When Ben was on math team as a sophomore, his team decided that when you had to take a guess, the answer was 7. It was right more often than you'd think, and they even considered shirts emblazoned with it.
That "7" would occur with extra frequency was not a surprise to me once I considered the matter. I suggested that -1 would also be common, and at upper levels, 2pi revolutions would show up more often than you'd expect. Seven is just beyond the level where you might get lucky and notice a relationship. If you saw a 216 in a long numerator and a 108 in the denominator, a clever person might pick up the connection and save computational steps. Anything ending in 5 or 0 is going to have obvious factoring. But seven, no one is going to see into a seven - relationship by luck.
These math test makers are essentially evangelists. They want you to see the elegant beauty of how complicated, messy conglomerations resolve to something simple. 29 is also beyond intuitive math, as is 9.7, but those aren't so much fun. You have to think like these math teachers - they think it is just very cool when numbers operate cleanly like that. But they don't want to make it too easy. Thus, the use of the answer -1, instead of just 1, which would of course be the ultimate in cool resolutions. With -1 you have to keep track of the signs. Heheheh, a lot of them won't be careful at this point and they'll forget to switch the sign. Won't they feel silly, then?
The SAT and other standardised test people don't design things this way. They might want to, but they have to make you grind out the answers, so that 13.2 is a real possibility. They're just trying to test you accurately, not convince you of math's elegance.
You have to think like the people making the test. As the remarkable book Up Your SAT (the precursor to Up Your Score) puts it, the paragraph in the comprehension section is not going to say that Beethoven sucks. That will never be one of the main ideas you're supposed to carry down to the multiple-choice questions below. Being able to think like a test-maker is worth an unfair number of points. Of course, one could argue that figuring out how a test-maker thinks is itself a measure of intelligence.
Math team, when in doubt, guess 7, or -1 if they're playing with the signs. There might be some bias toward those answers on the SAT, but nowhere near as strong.
5 comments:
I am Shocked! Shocked! I tell you.
I am SURE that I was taught that the answer is 42.
Captcha looks like "You Know Me" (unomi).
True. And in the game Catch Phrase, if you don't know, you always guess Abraham Lincoln. Not that it's more likely. We just do. I loved Up Your Score. Best standardized test prep book I've read (and I've taken 9 separate standardized tests in my lifetime, not counting the pSATs)
Hey, Up Your Score....that's the book I borrowed from you to study for the SATs! It was good. Got me quite a bit in scholarship money.
Anyway, the really funny point for me was the 2pi answer. A couple months ago I was trying to take a computer programming class at UMASS, and they informed me that I needed to take a math test before I could register (engineering degrees apparently aren't quite good enough...I had to take their test). I was still working night shift at the time and was running on 22 hours with no sleep, so I didn't notice they gave me the wrong test (business math, if you're curious). When I finished said wrong test, I realized the error and had to request the right test all over. They said I could do it, but I couldn't be given any more time. This test had all sorts of geometry on it and various proofs, and I was way too tired, so I just looked at the questions and filled in what I remember the common answers being. 2pi came up very very often. This must have been the least creative test ever, because I apparently still passed by a substantial margin.
The end note is that I at least got to have my triumphal moment where the woman who argued with me that they didn't really know if an engineering degree given by another school would qualify me to do math or not told me she'd never seen someone finish two math tests in 2 hours. They were 40 question tests, so that was a little sad actually. Either way, I proved my point, and probably answered 2pi to at least 4 out of 40 questions.
I never had to guess on the math part of such tests, but I figured out a way to get through the reading part of the GRE: choose the answer that best appears to have been written by a sociologist. Choose the impenetrable prose for the answer.
I am one of those who test better than I perform, so I always come off as an underachiever.
I liked BS King's story about the math test. As if you could get an engineering degree and be a math doofus!
This strategy always worked for us since Math Team is predicated on the idea that everyone was trying so hard and freaking out over so many the details that they'd miss the nose in front of their face. Our team could never scrape together enough members to qualify for any prizes, and we always ended up with an Algebra I student in the Advanced Geometry section (you can only do a limited number of sections each meet - I think it was three - and 80% of our team was usually freshmen each year). Once you reach the point where you've got nothing on the line, it's easier to sit back and say "y'know, I bet the whole thing's a trick question."
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