Risk aversion and SAT guessing

I just listened to a Planet Money story that I wanted to share with you. It's a 4:26 long discussion of risk aversion and how some experts see it distorting the American housing market. I'm not recommending it because I think you need to be thinking about the housing market, though. I'm posting this because the whole time I was listening, I was thinking about the psychology involved in guessing on the SAT. To paraphrase one expert in the story, people are afraid to guess because losing feels more intensely bad than winning feels good.

I actually think the SAT is a better application of the theory in question than the housing market, since home buyers and sellers generally don't get to buy and sell often enough for the "if you flip the coin 1000 times" argument to really make sense.

On the SAT, you lose 1/4 of a point for an incorrect answer, and gain a whole point for a correct one. Since there are 5 choices per question, if you are deciding whether to guess or leave a question blank more than a few times per test, you're in a position where, statistically, random guessing is a complete wash (thorough explanation here). From there, if you feel like your guess is even a little bit better than random, the "rational" move is to guess, since the scales tip slightly in you favor once you eliminate even one incorrect choice.

I'm not saying you need to guess, but listen to the story, and see if any of it resonates with you. It may or may not inform your future guessing strategy on the SAT.

Weekend Challenge - Black Friday

Source: Nature's Graffiti.

Do you guys do the Black Friday thing? One time, about 7 years ago, I got up at 3 in the morning and met some friends to wait outside Best Buy. It was complete pandemonium, and I was not fast or ruthless enough to get the TV I wanted. Then, I got the same TV for the same price a week later online. I still have it. I'm staring at it right now, actually. And that's the story of why I hate Black Friday. The end.

As you may or may not know, the Beta for the Math Guide is closed since the book is almost done. I haven't really figured out what to give away as a prize for these challenges now that I don't have the Beta. I might come up with something good in the future, but this one's just for good old fashioned bragging rights. So, I dunno, go on College Confidential and tell everyone you're super smart. You'll fit right in! (I kid, I kid. That site is a fantastic resource.)

x is directly proportional to y

x is inversely proportional to z

If the two statements above are true, and y = 10 and z = 5 when x = 2, what are x, y, and z when x + y + z = 32 and
x < y < z?

Good luck, troops. I'll post the solution Monday (probably late).

UPDATE: Jeffery nailed it. Bragging rights awarded. Go lord it over everyone you know. :)

Solution below.

How common are plug in questions?

In the Blue Book, about this common:

Screengrab from the PWN the SAT Math Guide

I'm not saying you need to plug in numbers for each (or even most) of these. But I am saying you should be aware of how often you have the option.

Weekend Challenge - End of the Road

Image found at this...awesome site.

This will be the last Weekend Challenge question that has access to the Math Guide Beta Program as its prize. I'm going to be closing the Beta to new users soon, as the book nears completion. If, by the way, you're interested in the day-to-day progress I'm making on the book, you can check in on me at Google+.

When I write questions (and I have to imagine this is the same way every question writer does it) I just put in placeholder numbers while I write and then I go back and solve. If the numbers don't work out nicely (say, a fractional child, or something) I'll change them around. But when I wrote this one, the numbers worked out perfectly the first time. That feels awesome. Anyhoo, Beta access to the first non-anonymous commenter to PWN the following question:

At Masuk High School, 200 people are in the chorus, 130 people are in the band, and 45 people take AP calculus. If, in total, 92 people take two of the three classes, and 80 take just one of the three, how many students take all three classes?

I'll post the solution Monday. Good luck, and have a great weekend.

UPDATE: Nice work, Jeffery. You're officially the last person into the Beta. I hope you enjoy it.

Solution below (although Jeffery and JD both posted rather nice ones in the comments).

Math Guide status update

I already emailed participants in the Beta about this, but I figured I'd make one last post about my book on the main site before it moves into the final development stages. It's pretty much written, to the point where I can say that, give or take 10 pages, it'll be about 350 pages long. Those pages will contain everything useful I've written about math on this blog (and a bunch of stuff I haven't posted), along with short drills at the end of every chapter to drive concepts home, and 4 longer drills at the end of the book. They will contain (but don't just yet) handwritten solutions to all of these problems, and a few handy Blue Book reference tools.

I'm really grateful to everyone who has participated in the Beta program. These brave pioneers pointed out countless spelling errors, missing words, unclear explanations, and bad formatting, and the book will be much better when it's released as a result of their efforts. If you're a Beta tester, thank you. Seriously.

If you've been meaning to get into the Beta and just never pulled the trigger, it's basically now or never. I'm going to be closing the Beta to new members by the end of November, because the book will be pretty much done, and it'll be time to start selling it for real. I'm hoping that copies will be available for purchase on Amazon by the end of December.

All future updates about the book will be made on my new Google+ page. Feel free to add me there, or just check in once in a while. I won't be posting about the book again here until physical copies are actually available for sale.

Weekend Challenge - Veterans Day edition

I've been having some minor technical issues with the blog. I think it has something to do with the code I wrote to make vocabulary words turn red when the page loads interacting badly with the code for DISQUS, which is the commenting system. But since I'm not a computer programmer, I have no idea how to fix it. All of which is to say: I'm sorry that this weekend challenge includes an additional element of frustration in that you may have to reload the page a few times if the comment system doesn't properly load the first time. I'd be happy to pay a programmer to fix it if any of you want to pay me to pay the programmer. :)

First correct comment wins access to the coveted PWN the SAT Math Guide. Make sure your friends are sitting down when you tell them you won. We don't want anyone to fall and sustain head trauma.

Seven years ago, Thom was half as old as Phil and three times as old as Melanie. If Thom is 19 years old now, how many years will it be until Melanie is half as old as Phil?

I'll post the solution Monday. Have a great weekend, y'all.

Nice work Cindy and Stephanie. Solution below.

Weekend Challenge - November SAT edition

First of all, if you're taking the November test, good luck. If you're prepared well, you have nothing to fear. Get in there and beast it.

Of course, many people aren't taking the November SAT, and they deserve some love, too. If you're not taking the test tomorrow, here's one tough question to noodle on while your contemporaries are out achieving glory. 

Prize for the first correct response: access to the PWN the SAT Math Guide. You must not be anonymous to win. 

In the figure above, B is the midpoint of AC and the center of the green circle. All other labeled points are also the centers of circles. If the green area is 9π, what is the area of the circle with center E?

I actually cackled sinisterly when I made this diagram. Good luck! :)

UPDATE: Congrats to "emolano82" for getting it first. Solution below!

SAT prep roadmap for self-studiers

As I see it, SAT prep has two main objectives:

1. Discover the most efficacious ways to solve common problem types.
2. Become proficient at recognizing opportunities to use those techniques in the wild.

Dangling modifier (artist's rendition)
Source.

It's important that you devote equal time and effort to both. In other words, if you only take practice tests repeatedly, or if you only study techniques without ever taking a practice test, you're doing it wrong. That's why all smart tutors and good prep courses make you take full length tests in addition to showing you the important techniques. Because it's one thing to be able to get a bunch of dangling modifier questions right when you know they're coming. It's another thing to have a dangling modifier jump right off the page for you when you're taking the actual SAT and you'll only see about two in a section.

If you're going it alone, you should consider following a similar recipe to the one tutors and course use. Here's a bare-bones SAT prep plan to help you go through this process:

The Size of the Fish

Disclaimer: This post is intended as pragmatic advice, not rebuke. Please don't misconstrue anything herein as nastiness. This blog is still a big love fest, and any appearance otherwise is simply a result of a temporary inarticulateness. Promise.

I don't like to talk about it in real life because honestly nobody wants to hear about it, but obviously part of my credibility as an SAT expert comes from the fact that I can score a 2400 myself, so I have to mention it here once in a while. I sometimes bolster my bona fides further by telling students that I was the valedictorian at my high school. Awesome, right? I know. 

The point of this post isn't to preen, though. It's to point out that that I graduated, ran a summer victory lap that went horribly awry, and then matriculated to Brown, where I had to adjust very quickly to a new peer group. At Brown, nobody cared that I was valedictorian back home. About half of my friends had been, too, and many more had acquitted themselves well at high schools whose rigorous curricula put my own's to shame. I struggled more in that first semester than I ever had in an academic setting, and than I ever have since. It was a semester-long lesson in humility and the nature of truly hard work.