Tuesday, February 04, 2003

Why Being Smart Isn't Necessarily Smart

I've never been a big fan of standardized testing, because as I once showed my Algebra teacher who was failing me for getting the right answer the "wrong" way, there's almost always more than one correct answer to a problem. And let me tell you, Algebra teachers don't like being shown that their way isn't the only way.

So I followed a link today to this SAT question of the day site. And after viewing today's question, I have to call some serious bullshit at what they think is the right answer.

Here's today's Question, followed by the multiple choice answers:

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?

1). 3/16
2). 1/4
3). 11/30
4). 3/8
5). 7/12

After a small amount of careful re-reading, I deduced that if I, a professional artist, were going to mix paints the way they just descirbed, I would have mixed three parts yellow, then 3 parts red, and 2 parts blue. So, a total of 3 parts yellow, out of a total 8 parts, so 4). 3/8 was my answer.

And according to the site, it's somehow wrong. Here's thier fucked up go-around-your-elbow-to-get-to-your-ass way to mix paints, according to some magical formula for paint mixing. Maybe they studied this in Calculus: Paint Mixing or something:

Suppose that x quarts of the final mixture of dye will be made. Since it is to be made from equal amounts of orange and green dye, it will consist of (1/2)x quarts of orange dye and (1/2)x quarts of green dye. Since the orange dye has 2 parts yellow dye for each 5 parts total dye, 2/5 of it is yellow dye. Similarly, 1/3 of the green dye is yellow dye. The amount of yellow in the final mixture is given by 2/5(1/2)(x) + 1/3(1/2)(x) = (1/5)x + (1/6)x = (11/30)x quarts

So, 11/30 of the final mixture is yellow dye.

Note: Although 'quarts' were used to express the amount of the final mixture, it could have been pints or any other unit of liquid measure.

Difficulty: Hard

You know why it's hard? Because some fucking math wizard thought this was a good idea. You know how we mix paint? We keep mixing it until it looks the right way. And then if some fucking genius wanted to mix orange with green, we'd all point and laugh at the stupid math major who thought that would be a good idea. And if parts is not a quantitative measure of units, wouldn't it *still* be one part yellow, *two* parts blue, regardless of the volume? So wouldn't the answer still be 3/8? Evidently it's not.

I decided to check their math, and do some division. I converted my answer, and their answer to decimals.

3/8 = .375

11/30 = .367 (it's really 0.366666666666666666666666 ad infinitum so I rounded up)

I know a math major or an SAT administrator might think this is some significant difference, and that one answer is right, and the other is wrong, but guess what? Being off by eight thousandths is pretty fucking close enough in just about anyone's book as far as mixing paint is concerned. Any real-world answer to this question would have been "about 1/3 yellow."

Next I should go into my math class pizza question rant, which actually got applause in my college math class.

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