Weekend Challenge - pumpkins

EDIT: I'm home now so this is formatted right. Suffice to say I'll never use the Blogger Android app again.

I'm in Chicago without a computer so this will be short and sweet since I'm typing with my thumbs.

First correct and non-anonymous comment wins access to the Math Guide.

Chris bought a pumpkin last year that had a diameter of 10 inches and yielded the PERFECT amount of toasted seeds. His pumpkin this year has a diameter of 13 inches. Pumpkin skins generally have a thickness of one tenth of the radius of the pumpkin. Assume pumpkins are spherical and that each pumpkin has roughly equal amounts of seeds by volume. What will be the ratio of the amount of seeds Chris gets this year to the amount of seeds he got last year?

UPDATE: Nice work, Edward. Solution below the cut.

Prime factorization and the SAT

So this isn't a super important thing as far as how often it appears on the SAT, but it does pop up time and again, so if you're shooting for perfection (or close to it) you might want to pay attention. Otherwise, you can get by just fine without this little nugget (but you might as well read it, since you're here anyway).

Do you know what prime factorization is? Basically, the prime factorization of a number is the way you would build that number by multiplying together only prime numbers. To find the prime factorization of a number, divide by 2 if you can. Do that as many times as you can. Once you can't do that anymore, try dividing by 3 as many times as you can. Then by 5. Then by 7. Then by 11. I think you get the idea.

Let's try one together, like best friends

What is the prime factorization of 13728?

Whoa. Big number. Lots of people like to make trees when they do this. Let's do that. Damn I wish you and I were in the same room with a chalkboard right now. This is going to take flippin' forever.



See how, when I couldn't divide by 2 anymore, I went to three, and then to 11? I knew I was done when I had two prime numbers, 11 and 13. If I multiplied all those numbers back together, I'd get 13728 again. For serious. Try it:

2 × 2 × 2 × 2 × 2 × 3 × 11 × 13 = 13728

At this point it's important for me to tell you that I've never seen an SAT question ask directly about prime factorization.

So why the heck?

Because what I have seen the SAT ask about before (and if you took the October 2011 SAT, you can confirm) is the lowest multiple of two numbers that's also perfect square. It just so happens that prime factorization is a great way to find a perfect square.

A weekend challenge about rats. Rats are fun!

I'm going to tell you a secret: I don't sleep well at all the night before SAT scores are released. It's not like I even took it. I just get so excited for all the kids I've worked with that I can't sleep. So last night, after a sleepless night followed by a bunch of good news, I slept like a rock. And I woke up energized, and I got some much-needed work done on my book, and now I'm posing this weekend challenge in timely manner. I'm feeling very productive today. Yay me!

By now you know the drill I'm sure. First correct (and non-anonymous) comment gets access to the Math Guide Beta (to which I just added some more hard questions this very morning).

Adina keeps track of the number of rats she sees while she waits for the subway every morning. She noticed that there was a roughly 46% increase in the amount of rats she spotted between Tuesday and Wednesday. If she saw 19 rats on Wednesday, what will be the percent decrease in rat sightings if she sees the same number Thursday that she did Tuesday? Round your answer to the nearest percent.

Good luck, y'all. And have a great weekend! I'll post the solution early next week.

UPDATE: Nice work, Jessica. Enjoy the Beta. Solution is below the cut.

I wish we were meeting under happier circumstances, but welcome.

October SAT scores are out today, and that always means a prodigious increase in traffic to this site. Unfortunately, most of you first-timers are probably not here because you're ecstatic about your SAT scores. If that's the case, I'm genuinely sorry to hear it. I hope I can help you turn that around.

Aside from the Reading, Math, and Writing collection posts linked at the top of the blog, I figured I'd point out a few places that might serve well as jumping-in points.

• PWN the SAT Q&A. This is a Tumblr blog where you can ask me specific questions about questions you're struggling with. You can also ask for more generalized advice, but please know that I don't know you all that well, so be as specific as you can if you want a specific answer. One rule: submit one question at a time please. It's fine if you submit a bunch of different questions, as long as they're each in their own submission so I can spread the work of answering them out a little bit.
• Score Choice FAQ. If you're wondering how Score Choice works, and how to best present yourself as you finalize your application, you might find some help here.
• Philosophy. This is a collection of my musings about the test (in no particular order). I have a lot to say about it.
• You might also want to try some free diagnostic drills to give you a head start on prepping for the next test, especially if you're planning on taking the November test:
• Math - Diagnostic Drill #1
• Math - Diagnostic Drill #2 (This one is the hardest of the three, I think)
• Math - Diagnostic Drill #3
• Writing - Sentence Improvement Workout

Some more highlights from the question writing contest

When I posted that question writing contest a few weeks back, I thought I'd get some pretty good stuff. Because you guys are smart. And then, for a little while, not much happened. I was all </3. But then some great stuff started rolling in and I was all \\(*o*)//. I bet, reading this paragraph, you're all o_O. Right?

To the submissions!

From Debbie Stier:

• Candy bars were passed out among 10 students. If the average (arithmetic mean) number of candy bars that the students received was 11, what is the greatest possible number of candy bars that one student could have received?
  
  A) 11
  B) 20
  C) 101
  D) 109
  E) 110

Commenter Katie (fresh off a weekend challenge win) posted a few great grid-ins, too:

• Dan wrote a 7 digit phone number on a piece of paper. He tore the paper accidentally and the last two digits were lost. What is the max number of arrangements of two digits, using digits 0 through 9, he could use to find the correct number?
• If x + (1/x) = 4, what is the value of x² + 1/(x²)?
• The lengths of the side of an isosceles triangle are 30, n, n. What is the smallest possible perimeter of the triangle?
• If (a/4) + (b/8) + (c/24) = 1, what is one possible value for abc?

And of course, this great question was submitted to me by email.

Two problems

1. Some of these require some teensy clarifications before they're ready for prime time.
2. I have no solutions! 

Commenters, this is where you come in.

Return of the Weekend Challenge

I didn't do a Weekend Challenge last weekend. It's not like I didn't want to, y'all. Things just got totally cray-cray. My use of "cray-cray" in the previous sentence should be enough of an indication to you that things remain squarely thus.

I actually wrote two questions for this weekend, but I'm only going to use one of them. The other one is going into the strategic reserve. For emergencies.

If you're the first to answer this correctly (and not anonymously), I'll bestow upon you coveted access to the PWN the SAT Math Guide Beta.

Other ways you can gain access to my Magnum Opus:

• Buy it. It's $5. You get about 300 pages of useful SAT math help. I get a footlong meatball sub at Subway. 
• Send me a question of your own making. Added bonus: this is a fantastic way to solidify your knowledge of the test. 

On to the question:

In the figure above A is the center of the circle, A and D lie on BF and CE, respectively, and B, D, F, and G lie on the circle. If BC = 3, and DG (not shown) bisects BF, what is the total area of the shaded regions?

Good luck, and have a great weekend. I'll post the solution early next week.

UPDATE: Commenter Katieluvgold got it first. Nice work Katie!  Solution posted below the cut.

Be suspicious of "easy" answers to "hard" questions.

Since you've been paying such close attention, you know by now that the difficulty of math questions increases as a section progresses*. On a 20 question section, you can count on #1 to be super easy, #5 to be bit tougher, #10 to require more than a modicum of thought, and #20 to be a royal pain. Duh, right? You know this. If you've ever taken an SAT or PSAT, it's almost impossible not to have noticed this. But have you thought about what it means for you, the intrepid test taker?

This simple fact has 2 important implications:

1. Easy questions are more important than the hard ones for your score (covered a previous post).
2. You should be suspicious of "easy" answers to "hard" questions (covered here).

When you're faced with a question that's supposed to be more difficult, you should resist the urge to jump on an answer choice that seems immediately obvious. It's probably best to illustrate this with an example.

15. Stephen wins the lottery and decides to donate 30% of his winnings to charity. Then he decides to give 20% of what he has left to his mother. What percent of his winnings does Stephen have left for himself?
    
    (A) 67%
    (B) 56%
    (C) 54%
    (D) 50%
    (E) 14%

Interview: John Carpenter, author of Going Geek

John Carpenter. Smart dude.

I haven't used this space for this kind of thing before, but I used to love posting interviews of artists I liked back in the day when I was a music blogger, and after I read John Carpenter's Going Geek: What Every Smart Kid (and Every Smart Parent) Should Know About College AdmissionsI decided to send him an email and see if he'd be willing to answer some questions. 

I really thought John's book delivered good, solid advice about how smart kids—and if you're spending time reading an SAT blog, you probably qualify—should approach college admissions. And I dug the way he was able to set so much insightful advice about a truly labyrinthine process in a completely non-intimidating, conversational tone. So I got him to share some of that here, on my site, free of charge to you. You know how I do.

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PWN the SAT: I read Going Geek on the train, and said "YES!" out loud more than once, much to the chagrin of my fellow passengers. I hate to ask you to do this because you wrote so much excellent advice, but if you could distill the whole book down to one overarching theme, what would it be?

John Carpenter: Thanks for the positive feedback, and I have to admit that I love that image of you reading on the train and finding stuff you agreed with. Anyway, I actually like this question quite a lot, and the answer is easy to give.

Be intentional. Be thoughtful. Be organized. And for the really smart kid, all those things often mean just being yourself. The theme that I hope kids take away is that it's possible to create an amazing application by simply THINKING a little bit about what it is that gets you excited intellectually and then sharing that in a meaningful way.

PWN: What role does the SAT play in college admissions?

JC: Part of Going Geek is about the purpose of standardized tests in the admissions process; in fact, there's a whole chapter called "The Standardized Geek" that explains how admissions officers use SAT scores and why they're important at many colleges and universities. One purpose is to give admissions officers a way to compare students who are obviously very different and who have different strengths. In a society that's driven by data, it's easier to make difficult decisions when you can put numbers on things--even dissimilar things, or in this case, people. Also, admissions officers are looking for ways to find students who will likely be successful in college, and lots of studies bear out the idea that SAT scores often correlate with academic success at the undergraduate level.

PWN: Right. So although standardized testing is my bread and butter, it's only the tip of the admissions iceberg. What are some other things that should be on students' radar?

JC: The most important thing always, always, always is a student's academic achievement. That is usually measured by the level of difficulty of a student's coursework and grades. In other words, how challenging were the courses a student took in all four years of high school and how well did the student do across the board? But another way to highlight academic strength is to point out places where intellectual engagement has taken place in a student's life, and that gets more to the core message of the book.

PWN: What's the most common mistake you see really smart kids make as they apply to schools?

Will Latin help you on the SAT?

Note: I'm cross-posting this great question I got at qa.pwnthesat.com because it's easier to archive it here and I thought this was worth being able to refer back to. I hope you don't mind.

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Original Question: Would it be helpful to know Latin for the SATs?

Answer: This is a fantastic question! A lot of people (especially Latin teachers) will tell you that it's incredibly helpful to know Latin for the SATs. I know the Latin teacher in my old high school used to make a presentation every year to the incoming freshmen that said exactly that (and back in my day, vocabulary was even more important on the SAT because you had analogies and antonym questions, which were the effing worst). The idea is that since many English words have Latin roots, you might be able to figure out words you don't know based on roots. You might, for example, find it helpful to know that "circum-" means "around." But does that help you figure out "circumspect" on the fly? Well...maybe. I use the root as mnemonic to remember that one who is circumspect (which means prudent and considering all consequences before acting) looks at issues from every angle—from all AROUND. But every time I've tried to help a kid figure out the word by saying "well, you know the root 'circum-' means 'around'..." it hasn't led them to the right answer. So, many words in English do have Latin roots. But that wont always help you figure out what the English words mean.

Better late than never!

So the question writing contest I proposed a few weeks back didn't exactly explode onto the scene like I thought it would, but I still think it's a fantastic way for you to improve your skills, so just FYI: it's still open.

I got the question above in an email the other day. The writer prefers to remain anonymous, but I've given him Beta access to the Math Guide because it's an awesome question. It incorporates circle properties, shaded regions, and has great, well-planned incorrect choices. That's good hustle.

Q: Why read PWN the SAT?

A: Because I do a pretty good job coming up with questions that are similar to ones you might see on test day. Like this one (from my circles post):

It's not exactly the same, but if you had solved this question before the October test, I'd say you had a significantly better chance of answering that tough circle question correctly.