This is the latest in a series of How To Analyze articles that began with the general How To Analyze A Practice Problem article (click on the link to read the original article). This week, we’re going to analyze a specific IR question from the Multi-Source Reasoning prompt category.

These prompts typically come with multiple questions (similar to a Reading Comp passage). First, give yourself about 2 to 2.5 minutes to read the prompt and take short notes. Then take up to about 2 minutes to answer the question.

Click on this link for the prompt and question. In case that link changes or gets broken, I’ve also included the text below “ but it’s best to use the link if it works because then you’ll be doing the problem in its official format. When you’re done, leave that page open (don’t click next) and come back here to discuss the solution.

Multi-Source Reasoning prompts consist of 2 or 3 tabs of information. Here is the prompt:

Tab 1: Techniques

Island Museum analyzes historical artifacts using one or more techniques described below”all but one of which is performed by an outside laboratory”to obtain specific information about an object’s creation. For each type of material listed, the museum uses only the technique described:

Animal teeth or bones: The museum performs isotope ratio mass spectrometry (IRMS) in-house to determine the ratios of chemical elements present, yielding clues as to the animal’s diet and the minerals in its water supply.

Metallic ores or alloys: Inductively coupled plasma mass spectrometry  (ICP-MS) is used to determine the ratios of traces of metallic isotopes present, which differ according to where the sample was obtained.

Plant matter: While they are living, plants absorb carbon-14, which decays at a predictable rate after death; thus radiocarbon dating is used to estimate a plant’s date of death.

Fired-clay objects: Thermoluminescence (TL) dating is used to provide an estimate of the time since clay was fired to create the object.

Tab 2: Artifacts

Island Museum has acquired a collection of metal, fired clay, stone, bone, and wooden artifacts found on the Kaxna Islands, and presumed to be from the Kaxna Kingdom of 1250“850 BC. ReseNavigators have mapped all the mines, quarries, and sources of clay on Kaxna and know that wooden artifacts of that time were generally created within 2 years after tree harvest. There is, however, considerable uncertainty as to whether these artifacts were actually created on Kaxna.

In analyzing these artifacts, the museum assumes that radiocarbon dating is accurate to approximately ±200 years and TL dating is accurate to approximately ±100 years.

Tab 3: Budget

For outside laboratory tests, the museum’s first-year budget for the Kaxna collection allows unlimited IRMS testing, and a total of \$7,000”equal to the cost of 4 TL tests plus 15 radiocarbon tests, or the cost of 40 ICP-MS tests”for all other tests. For each technique applied by an outside lab, the museum is charged a fixed price per artifact.

And here is the question:

For each of the following combinations of Kaxna artifacts, select Yes if, based on the information provided, the cost of all pertinent techniques described can be shown to be within the museum’s first-year Kaxna budget. Otherwise, select No.

 Yes No 2 bone implements and 5 fired-clay cups decorated with gold 7 wooden statues and 20 metal implements 15 wooden statues decorated with bone

After trying the problem, checking the answer, and reading the given solution (if any), I then try to answer the questions listed below.

The correct answers are No, Yes, and Yes. I’m going to pretend that I picked Yes, No, and Yes (that is, I missed the first two statements).

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 an IR Multi-Source Reasoning (MSR) prompt. As usual, there’s quite a bit of text to read before I can answer the questions, so I have to expect to invest some up-front time, but that time will be spread over multiple problems (similar to Reading Comp). (Note: this particular prompt comes with 6 associated problems. We’re doing just one in this article.)

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 got it wrong, so clearly I missed something. I’m going to have to figure out why I made the mistakes I made in order to figure out why I messed up.

Did I understand the actual CONTENT (facts, knowledge) being tested?

I’m not sure yet. While I was doing it, everything seemed to make sense “ but, again, I got it wrong. Time to dig into my process.

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?

Here we go. First, they asked me to determine whether the cost of performing a certain number of tests would be within the budget, which tab 3 told me was \$7,000. I need to figure out what I can about the various potential costs of the tests. The first tab mentioned 4 tests: IRMS, ICP-MS, radiocarbon dating, and TL. Tab 3 says that I can do unlimited IRMS testing, so I can ignore that as far as the budget is concerned. (Notice what I did there? I’m starting to put myself in the problem. The budget is mine now. : ) ) What about the other three tests?

Tab 3 says that \$7,000 is equal to the cost of 4 TL tests plus 15 radiocarbon tests, or the cost of 40 ICP-MS tests. I can write a couple of formulas here: 7,000 = 4TL + 15RC and 7,000 = 40ICP. It also says that For each technique applied by an outside lab, the museum is charged a fixed price per artifact.

I overlooked that second part during the test “ and that’s definitely going to make a difference. Now that I’m reading it, my first instinct was to think that, no matter the artifact or the test, the price is the same. That can’t be it, though, because then 7,000 wouldn’t equal 40 of one type of test but only 19 of two other types of tests. Instead, it must be this: the price is calculated per item or per artifact, and the price involved depends on the test performed, not what the artifact itself is. Further, regardless of what the artifact is, the price for a particular test is fixed. In other words, in my formulas above, there really is only one price for any TL test, another price for any RC test, and yet another price for any ICP test.

Ok, what else? The second formula is easy: I can figure out exactly how much an ICP test costs. (I’m not actually going to break out the calculator unless I have to, though. I’m a big fan of avoiding unnecessary calculations!) The first one is more complicated, but I do have at least some information about all 4 tests now.

I’m going to analyze the third statement first because it’s the one I got right. Hopefully that means I actually knew what I was doing! If so, that might help me when I examine the two that I missed.

The third statement says:

15 wooden statues decorated with bone

Hmm. Something wooden is made of plant matter, so we’d have to do the radiocarbon dating test. If it also has bone, that also means we have to do the IRMS test. The IRMS test doesn’t cost us anything, but the RC test does. I know that \$7,000 (my budget) can pay for 4 TLs plus 15 RCs. If that’s the case, then certainly I can pay for 15 RCs alone, without any TLs. Yep, my reasoning was fine on this one; this statement is a Yes.

2 bone implements and 5 fired-clay cups decorated with gold

Bone is still free, so I can ignore those 2 implements. For the 5 cups, I need to do 5 TL tests (for the fired clay) and 5 ICP-MS tests (for the gold). If I can do 40 ICP-MS tests for \$7,000, then I can do 5 for a lot less than \$7,000. For TL hmm. I can do 4TLs plus 15 RCs for \$7,000, so why can’t I do 5 TLs? Oh, I see. Argh. I was just unconsciously assuming that they’re all around the same price. But let’s say the TLs cost \$1,500 each and the RCs are really cheap. Then I can’t do 5 TLs without going over budget. Okay, I see why this one’s a No.

So I didn’t really fully get straight in my head what they were telling me with those formulas, and that caused me to make a mistake. It’s not that I couldn’t understand what was happening – I just didn’t take the time to think it through.

7 wooden statues and 20 metal implements

Wooden again means doing an RC test and metal requires an ICP-MS test. If we can do 40 ICP-MS tests for \$7,000, then 20 will cost less. Oh, wait a sec. 20 will cost \$3,500 exactly, because each ICP-MS test costs the same amount. I didn’t think about this the first time. And for the wooden statues, if I can do 15 RC tests (plus 4 TLs) for \$7,000 let’s say that the TLs cost nothing and the 15 RCs cost the entire \$7,000. If I’m only going to do 7 RCs then that would cost a little less than half (\$3,500) because 7 is a little less than half of 15.

In other words, my costs are \$3,500 plus something a little less than \$3,500, which is a total of less than \$7,000. Argh! This one does work. Two things hurt me here. I glossed over the sentence that told me the per-artifact test price is constant. Second, I didn’t really dive into the math here. In fact, looking at my scrap paper, I didn’t write down any math at all for that second statement. I just didn’t do enough work here.

Did I have the SKILLS to follow through? Or did I fall short on anything? 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?

The steps I had to take weren’t super hard “ I just wasn’t systematic enough.

Am I comfortable with OTHER STRATEGIES that would have worked, at least partially? How should I have made an educated guess? Do I understand every TRAP & TRICK that the writer built into the question, including wrong answers?

That last detail about the per-artifact pricing and the fact that the cost for one type of test is constant “ yeah, we could kind of call that a trap. They probably wrote it that way figuring some of us would gloss over it. But look at Tab 3 “ the text is so short and the title of the tab is budget. Given that this question was about the budget, I should have re-read everything in that tab.

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’ve done this gloss over the details thing on Reading Comp in the past. Part of my problem is that I feel like I’ve already spent so much time reading that I have to rush rush rush to answer the question! But that’s useless if I rush so much that I start messing up. I think I need to work on knowing what I need to re-read “ I need to be able to make very conscious choices that, yes, it’s worth it to re-read these particular sentences or paragraphs because they really are going to help me answer the questions.

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?

Reading for Detail: basically anything that involves figuring out some specific details in order to answer a question, whether it’s an RC question or an IR question. When I see that, I know I have to figure out what to re-read and I have to make myself take the time to do so. Also, I have to write stuff down!

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. You’ll also notice that, for some of the analysis questions, I have quite long answers and, for others, I wrote barely anything at all. Pick and choose what you need to analyze based upon what happened when you were doing the problem.

Hopefully, this gives you a better idea of the way to analyze an IR 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.

#### Stacey Koprince

Stacey Koprince is an Instructor and Trainer as well as the Director of Online Community for Manhattan Prep. She's also a management consultant who specializes in corporate strategy. She has been teaching various standardized tests for more than fifteen years and her entire teaching philosophy can be summed up in five words: teaching students how to think.

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