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Ratios/Increases/Percentages Confusion
"If we can instill the habits of reading things such as “ratios”, "increase”, and “percentages” and still remember that it doesn’t necessarily mean “more” of something, then we will be less likely tricked on the answer choices." - Someone Else
Someone other than myself wrote this as a comment and I made note of it a while back... I've wrestled with it but can someone please explain this to me like I'm five? /explainlikeimfive
Specifically, how is it possible that an increase in something does not necessarily mean more of that thing?
Comments
I think it comes down to context and how the stimulus is presented. The LSAT writers will hide their flaws by mixing ratios and increases/decreases in numbers overall to confuse you.
An example I can think of is:
Last year at our banquet we served apple pie and 75% of the pieces were eaten. This year 90% of the pieces were eaten. Therefore, the total number of slices consumed this year was more.
In that argument, the assumption lies in that the total number of pie slices remained constant. If the total number of slices provided shrinks, the percentages can still hold. Usually in this situation we would see a weaken question but I could see where strengthening could occur if we can give info showing that the total consumed is still greater than the previous year. If we wanted to strengthen this, then we would need to show that the total number of slices available increased this year as well.
We could do a strengthen, weaken or a NA question on this (probably others too but that is what comes to mind haha). The test writer's love to leave us in the grey on numbers. Its one of my weak points sometimes I admit. I love the quote though and it is a great way to put the whole thing into perspective.
Hope this helps!
Oh yeah, there are some tricky LR questions (esp. flaw questions) that play on this idea of proportional vs. absolute change.
Let's say that we talked to every single person in City A (the entire population) in two separate years and asked them whether they prefer driving or public transportation.
In 2010: 35% of people said they prefer to drive instead of using public transportation.
In 2018: 15% of people said they prefer to drive instead of using public transportation.
Does this mean that fewer people in City A prefer to drive now in 2018 than in 2010?
No, it doesn't. Sure we can say a smaller percentage of people prefer to drive now, but we can't say a smaller number of people (an absolute value).
So why can't we? Let's attach some numbers to our results.
70/200 is still 35%, 150/1000 is still 15%. But, well, we know that 70 is less than 150. So, in absolute terms, a greater number of City A's population prefers to drive in 2018 than in 2010.
Essentially, what percentage doesn't tell us is the total number that makes up the pie that we're measuring. From just the percentages, we can't tell that City A had a population increase (the pie got larger). We have to see the hard numbers for that. And that is the issue with using percentages (proportions, or any other "comparative" measure) to make statements regarding absolute values.
Not sure if this was ELI5-enough, but hope this helps!
I used to struggle on these but when you see a set of ratios/percentages being compared, you just have to ask yourself:
"what are these percentages of?"
or
"sure I know the size (%) of the slice, but what is the size of the pie?"
Even though a question tells you a percentage changes, there's no meaningful point of comparison without knowing what they are percentages of
So, as others have mentioned above:
Among the situations compared, the size of the pie can do 1 of 3 things:
1.) Stay the same
2.) Increase in size
3.) Decrease in size
Without knowing the size of the pie, you have no idea what say 30% vs. 50% means.
For extra practice, you could check out question: 19.2.18
Hope this helps!
The answers above were fantastic. I would also add that if someone said that a deficit increased, that means that there is less of something. Say that a company's budget remains the same year to year, but this year their deficit increased. That means that they had less income, less cash available. So that's a possibility. LSAT questions are written to be as confusing as possible, so you just have to be very skeptical and with an eagle eye all the time.
Yeah, great explanations already. It's all about the size of the pie.
http://i49.tinypic.com/157ystt.jpg
Thank you so much everyone! It has officially clicked.
@akeegs92 The banquet pie example really helped.Thank you!
@"Habeas Porpoise" Your explanation of proportional vs. absolute change and the public transportation example totally clarified things! Thanks!
@Mike_Ross I'll be sure to use this question prompt the next time I see a a set of ratios/percentages being compared: "Sure I know the size (%) of the slice, but what is the size of the pie?". Thanks!
@"Leah M B" Thanks for bringing to my attention the tricky meaning of deficit increase. Duly noted.
And, yes, @"Cant Get Right", it is all about the size of the pie ahaha