Sunday, July 24, 2011

meanwhile, in GRE-land...

Scores for the Problem Solving practice set (Quantitative):

Basic: 10 out of 10

Intermediate: 8 out of 10

Advanced: 9 out of 10

It's sometimes hard to tell what makes the advanced-level problems advanced. The advanced problem that tripped me up turned out to be relatively simple to set up; I had made a mistake in conceptualizing the problem, which was this:

Phillip has twice as many tropical fish as Jody. If Phillip gave Jody 10 of his tropical fish, he would have half as many as Jody. How many tropical fish do Phillip and Jody have together?

(excerpted from Kaplan New GRE Math Workbook, 8th Edition, p. 45)

Figuring out that P = 2J was no problem. That's a good algebraic rendering of the first sentence. The second sentence threw me off, though: how exactly was I to interpret "half as many as Jody"? Did this mean "half as many as Jody had after Phillip had given her the fish," or "half as many as Jody originally had"? Unsure how to proceed, I tried setting the problem up several different ways, and that's what kept me from getting the right answer: I had no firm basis on which to choose the correct approach, so in the end I chose none.

The Kaplan manual says this:

Let P represent Phillip's fish and J represent Jody's fish. If Phillip has twice as many tropical fish as Jody, you can write: P = 2J.

If Phillip gives Jody 10 fish, then he will have 10 fewer, or P - 10, and Jody will have 10 more, or J + 10. In this case Phillip would have half as many as Jody, so

P - 10 = (1/2)(J + 10).

The rest is easy, because now it's just a systems of equations thing. But as you see, the problem takes "half as many as Jody" to mean "half as many as Jody had after Phillip had given her the fish." Is this a commonsense reading of the problem? Am I wrong to think the wording is a bit unclear? I've often found myself frustrated by math and logic problems because I often seem to see multiple possible interpretations of the wording.

The other two problems I got wrong aren't worth displaying here; I was careless in my setup, but not because of any misinterpretation.

A 27 out of 30 puts me in about the same 710-ish range I've been in all this time. The goal is to get 30 out of 30, consistently. This will mean a reduction in the carelessness department, and a quicker ability to grasp how to set problems up. At YB where I teach, the kids learning SAT Math go through a section of "English to algebra translation." I should probably sit in on one of those sessions myself.



Charles said...

I don't know, it seems pretty common sense to me. Giving someone something requires they they accept it, otherwise you haven't given it to them. Until Jody has the fish in her possession, Phillip still owns them. There is no in between, unless Phillip tosses Jody the fish and we are asked to figure the totals while the fish are still in mid-air.

Honestly, I think you may have overthought this one.

The real question here is what exactly did Phillip get from Jody in exchange for the ten fish? Tropical fish aren't cheap.

Kevin Kim said...

If it happened on Steak and Blowjob Day, then we know what Phillip got.

You may be right that I've overthought this problem, but it's hard to shake the feeling that the second equation could have been set up as

P - 10 = (1/2)J

--thus yielding

2J - 10 = (1/2)J

4J - 20 = J

3J = 20

...leaving us with fractions of fish. OK, so maybe that doesn't work.

Charles said...

I wasn't even thinking of the math. Just looking at the language, it seems pretty obvious to me what they meant. It never even occurred to me that there could be any other interpretation. My conclusion: your indoctrination in Po-Mo theory in the U.S. graduate school system has made you unable to see things as they are without deconstructing them and trying to find the holes. (Then again, I will blame anything and everything on Po-Mo, given the chance.)

I didn't even bother with equations when I saw that problem. I just read it and thought, "Hmm. Twice and half are inverses, so if the exchange of ten fish flips this relationship around, this (ten) is also the number of fish that Phillip and Jody each have to have if we leave out the ten fish being exchanged."

(I realize this explanation will make no sense to anyone but me, but again, I suck at maths.)

I had never heard of Steak and Blowjob Day, by the way. Beats White Day, that's for sure.