b. 1/4 c. 11/30 d. 3/8 d. 7/12 -- From the SAT question of the day email I get as Ian signed me up as well to get these questions. Now, he figured this out (good for him) but it stumped me because I view the concept of "parts" to be abstract, making it impossible to equate "equal amounts of green and orange". I guess that's what I get for dealing with object oriented programming languages and always thinking too hard about math word problems. I guess if you consider "part" as a variable, like in: 5po=3pr + 2py 3pg=2pb + 1py then the "p" gets completely factored out. But in my thinking, the "parts" for making orange can be very different than the "parts" for making green. Which is another thing that I always had a problem with in word problems. If something can be completely factored out in the math, then why is it even used as a word in the problem? I've always attached meaning to the words in a math problem, when in reality, a lot of those words simple disappear in the math expressions. Wierd. Oh well, back to my abstractions and other imaginary worlds that I live in. Marc
Somehow, this will be used as an interview question for some poor programmer interview-e
MrPlankton
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The intrinsic assumptions here are that: (A) The same measure can and is applied to all colors. (B) The measure is additive, i.e. mixin A parts of X and B parts of Y gives (A+B) parts of whatever. Given that, the measure can be anything, a weight, a volume, the amount of paint Shlemiel the painter[^] uses on day 15. ('Part' can not be, however, the number of days Shlemiel needs to use the amount, since it's not linear, so mixing would not be additive) So, 5 parts of orange are contain 2 parts of yellow, so one part of orange dye contains 2/5 parts of yellow. Similary, 1 parts of green contain 1/3 part of yellow. 1 parts of yucky contain 1/2*(2/5+1/3) = 11/30 yellow. (c)
Math text questions always contain such assumptions, and recognizig them is an intrinsic part of solving such a question. A common problem of quite some bright minds is not recognizing the intrinsic assumptions, because their filter is crystal clear on the algebra/calculus stuff, but pithc black on the "common sense" part. In a bad education system, they simply need to know which question patterns are subject of this test, and which pattern is this? Simple and boring, because they see the pattern long before they understood the "real world problem" the question is trying to pose . In a good education system, they are immensely more challenged, and need some kind of reverse reasoning: (A) What kind of result is expected? (a value? a formula? a proof a solvability verdict?) (B) Consider all hidden assumptions necessary to arrive at such a result (C) Pick the assumptions that are most simple while requiring all - or the majority - of the information given. This contains two other hidden assumptions: the question is solvable with the information given, and there is no - or not much - redundant information. This is (often much) more complicated than applying common sense - because there's an infinite pool of possible assumptions. A simple fractional arithmetics question, solved in 30 seconds by some guy who needs five minutes to recognize the pattern, suddenly becomes open ended:
If we drop the "additive measure" requirement: Be O=O(R,Y) the number of parts of orange dye acquired from mixing R parts of red and Y parts of yellow. Similary, define G=G(B,Y) and U=U(O,G). this gives U = U
peterchen wrote:
(A) The same measure can and is applied to all colors.
That's helpful, but not required.
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To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what is the proportion of yellow dye in the new mixture? a. 3/16 b. 1/4 c. 11/30 d. 3/8 d. 7/12 -- From the SAT question of the day email I get as Ian signed me up as well to get these questions. Now, he figured this out (good for him) but it stumped me because I view the concept of "parts" to be abstract, making it impossible to equate "equal amounts of green and orange". I guess that's what I get for dealing with object oriented programming languages and always thinking too hard about math word problems. I guess if you consider "part" as a variable, like in: 5po=3pr + 2py 3pg=2pb + 1py then the "p" gets completely factored out. But in my thinking, the "parts" for making orange can be very different than the "parts" for making green. Which is another thing that I always had a problem with in word problems. If something can be completely factored out in the math, then why is it even used as a word in the problem? I've always attached meaning to the words in a math problem, when in reality, a lot of those words simple disappear in the math expressions. Wierd. Oh well, back to my abstractions and other imaginary worlds that I live in. Marc
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Andy Brummer wrote:
Why bake bread in space anyway
Bite your tongue! Even prospectors on the gold rush trail to the Yukon would bake bread on the side of the trail when they stopped for the night, the cook would keep the sourdough starter in his pocket so it wouldn't freeze. When Richard Branson gets his space hotel in orbit up and running, I'll be the dude making a fortune on my microgravity bread machine! ;)
When everyone is a hero no one is a hero.
John C wrote:
the cook would keep the sourdough starter in his pocket so it wouldn't freeze.
Sounds yummy.
This blanket smells like ham
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peterchen wrote:
(A) The same measure can and is applied to all colors.
That's helpful, but not required.
Is it not?
We are a big screwed up dysfunctional psychotic happy family - some more screwed up, others more happy, but everybody's psychotic joint venture definition of CP
blog: TDD - the Aha! | Linkify!| FoldWithUs! | sighist -
I think the more important question is...who the crap would want to mix green and orange? What puke color is that?
Kschuler wrote:
I think the more important question is...who the crap would want to mix green and orange? What puke color is that?
umm, err, CodeProject? :(
-Sean ---- ????? ?????????
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Kschuler wrote:
I think the more important question is...who the crap would want to mix green and orange? What puke color is that?
umm, err, CodeProject? :(
-Sean ---- ????? ?????????
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To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange are mixed, what is the proportion of yellow dye in the new mixture? a. 3/16 b. 1/4 c. 11/30 d. 3/8 d. 7/12 -- From the SAT question of the day email I get as Ian signed me up as well to get these questions. Now, he figured this out (good for him) but it stumped me because I view the concept of "parts" to be abstract, making it impossible to equate "equal amounts of green and orange". I guess that's what I get for dealing with object oriented programming languages and always thinking too hard about math word problems. I guess if you consider "part" as a variable, like in: 5po=3pr + 2py 3pg=2pb + 1py then the "p" gets completely factored out. But in my thinking, the "parts" for making orange can be very different than the "parts" for making green. Which is another thing that I always had a problem with in word problems. If something can be completely factored out in the math, then why is it even used as a word in the problem? I've always attached meaning to the words in a math problem, when in reality, a lot of those words simple disappear in the math expressions. Wierd. Oh well, back to my abstractions and other imaginary worlds that I live in. Marc
Just fill in your own unit of measurement...
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Amusingly enough, if all of us college graduates had to retake the SAT's now, we'd probably all fail and never get admitted a second time round :)
¡El diablo está en mis pantalones! ¡Mire, mire! Real Mentats use only 100% pure, unfooled around with Sapho Juice(tm)! SELECT * FROM User WHERE Clue > 0 0 rows returned Save an Orange - Use the VCF! VCF Blog
Maybe, but after they watered down the SAT several years ago I bet I could still ace the thing - drunk.
"A Journey of a Thousand Rest Stops Begins with a Single Movement"
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You never know when you'll have to make concrete with cement, sand, gravel and water. You already have solar power, you're halfway to having your own compound already.
This blanket smells like ham
right. yellow-green concrete is my favorite one. :)
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
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I think the more important question is...who the crap would want to mix green and orange? What puke color is that?
haven't you tried it by now? they are on about it for hours already....
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
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Show off... I did it as (2/5 + 3/5) + (1/3 + 2/3) == (6/15 + 9/15) + (5/15 + 10/15) looking at the numerators only, I see 30 parts, 11 of which are yellow.
But that is o so wrong. how can
0 == 0prove or solve anything? :wtf: you should have used real numbers here.Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
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Is it not?
We are a big screwed up dysfunctional psychotic happy family - some more screwed up, others more happy, but everybody's psychotic joint venture definition of CP
blog: TDD - the Aha! | Linkify!| FoldWithUs! | sighistBy which I mean that different units may be used at each step.
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right. yellow-green concrete is my favorite one. :)
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
/ lol, I'm kinda partial to gray myself.
I can imagine the sinking feeling one would have after ordering my book, only to find a laughably ridiculous theory with demented logic once the book arrives - Mark McCutcheon
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But that is o so wrong. how can
0 == 0prove or solve anything? :wtf: you should have used real numbers here.Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
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Yeah, adding a class, a using statement and a couple of double quotes may help you out. Provided the class has passed SAT of course. :-D
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
modified on Thursday, February 21, 2008 7:45 PM
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Yeah, adding a class, a using statement and a couple of double quotes may help you out. Provided the class has passed SAT of course. :-D
Luc Pattyn [Forum Guidelines] [My Articles]
This month's tips: - before you ask a question here, search CodeProject, then Google; - the quality and detail of your question reflects on the effectiveness of the help you are likely to get; - use PRE tags to preserve formatting when showing multi-line code snippets.
modified on Thursday, February 21, 2008 7:45 PM
Luc Pattyn wrote:
using statement
Users are losers. :-D Actually I made a small console app -- applet? -- appletini! A very small app. :-D
namespace Calc
{
public partial class Calc
{
[System.STAThreadAttribute()]
public static int
Main
(
string[] args
)
{
int result = 0 ;try { if ( args.Length > 0 ) { System.Console.Write ( PIEBALD.Types.Rational.ParseInfix ( args \[ 0 \] ).ToString() ) ; } else { System.Console.Write ( "Syntax: CALC expression" ) ; } } catch ( System.Exception err ) { System.Console.Write ( err.Message ) ; } return ( result ) ; } }}
OK, so it still requires quotes, but it would if I used floating point too. And the class is off-the-shelf, it's been there getting dusty for some time now.
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Amusingly enough, if all of us college graduates had to retake the SAT's now, we'd probably all fail and never get admitted a second time round :)
¡El diablo está en mis pantalones! ¡Mire, mire! Real Mentats use only 100% pure, unfooled around with Sapho Juice(tm)! SELECT * FROM User WHERE Clue > 0 0 rows returned Save an Orange - Use the VCF! VCF Blog
>> Retaking the SATs. Well, here's my experience. 1979 (age 17): 1280 (680M, 600V) 1999 (age 37): 1490 (750M, 740V) Of course, circa 1995, the scoring was "recentered", so score from before that "aren't comparable" to scores after. These day, ETS is a bit more forthcoming with details, so I was able to learn that the 1490 was the result of getting a total of 7 questions wrong over the entire set of tests.
Truth, James
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Maybe, but after they watered down the SAT several years ago I bet I could still ace the thing - drunk.
"A Journey of a Thousand Rest Stops Begins with a Single Movement"
I aced nearly all of my apprenticeship electronics exams Beverly hung over or even still drunk from the night before. One of my classmates once even passed out after finishing his exam too quickly. Electronics is very easy on the theory side, if they go easy on calculations.
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Part in this case means same sized container of indeterminate size, essentially unit of measure. The important thing in this setup is that the container used is the same size throughout, like a scoop or a coffee cup. That terminology is used in re-sizing a recipe for example. 5 parts flour to 1 part of sugar. Part can be 1 cup or 10 cups depending how much you are making. I'll pre-mix pancakes and use those types of ratios when I'm mixing it up ahead of time. That way I don't have to grab a specific measuring cup, just a large enough bowl. Math equations exist independently of the models, so the equations you wrote down can be understood as lines on a plane, or ratios of mixed components. Another one would be two lines through the origin intersecting with a third line. Math is the study of the abstract systems without considering the models. What gets really strange is when the same relationships can be re-used within the same model. In projective geometry, the geometry used to generate projections of 3d objects on a 2d surface. Statements like: Between any 2 points there is one line have a corresponding dual interpretation: every 2 lines intersect in one point. Every theorem about lines has a corresponding dual theorem about points. It's the same theorem you are just plugging in different "parts" that you are operating on. It's all very generic and functional programming style.
This blanket smells like ham