### 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 quartsSo, 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.