The authors of the LSAT love to play with numbers. This makes sense when you consider that the LSAT is a test of logical reasoning, and math is completely logical. While it’s true that they do sometimes test our understanding of actual numerical concepts, like averages and ratios, most of the questions are not testing your math skills. Don’t worry – there won’t be any questions that rely on your remembering the Pythagorean theorem! Instead, they are about logical relationships that happen to involve numbers and percentages. When you encounter them (and you will – there were at least 5 such questions on each of the June and September 2016 tests, and at least 6 on the December 2016 test) it can sometimes help to supply some numbers of your own to make sense of things.
Take, for example, a question on the December 2016 test that told us about a car company (I’ll call them Company X here) selling most of their cars last year to the residents of a particular town. When I see that key word “most”, I immediately insert some numbers. I like to keep them simple, so I imagine that the total (in this case, the total number of cars that Company X sold last year) is 100. “Most” means more than half, so that means Company X must have sold at least 51 cars to the folks in that town. Maybe more, sure, but at least that many. Now, with those numbers in my head, I can begin to really visualize and understand what the stimulus is telling me.
The stimulus goes on to tell us that most of the cars that the folks in that same town bought last year were not from Company X. Thinking some more about my numbers now, that means the 51 cars they bought from Company X are less than half of the total number of cars they bought. They must therefore have bought at least 52 cars from one or more other companies, and that means they bought a minimum of 103 cars last year (51 from Company X and 52 not from Company X). At this point, that’s all I know.
The wrong answers to that question talk about comparing last year’s sales in that town to other years’ sales or about who else sold cars to the people in the town. I have no info about any of that. The stimulus did throw in that Company X did have its best year last year, but told us nothing about prior years’ sales to residents of the town. I don’t know if sales went up or down in the town, I don’t know anything about their overall market share, or about what the townspeople bought or didn’t buy in other years. I also have no information about where those 52 other cars came from. Perhaps from one competitor, or perhaps from a combination of many competitors.
What do I know? Using my numbers as a guideline, I know that the people in that town bought more cars (at least 103) than Company X sold last year (100). Make up any numbers you like and you will come to the same, inescapable conclusion. It must be true – the numbers don’t lie! That’s the correct answer to that question.
Whenever you encounter claims in LR about numbers or percentages, try putting them into context by supplying simple numbers (100 works great for any problem involving percentages) and seeing if the evidence you have supports the conclusion. When you are asked to compare two groups, ask yourself if you know the relative sizes of the groups, and if not, try imagining that one group has 100 people or things in it and the other has 1,000,000 (and then, if you still aren’t sure, flip those numbers around). “Most of the people in Hickory do not smoke cigarettes, but most of the people in Hickory do drink alcohol” is a comparison of one group – the people of Hickory – to itself, so we can make at least one solid inference: there are more people there who drink than who smoke. However, “Most of the people of Hickory do not smoke, but most of the people of Saxapahaw do smoke” gives us a comparison of two groups (people of Hickory and people of Saxapahaw) whose relative sizes are unknown. Can I be sure that there are more smokers in Saxapahaw? Not without knowing that the two groups are at least the same size or that Saxapahaw is bigger! Supplying numbers can help clear that up quickly and easily – imagine Saxapahaw has a population of 100 and Hickory has a population of 1,000,000 and you can see that such a numerical conclusion based solely on the claims about “most” (which is, after all, a percentages concept – more than 50%) is not supported. Percentages alone do not prove numbers, and numbers alone do not prove percentages.
Be suspicious of claims involving numbers and percentages on the LSAT, because most of them are flawed. When in doubt, make up some numbers and see what you can and cannot prove! Count on it!
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Photo “Numbers” courtesy of Andy Maguire