SAT question of the day
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By which I mean that different units may be used at each step.
see my reply below - that's what I thought you thought of. I wasn't very clear with the distinction of measure and _unit.
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Well, let's see..... if you have an equation that reduces to 0==0, then you know (depending on the equation being solved) either the input was correct, or the variables don't affect the outcome. If you assigned values to all the variables and found that 0==0, then there aren't any contradictions in the equation. If you left values out of the variables, and simplifying the equation made the variables go away, then the variables cancelled each other out, which means they didn't mtter. Not that that has anything to do with the post you were replying to. Why did you even post a statement about 0==0? The previous post reduced to 1==1, which should always be the case. And I believe all those fractions that were used were real numbers. "Of course, I could be wrong..... but I'm not."
Trevortni wrote:
Of course, I could be wrong..... but I'm not
OMG just started, and abundantly balmy already. Got any clue why your answer [^] isn't even amongst the choices[^]? :suss:
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What ARE you smoking? There is only one correct answer: 1 gallon = 4 quarts. Therefore, the Green comprise 4 of the 5 parts of this equation, while the Orange comprises 1 of the 5 parts. 1/3(Yellow in Green) * 4/5(Green in final solution) = 4/15(Yellow in final solution from Green) 2/5(Yellow in Orange) * 1/5(Orange in final solution) = 2/25(Yellow in final solution from Orange) 4/15(Yellow) + 2/25(Yellow) = 20/75(Yellow) + 6/75(Yellow) = 26/75(Yellow) The only way you could get 39 parts yellow is if you deliberately wanted to confuse your readers by not keeping the ratios as reduced fractions. This would require both the numerator and the denominator to be multipled by 1.5, which would give a ratio of 39/112.5, which is not only NOT REDUCED, but it has a decimal as part of a fraction, which is very bad form, kind of like making the claim thatg mathematics is not determinable. Come on, I thought people were supposed to know at least a little bit about elementary (as in the level of schooling, not as in a synonym for "basic") mathematics around here.
Trevortni wrote:
What ARE you smoking? There is only one correct answer
Au contraire. The answer 29 is not wrong. Neither is 29,000, or 3.14159, or even 1! They are all correct. Depends on how big a "part" is, which is undefined in MY question. Mixing gallons and quarts, you've come up with some number 75, which is NOT an ENGLISH unit of measure. So, since I asked the question, I could rule your answer INCORRECT, by saying I was looking for an answer in a common unit of ENGLISH measure, so the answer should be in TEASPOONs, making 26 an INCORRECT answer, obviously. The question never asked for a REDUCED figure. Again, it is your assumption, just as the original question ASSUMED that parts are equal. The problem with an indistinct question is there can be multiple answers.
Trevortni wrote:
The only way you could get 39 parts yellow is ...
Yes, which makes 39 a correct answer, just like the other gazillion possible answers! The problem is that the question forces the reader / test taker to make an ASSUMPTION, that may or may not be correct. Of course, the possible multiple choice answers in the original test question hint that they want reduced numbers, and I would mark the same answer correct as most people. If the answer choices had been: a. 3/16 b. 1/4 c. 22/60 d. 3/8 e. 7/12 Which would be the correct answer? :confused: 22/60, of course, contradicting your premise. Look at the problem a different way. On the color wheel, EQUAL MEASUREMENTS of red and yellow make orange. EQUAL MEASUREMENTS of blue and yellow make green. Anything other than equal measurements, and the color is not true orange or true green. So if I mix 3 parts red dye with 2 parts yellow dye to get orange, then the "part" size of the red dye is 2/3 the size of the "part" size of the yellow dye. Likewise, if I mix 2 parts of blue dye with 1 part yellow dye to get green, then the "part" size of the blue dye is 1/2 the "part" size of the yellow dye. So, when I mix EQUAL amounts of the green and the orange, I'm mixing 1/2 yellow + 1/2 red to 1/2 blue + 1/2 yellow, or 2/4 yellow, 1/4 red and 1/4 blue in the whole mixture. The correct answer - 1/2 or 2/4 - is not on the list. Again, we might ASSUME the red dye is weaker than yellow dye so you need more red dye? I do math, I do colors, I don't mix friggen dye, so how would I know where the ASSUMPTION lies in the question?
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Trevortni wrote:
Of course, I could be wrong..... but I'm not
OMG just started, and abundantly balmy already. Got any clue why your answer [^] isn't even amongst the choices[^]? :suss:
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Trevortni wrote:
What ARE you smoking? There is only one correct answer
Au contraire. The answer 29 is not wrong. Neither is 29,000, or 3.14159, or even 1! They are all correct. Depends on how big a "part" is, which is undefined in MY question. Mixing gallons and quarts, you've come up with some number 75, which is NOT an ENGLISH unit of measure. So, since I asked the question, I could rule your answer INCORRECT, by saying I was looking for an answer in a common unit of ENGLISH measure, so the answer should be in TEASPOONs, making 26 an INCORRECT answer, obviously. The question never asked for a REDUCED figure. Again, it is your assumption, just as the original question ASSUMED that parts are equal. The problem with an indistinct question is there can be multiple answers.
Trevortni wrote:
The only way you could get 39 parts yellow is ...
Yes, which makes 39 a correct answer, just like the other gazillion possible answers! The problem is that the question forces the reader / test taker to make an ASSUMPTION, that may or may not be correct. Of course, the possible multiple choice answers in the original test question hint that they want reduced numbers, and I would mark the same answer correct as most people. If the answer choices had been: a. 3/16 b. 1/4 c. 22/60 d. 3/8 e. 7/12 Which would be the correct answer? :confused: 22/60, of course, contradicting your premise. Look at the problem a different way. On the color wheel, EQUAL MEASUREMENTS of red and yellow make orange. EQUAL MEASUREMENTS of blue and yellow make green. Anything other than equal measurements, and the color is not true orange or true green. So if I mix 3 parts red dye with 2 parts yellow dye to get orange, then the "part" size of the red dye is 2/3 the size of the "part" size of the yellow dye. Likewise, if I mix 2 parts of blue dye with 1 part yellow dye to get green, then the "part" size of the blue dye is 1/2 the "part" size of the yellow dye. So, when I mix EQUAL amounts of the green and the orange, I'm mixing 1/2 yellow + 1/2 red to 1/2 blue + 1/2 yellow, or 2/4 yellow, 1/4 red and 1/4 blue in the whole mixture. The correct answer - 1/2 or 2/4 - is not on the list. Again, we might ASSUME the red dye is weaker than yellow dye so you need more red dye? I do math, I do colors, I don't mix friggen dye, so how would I know where the ASSUMPTION lies in the question?
Wow. You really are a Grade A moron, aren't you? Or are you just trying to be difficult? I sincerely hope it's the latter, because the former make me question whether (as has been repeatedly brought up in this discussion) I want to trust any serious calculations to your ineptitude. You are right, though, that answering with a unit-less number is nonsense. However, looking back through this subtree of the discussion, the only person I see making that mistake is you (correct me if I'm wrong - I may have overlooked something). A part is a perfectly valid unit of measure - specifying not a predetermined fixed amount, but a fixed amount to be used within the scope of a given problem. For those of us who only speak codese, this is (loosely) like saying that we have a Unit of Measure defined within a function block. Outside of the function block, the UOM has no meaning, but WITHIN THE CONSTRAINTS OF THE SCOPE for which it is defined, this "part" is a valid UOM for the purposes of defining the ratios between ingrediants. As for your statement that you could say you were looking for a different UOM (specifically, an English UOM): sure, you could say that. But then you would be LYING. Your original question was: how many *PARTS* of yellow dye are in the whole. When you do this, you are explicitly stating that the answer must be a ratio. The only way you can get around this is by explicitly (not implicitly, as I erroneously put here at first; more on this later) stating that the whole is supposed to be cut into a certain number of parts, thus specifying how many parts the whole is made out of. The answer would then be converted to be based on the divisions you have specified. The way this twist would be solved would be by multiplying the RATIO by your number of parts. You see, my answer was not 26. My answer was 26/75. This is how many parts of yellow is in the whole. When you say "in the whole," you are explicitly (I said I would get back to this later) stating that the standard of measure is: 1 part = everything that has been mixed together. My answer is that there are 26/75 of a part of yellow in the whole. Saying that there are 26 out of 75 parts is a valid answer as well, but as you have nitpicked, this doesn't properly answer the question that is being asked: it multiplies both the question and the answer by 75. And finally, your misunderstanding of reduced numbers: 22/60 does not contradict my premise, since 22/60==11/30. They are exactly the same number (they both divide out to .36666666
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see my reply below - that's what I thought you thought of. I wasn't very clear with the distinction of measure and _unit.
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
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(A) The same measure can and is applied to all colors. Partly my misunderstanding as well, I read it as "measuring can". :doh: Still, it's concievable that weight could be used in one step, mass in another, and volume in the third, but I suspect that something like specific gravity will muck it all up.
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Ummm, let's see..... maybe because that was an answer to a DIFFERENT QUESTION? Wow, I simply can't think of a remark quite sardonic enough to properly finish this reply.....
Trevortni wrote:
I simply can't think of a remark quite sardonic enough to properly finish this reply
That's too bad. I'm sure we are missing out on something here. Anyway, if you want to change both the question and the answer, you'd better start a new thread, avoiding things getting messy... :)
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Trevortni wrote:
I simply can't think of a remark quite sardonic enough to properly finish this reply
That's too bad. I'm sure we are missing out on something here. Anyway, if you want to change both the question and the answer, you'd better start a new thread, avoiding things getting messy... :)
Luc Pattyn [Forum Guidelines] [My Articles]
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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
My confusion is this: Do the formulas listed for making orange and green dye yield equal amount of dye? If they do, then the "parts" used are not equal measurements -- you'd have to do the math around each yield of the formulas being 1, which is a little tougher. If the parts are equal, and the yields are different, it's a very simple problem to solve. But they really don't specify that. It's the difference between 1/3 + 2/5 = 11/15 vs. 2 + 1 / 5 + 3 = 3/8 I guess since the first answer isn't an option, it's the latter (parts equal, yields not). But they really should have clarified that a little bit, IMO.
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Wow. You really are a Grade A moron, aren't you? Or are you just trying to be difficult? I sincerely hope it's the latter, because the former make me question whether (as has been repeatedly brought up in this discussion) I want to trust any serious calculations to your ineptitude. You are right, though, that answering with a unit-less number is nonsense. However, looking back through this subtree of the discussion, the only person I see making that mistake is you (correct me if I'm wrong - I may have overlooked something). A part is a perfectly valid unit of measure - specifying not a predetermined fixed amount, but a fixed amount to be used within the scope of a given problem. For those of us who only speak codese, this is (loosely) like saying that we have a Unit of Measure defined within a function block. Outside of the function block, the UOM has no meaning, but WITHIN THE CONSTRAINTS OF THE SCOPE for which it is defined, this "part" is a valid UOM for the purposes of defining the ratios between ingrediants. As for your statement that you could say you were looking for a different UOM (specifically, an English UOM): sure, you could say that. But then you would be LYING. Your original question was: how many *PARTS* of yellow dye are in the whole. When you do this, you are explicitly stating that the answer must be a ratio. The only way you can get around this is by explicitly (not implicitly, as I erroneously put here at first; more on this later) stating that the whole is supposed to be cut into a certain number of parts, thus specifying how many parts the whole is made out of. The answer would then be converted to be based on the divisions you have specified. The way this twist would be solved would be by multiplying the RATIO by your number of parts. You see, my answer was not 26. My answer was 26/75. This is how many parts of yellow is in the whole. When you say "in the whole," you are explicitly (I said I would get back to this later) stating that the standard of measure is: 1 part = everything that has been mixed together. My answer is that there are 26/75 of a part of yellow in the whole. Saying that there are 26 out of 75 parts is a valid answer as well, but as you have nitpicked, this doesn't properly answer the question that is being asked: it multiplies both the question and the answer by 75. And finally, your misunderstanding of reduced numbers: 22/60 does not contradict my premise, since 22/60==11/30. They are exactly the same number (they both divide out to .36666666
Trevortni wrote:
You really are a Grade A moron, aren't you?
:(( :confused: Nope. A member of both Mensa and of Intertel (look it up here Intertel[^]). Anyhow, this is the lounge, so get a little less serious, okay?
Trevortni wrote:
the only person I see making that mistake is you (correct me if I'm wrong - I may have overlooked something).
Well, you're wrong, and that was the WHOLE POINT of the thread that Marc started.
Marc Clifton wrote:
it stumped me because I view the concept of "parts" to be abstract,
Trevortni wrote:
A part is a perfectly valid unit of measure
On what planet? Can you covert them to metric?
Trevortni wrote:
Your original question was: how many *PARTS* of yellow dye are in the whole.
And your answer is 26/75!? That's just plain wrong. I didn't ask for a ratio. In my book, the number of *PARTS* is always greater than one. In fact, using your logic, the answer is 26, not some fraction less than one. 26 PARTS of yellow, 49 PARTS of something else. Look at it another way. I have a box, and in the box are 5 orange slices (parts) and 3 lime slices (parts). How many orange parts are in the (whole) box. The answer is 5, NOT 5/8.
Trevortni wrote:
They are exactly the same number
Validating my statement that there are multiple *right* answers, and contradicting yourself. Um, square root of 2 maybe? You totally missed the original posting. "Parts" is an arbitrary thing. Yes, one can make certain assumptions, but is it the right assumption? Good system design removes ALL ambiguities, and this is where Marc was coming from, I believe. Fire missile at any foreign object coming over the horizon. Nice, clear, and concise. Oops, I didn't mean the Moon. Lighten up now. :rose:
Gary
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Trevortni wrote:
You really are a Grade A moron, aren't you?
:(( :confused: Nope. A member of both Mensa and of Intertel (look it up here Intertel[^]). Anyhow, this is the lounge, so get a little less serious, okay?
Trevortni wrote:
the only person I see making that mistake is you (correct me if I'm wrong - I may have overlooked something).
Well, you're wrong, and that was the WHOLE POINT of the thread that Marc started.
Marc Clifton wrote:
it stumped me because I view the concept of "parts" to be abstract,
Trevortni wrote:
A part is a perfectly valid unit of measure
On what planet? Can you covert them to metric?
Trevortni wrote:
Your original question was: how many *PARTS* of yellow dye are in the whole.
And your answer is 26/75!? That's just plain wrong. I didn't ask for a ratio. In my book, the number of *PARTS* is always greater than one. In fact, using your logic, the answer is 26, not some fraction less than one. 26 PARTS of yellow, 49 PARTS of something else. Look at it another way. I have a box, and in the box are 5 orange slices (parts) and 3 lime slices (parts). How many orange parts are in the (whole) box. The answer is 5, NOT 5/8.
Trevortni wrote:
They are exactly the same number
Validating my statement that there are multiple *right* answers, and contradicting yourself. Um, square root of 2 maybe? You totally missed the original posting. "Parts" is an arbitrary thing. Yes, one can make certain assumptions, but is it the right assumption? Good system design removes ALL ambiguities, and this is where Marc was coming from, I believe. Fire missile at any foreign object coming over the horizon. Nice, clear, and concise. Oops, I didn't mean the Moon. Lighten up now. :rose:
Gary
OK, so I wasn't going to reply to this, but the assumption that being a member of MENSA (oooh!) makes you somehow not be an idiot..... that was just to rich to pass up making a wry comment about. Mensa only makes you elitist. And somebody who is elitist can still be just as dead wrong as anybody else.... they just refuse to admit it when they are. I think I'll skip most of the rest of your sorry responses, and just point out two major flaws in what you're babbling about: Stating that two numbers are the same number is not in any conceivable way saying that there are multiple right answers. You are trying to prove that there are multiple right answers by showing multiple expressions of the SAME right answer. This is nonsense which you are attempting to use to confuse your audience (and I stand by my hope that it is only your audience that you are trying to confuse, and not yourself). And finally, you claim that this system has ambiguities, and that was the whole point of the discussion that Marc started. Yes, that was the conversation that Marc started. Then people who had a better grasp of mathematics and English than he did took it upon themselves to correct his mistakes. Then other people who want to confuse the matter, such as yourself, have taken it upon themselves to rail against the establishment, presumably because decrying something that is very useful (and, I might add, a lot more thoroughly tested than any truly useful and well-written software I've come across) makes you feel better about your laziness that prevents you from grasping the really simple concepts. Or maybe you weren't hugged enough as a kid? But this system really contains no contradictions, and as I have pointed out (though I suppose maybe it just wasn't clear enough? Maybe I'll have to write a textbook about this trivial matter) what you call assumptions were CLEARLY STATED in the question. Now please stop confusing the kiddies. It doesn't help them out, and it makes you look like a Grade A moron.
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OK, you are just yanking my chain here, right? You did look at the start of that sub-discussion that posed the question that this answer was actually for? Right? Riiiiiiight? Please tell me you're not really this stupid.
open to doubt now? aim achieved then. :|
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While I agree they are words most of your exceptions are due to puting a prefix or a postfix on the root word. Naturally any verb that begins in an i can form a "ei" combo by adding a re- in front, or one that ends in a e with an -ing. The others though a amusing none the less. Also alot/most you'll note were borrowed from french or german, I challenge you to repeat said joke only using words derived from old english. ;P P.S. why did the US decide on math and vocab as the standard for college admissions anyways? Say your planning on doing pure math. Sure your math scores should be through the roof, but your need for vocab is limited as you need a small subset of vocab to be able to do your job.
"I challenge you to repeat said joke only using words derived from old english" Just how old do you want the English to be? If I remember my history correctly (I may not, if so someone please correct me!), the English were repeatedly invaded by Saxons (hence Anglo-Saxon), Vikings, and Normans. Indeed, after the Norman invasion of 1066 (that's nearly 1000 years ago now), French was, for a while, the official language used in any treaties etc. Add to that Latin influences, Irish, Welsh and Scottish influences. Even the Celts were originally invaders (albeit, quite likely the original ones). I suspect you'd find it hard to find many remnants of written English that old - those influences were entrenched by the time of Magna Carta, The Domesday Book and Chaucer.
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deltalmg wrote:
most of your exceptions are due to puting [putting] a prefix or a postfix on the root word.
Nope. Count em. I left most of the re-i and e-ing words out. I needed some for context, however, to make the story flow. College is for all disciplines, not just math and engineering. Why do assume ALL programmers need math? No math is needed to build a web site (for-loops excepted). Similar question, why does a language major need to know math??
deltalmg wrote:
P.S. why did the US decide on math and vocab as the standard for college admissions anyways?
I dunno. That was before my time. I'm not a history buff. :)
deltalmg wrote:
Say your [you're] planning on doing pure math...but your need for vocab is limited
Vocab is important, none the less, so students can hear, read and understand the homework assignments. X|
Gary
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I before E except after C - when the sound is 'ee', was what I was taught, which reduces the number of exceptions considerably.
Bob Emmett
Bob Emmett wrote:
I before E except after C - when the sound is 'ee', was what I was taught, which reduces the number of exceptions considerably.
I don't think it actually rules out that many. I hadn't included words like science, where the 'ee' rule exception exception would apply, or species where it doesn't. :)
Gary
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"I challenge you to repeat said joke only using words derived from old english" Just how old do you want the English to be? If I remember my history correctly (I may not, if so someone please correct me!), the English were repeatedly invaded by Saxons (hence Anglo-Saxon), Vikings, and Normans. Indeed, after the Norman invasion of 1066 (that's nearly 1000 years ago now), French was, for a while, the official language used in any treaties etc. Add to that Latin influences, Irish, Welsh and Scottish influences. Even the Celts were originally invaders (albeit, quite likely the original ones). I suspect you'd find it hard to find many remnants of written English that old - those influences were entrenched by the time of Magna Carta, The Domesday Book and Chaucer.
I'm not sure what is the threashold of something being OE. But there is numerous words where my Webster's dictonary says the root is from OE (old english). Modern english words are mostly greek, latin, german and french but there is some old french and english thrown in there as well.
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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
Marc Clifton wrote:
But in my thinking, the "parts" for making orange can be very different than the "parts" for making green.
Correct. It does not matter. The ratio of yellow to red in orange is fix. It does not change. The color is mixed, and it was mixed to a certain ratio. That means, no matter how small the quantity you take, the ratio of red to yellow remains the same. The same is true for the green mix. (To make this more clear: The ratio determines what color the mix is, right? Now, if you remove any given amout of paint, will the color in the remaining paint change? Or in the paint you took? No! Because the ratio did not change.) Now, consider the remainder of the question: it says "equal amounts". Forget about the "parts" at this point. You now have a mix that contains, say, 5 oz. orange and 5 oz. green. Now, to calculate the result, we use the RATIO (which is abstract): 2/5 of yellow in the orange mix, 1/3 of yellow in the green mix. Now, one immediately realizes, neither 8, nor 12, 16 or 4 can be reached from the given ratios, because no basic arithmetic operation will get you there from the starting quantities. It has to be 11/30, which, coincidentally is what you get when you add the numbers and multiply the result by 0.5.
Cheers, Sebastian -- "If it was two men, the non-driver would have challenged the driver to simply crash through the gates. The macho image thing, you know." - Marc Clifton