- Wed Aug 30, 2017 2:47 pm
Numeric distributions are the sort of things you should be working on identifying in the diagramming stage of the game, tld5061. Always think about the numbers in every game you do! Here, numeric ideas are a big deal, starting with the fact that you must pick 6 of 10 stones. Numbers should be foremost in your mind from the get-go. Then we hit not one, but two number-related rules - you have to have at least two topazes, and if you have exactly two sapphires you must have exactly one ruby. With three types of stones to choose from, you should definitely be considering the various numeric distributions that might happen in this game, like this:
Could we do a 2-2-2 distribution, meaning two stones of each type? No, because two sapphires means one ruby (and, by implication, three topazes - play with that a bit to see which ones must be included).
How about a 3-2-1? Yes indeed, that's the two sapphires situation just discussed, although perhaps it could be all three of them, or maybe just 1.
What about a 3-3-0 - can we do that? Looks like it, since they never said you have to have at least one of each type. For example, what about FGH with XYZ, or JKM with XYZ?
Finally, since there are four topazes, can we do either a 4-1-1 or a 4-2-0? No, because W and Z cannot be selected together. The maximum number of topazes is 3.
Having done that work and determined that both 3-2-1 and 3-3-0 are possible, and perhaps having found a couple of templates or solutions that fit within each of those, you could tackle this question without waiting until the rest of the questions have been answered.
A doesn't have to be true - I just have to look at one of my hypotheticals (JKMXYZ) to prove I don't need G.
B doesn't have to be true - I would just look at my other 3-3-0 possibility, FGHXYZ, to prove J isn't required.
C is interesting - X is included in both of my hypotheticals, so perhaps it's needed, but there may be other solutions I haven't tried, so I don't know yet. I'll keep it as a contender.
D doesn't have to be true, because I know that my 3-3-0 distribution works.
E must be true! Only two distributions are possible, and they both have at least one 3 in them. Winner! I now know that X must not be required, even though I haven't played with it yet.
Numerical distributions tell you a lot about the shape of the game and about what is possible and what is not. Also, they often are directly tested in the questions, as in this case, so giving them due consideration from the beginning can help you quickly, confidently, and accurately select answers as you move through the questions. Don't wait to think about the numbers, tld5061, but tackle them head on and make big, important inferences from them, including, perhaps, templates that will allow you to crush the game. The time invested in the diagramming stage will almost always pay off big dividends in the form of even more time saved when working through the questions.
Count on it!
Adam M. Tyson
PowerScore LSAT, GRE, ACT and SAT Instructor
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