How to Analyze a Practice Data Sufficiency Question
This is the latest in a series of “How To Analyze” articles that began with the general “How To Analyze A Practice Problem” article. In this article, we’re going to analyze a specific Data Sufficiency question.
First, set your timer for 2 minutes and try this GMATPrep problem:
* ” A contractor combined x tons of gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?
“(1) y = 10
“(2) z = 16”
After trying the problem, checking the answer, and reading and understanding the solution (read the original article, linked above), I try to answer these questions:
1. Did I know WHAT they were trying to test?
- Was I able to CATEGORIZE this question by topic and subtopic? By process / technique? If I had to look something up in my books, would I know exactly where to go?
The question is a Data Sufficiency question from the Statistics chapter of my Word Translations book. It’s testing the concept of average (arithmetic mean) and, more specifically, it’s testing the concept of weighted average. The problem never mentions the word “average” but I figured this out because the problem talks about 2 sub-groups that are combined in some way to make a 3rd overall group, or mixture of the original 2 sub-groups.
- Did I COMPREHEND the symbols, text, questions, statements, and answer choices? Can I comprehend it all now, when I have lots of time to think about it? What do I need to do to make sure that I do comprehend everything here? How am I going to remember whatever I've just learned for future?
I noticed that the problem has three variables: x, y, and z. It asks me to solve for the value of x. One of the statements gives me the value for y and the other gives me the value for z. I’m already thinking E is probably not the right answer (think about why before you keep reading – I’ll explain this under the “Other Strategies” question, below).
- Did I understand the actual CONTENT (facts, knowledge) being tested?
What kind of average is this problem discussing? Regular average / mean is characterized by the formula A = S/n, where A is the average of the set, S is the sum of the items in the set, and n is the number of items in the set. Is this problem testing “regular” averages? Let’s see: a “regular” average of 10% gravel and 2% gravel would be (10+2) /2 = 6. But the problem says the resulting mixture is 5% gravel, not 6% gravel – so this isn’t a “regular” average.
That means this problem must be about the more complicated weighted average. In a weighted average, some of the elements are weighed, or counted more heavily, than other elements, so the calculation has to take that into account. (And I have to know how to do that… more on that later.)
2. How well did I HANDLE what they were trying to test?
- Did I choose the best APPROACH? Or is there a better way to do the problem? (There's almost always a better way!) What is that better way? How am I going to remember this better approach the next time I see a similar problem?
(See the original article, linked at the top, for a detailed discussion of the best approach. Here, I’ll pretend that I didn’t use the best approach.) Weighted average problems can be solved by using the weighted average formula, which is what I tried to do. I got into trouble with it though – I didn’t set it up properly and so I couldn’t finish it to see whether I could solve.
There’s a shortcut solution method that I could have used, but I forgot about it when I was doing this problem. (See original article for this shortcut solution method.)
- Did I have the SKILLS to follow through? Or did I fall short on anything?
I ended up having to guess because I couldn’t solve the “official math” way and then I forgot to try the easier “shortcut” way. I’m going to redo this problem using the easier shortcut, and I’m also going to go find a couple of additional weighted average problems and do those with the easier shortcut way so that I can make sure that (a) I know how to do it this way, and (b) I remember / recognize when I can do it this way.
I should still also learn how to do this using the “official math” weighted average formula, just in case I ever have to use the long way.
- Did I make any careless mistakes? If so, WHY did I make each mistake? What habits could I make or break to minimize the chances of repeating that careless mistake in future?
When I tried to use the “official” formula, I couldn’t remember exactly how to set it up, so I ended up setting it up with too many variables, and then of course I couldn’t solve. It’s data sufficiency, so knowing I can’t solve is sufficient… except that I knew I was doing something wrong because I couldn’t really remember the formula. I need to go and study that formula. I should make a flash card with “weighted average formula” on one side, and the couple of different ways the formula can be written on the other side. (Those different ways are listed in my Word Translations strategy guide.)
- Am I comfortable with OTHER STRATEGIES that would have worked, at least partially? How should I have made an educated guess?
I was pretty sure it wasn’t E because it looks like you can set up a three-variable equation, and then we’re supposed to solve for x. Each statement gives us only one of the two remaining variables, so it “looks like” it can’t be done unless you have both of the other variables… which you would for answer choice C. So, at the least, C does work and it’s not E.
I ended up guessing C but, in hindsight, that’s a trap too. I could ask my 14-year-old niece: if you have an equation with three variables and you want to solve for one of those variables, what do you need to know? And she’d say “The other two variables.” (And then she'd probably think, “Duh, Aunt Stacey.”) This test isn’t for my 14-year-old niece, though, it’s for people who have already graduated from college. So that’s too easy. And that’s really interesting, because that means that you most likely CAN actually solve given just one statement. Each statement represents one of the two unknown variables, so if one works, it’s fairly likely that the other one works too… so I probably should have guessed D.
- Do I understand every TRAP & TRICK that the writer built into the question, including wrong answers?
See above – I think C and E are both trap answers on this one, and C is especially tempting.
3. How well did I or could I RECOGNIZE what was going on?
- Did I make a CONNECTION to previous experience? If so, what problem(s) did this remind me of and what, precisely, was similar? Or did I have to do it all from scratch? If so, see the next bullet.
- Can I make any CONNECTIONS now, while I'm analyzing the problem? What have I done in the past that is similar to this one? How are they similar? How could that recognition have helped me to do this problem more efficiently or effectively? (This may involve looking up some past problem and making comparisons between the two!)
Yes, I did make a connection, but I also missed one. I did recognize that this was a weighted average problem even though it didn’t explicitly mention the word “average,” so I’m happy about that. I didn’t recognize, however, that I could have used a big shortcut that would have saved me a lot of time and frustration. I need to go study that shortcut, how to recognize it, how to use it, etc – and maybe make a couple of flash cards.
- HOW will I recognize similar problems in the future? What can I do now to maximize the chances that I will remember and be able to use lessons learned from this problem the next time I see a new problem that tests something similar?
I need to do everything I already described in my notes above. I’m also going to re-do this problem from scratch– actually make myself write out the best way to do it, alternate ways to do it, how to make a guess, and so on, so that I really remember the lessons. Then, because my big problem on this one was with recognizing that I could use a shortcut and then actually using it, I’m going to find other weighted average problems that I’ve already done in the past and practice: (1) knowing how to recognize that it’s a weighted average and that it qualifies for the “weighted average shortcut,” (2) working through the problem using that shortcut, and (3) thinking about how to make an educated guess. Then I’m going to do new weighted average problems as part of a mixed set of problems consisting of things I've messed up recently and other random things (so that I don’t know exactly what I’m getting for each problem) and see whether I can quickly recognize and apply what I just learned.
And that’s it! Note that, of course, the details above are specific to each individual person – such a write-up would be different for every single one of you, depending upon your particular strengths, weaknesses, and mistakes. Hopefully, though, this gives you a better idea of the way to analyze a problem. This framework also gives you a valuable way to discuss problems with fellow online students or in study groups – this is the kind of discussion that really helps to maximize scores.
* GMATPrep? question courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.