Numbers and Percentages, Weaken and Strengthen Questions

[Faith123]

Hello,
Pages 525 and 532 of the LR Bible, 2015 version, states a general rule for solving Weaken and Strengthen questions that contain numbers and percentages. The rule states:

"To weaken or strengthen an argument containing numbers and percentages, look carefully for information about the total amount(s) - does the argument make an assumption based on one of the misconceptions discussed earlier?"

I don't quite understand what this means. I understand that "total amounts" refers to numerical information (I may be wrong here, so please correct me if I am), but how exactly am I supposed to use this information to help me arrive at the correct answer?

Thank you.

Faith

[Nikki Siclunov]

Hello Faith,

Thanks for your question. The instructions in the LRB are indeed quite general, and this is intentional: there is a whole range of situations that might involve numbers and percentages, each of which would require a slightly different approach. Generally speaking, however, %# questions tend to confuse numbers with percentages, and vice versa. They also frequently fail to provide you information about the totals. For instance:

Let's say I told you there are more violent crimes in Gainsville this year than ever before, and concluded that the average resident in Gainsville is now more likely than ever to fall victim to a violent crime. Hopefully you can see this as a terrible argument: clearly, we don't know how the Gainsville population has changed over time. The conclusion is about likelihood (i.e. a percentage idea), whereas the premise describes an increase (a numerical idea). If the total population of Gainsville has tripled over the years, an increase in the total number of crimes wouldn't necessarily mean that the average person is more likely to become a victim. In fact, the crime rate - usually measured by the number of crimes per 100,000 people - could easily have gone down!

So, to weaken the argument, we can propose that the Gainsville's total population has drastically increased over the years. And, inversely, to strengthen the argument we can say that its population has decreased: more crime, spread across fewer people, would guarantee that the crime rate is now higher, and that your risk of being a victim has increased. If they ask you to identify an assumption upon which the argument depends, it would be that Gainsville's population has not substantially increased over the years. (Another assumption would be that we haven't changed the definition of what constitutes a "violent crime".) Does that make sense?

Don't forget that there is a wide variety of situations in which they can test your understanding of numerical evidence and its limitations. Most arguments using such information tend to be flawed, so carefully examine the evidence and figure out if it truly proves the conclusion of the argument. In most cases, it does not.

Hope this helps! Let me know.

Thanks!

[Faith123]

Hello Nikki,
Thank you for your explanation

The reason I asked the question was because I failed to answer the problem that corresponded to the general rule correctly. The problem I am referring to is on page 523, which is a Weaken question involving Numbers and Percentages.
My understanding of this problem is that the stimulus makes the misconception of concluding that an increase in the percentage of plastics being disposed of in landfills means that the amount (the "number") of plastics disposed of in landfills also increases. Using this information, I prephrased that the correct answer would be somewhere along the lines that the "number" of plastic being disposed of in landfills should decrease. Is my reasoning correct? or is it off? Did I interpret the stimulus correctly? I may have also misunderstood your explanation of the general rule in arriving at this reasoning. Can you help me with this?

Thank you.

Faith

[Nikki Siclunov]

Hi Faith,

Thanks for your question. The question you're asking about concludes that people have not reduced the amount of plastic they throw away, because plastics make up an ever-increasing percentage of the waste. Your reasoning is correct: the author conflates a percentage with an amount. If the overall amount of trash being thrown away has decreased significantly, the percentage of plastic in the waste would increase even if the actual amount of plastic waste was reduced. This is why answer choice (D) is correct. Inversely, if the total amount of waste remained the same (or increased), and apparently plastic waste makes up a higher percentage of that waste, then the conclusion would be strengthened: a higher percentage of the same (or larger total) would suggest a higher amount.

As suggested on page 525, focus on the total amount(s)!

Let me know if this clears things up.

Thanks!