#22 - Most of the new cars that Regis Motors sold last year

[Administrator]

Complete Question Explanation

Must Be True. The correct answer choice is (D)

This kind of "quantifier" problem is a classic of LSAT Logical Reasoning, and although it may seem old-hat for those who have worked through a lot of argument problem sets, the logic underlying these problems is surprisingly modern, nuanced, and sophisticated. Fortunately for us, we can keep things reasonably simple if we adhere to the plain meaning of words and track the information as it is presented.

1. Cars sold by Regis Motors last year Sold to residents of Blomensville
2. Total cars sold by Regis Motors last year > Total cars sold by Regis Motors in any previous year
3. Cars sold to residents of Blomensville NOT Cars sold by Regis Motors

There are actually few definite inferences to make here. We know from (1) and (3) that

• Total cars sold in Blomensville last year > Total cars sold by Regis Motors last year

(2) is a bit of a red herring since it can lead to some mistaken inferences. For instance, students may want to combine (1) and (2) to conclude that Regis Motors sold more cars to residents of Blomensville last year than it had in any previous year. This is not necessarily true. It could be possible that Regis Motors had sold more cars to residents of Blomensville in an earlier year if Regis Motors sold even fewer cars elsewhere in that year.

As always, diagramming can be an invaluable tool for problems such as these, but it also bears repeating that it's useful at least once to read through the stimulus and describe for yourself what's going on and any immediate observations you can make. In this manner, even in the event you need to diagram, you can have a better grasp of what connections are possible and not possible.

Answer choice (A): As mentioned in the paragraph above, we do not know this for sure. It could be possible that Regis Motors had sold more cars to residents of Blomensville in an earlier year if Regis Motors sold even fewer cars elsewhere in that year.

Answer choice (B): Again, we do not know this for sure. It could be possible that Blomensville residents had purchased an even greater total number of cars in some prior year if in that year they purchased a large number of cars from some retailers other than Regis Motors.

Answer choice (C): We get a bit of a break from the tough categorical syllogisms with some cut-and-dried outside information here. We don't know anything in particular about any other car retailer.

Answer choice (D): This is the correct answer choice. If you noticed this inference in your prephrasing, hats off to you! If not, no worries; consider statements (1) and (3). We know from (1) that Regis Motors sold most of its cars last year to residents of Blomensville. Therefore, the total number cars sold by Regis Motors last year was less than double the amount they sold to residents of Blomensville. Further, from (3) we know that most cars sold in Blomensville last year were not from Regis motors. Therefore the total number of cars sold to residents of Blomensville last year was more than double the amount sold by Regis Motors to residents of Blomensville. Since the amount of cars sold by Regis Motors to residents of Blomensville plus the amount sold by Regis motors to non-residents is less than double the amount sold by Regis Motors to residents of Blomensville, it follows that the total number of cars purchased by residents of Blomensville is greater than the total number of cars sold last year by Regis Motors. Phew!

If you prefer algebra, it looks like this:

• Cars sold by Regis Motors last year to residents of Blomensville: RMB
  Cars sold by Regis Motors last year to non-residents: RMB
  Cars purchased by residents of Blomensville last year from other retailers: BRM

• From (1): RMB > RMB
  From (3): BMR > RMB
  By transitivity we may conclude BRM >RMB
  By additivity we may conclude BRM + RMB > RMB + RMB

This is why I strongly recommend trying to make some initial observations first and dispensing with the geometric proofs!

Answer choice (E): Another one of these not-necessarily-true situations: even though Regis Motors sold more cars in Blomensville last year was more than they had in any previous year, they might have had a larger marketshare in Blomensville in some previous year if there was a lower total sales number in that year AND other retailers had sold proportionately fewer cars, allowing Regis Motors' percentage of the market to be greater. This is a standard numbers and percentages fallacy.

[freddythepup]

Hi, when I revisited the question, D popped out as the right answer (and quite obviously for some reason the second time around). but reading your explanation I got a little confused. Can you please explain how we know this :

"We know from (1) that Regis Motors sold most of its cars last year to residents of Blomensville. Therefore, the total number cars sold by Regis Motors last year was less than double the amount they sold to residents of Blomensville. " ?

Thanks!

[Claire Horan]

Hi Freddy,

You asked for an explanation of how we know this:

"We know from (1) that Regis Motors sold most of its cars last year to residents of Blomensville. Therefore, the total number cars sold by Regis Motors last year was less than double the amount they sold to residents of Blomensville. " ?

Sometimes choosing numbers helps with this kind of reasoning. Let's say RM sold 100 new cars last year. More than 50 of them were to residents of Blomensville (most = more than half). 100 is "less than double" 51, the smallest number of cars RM could have sold to Blomensville.

I hope this explanation helps! For most people, this problem will be more time-consuming than average, so if problems like this give you trouble, I recommend skipping them on your first pass through the section.

[MusaMuneer9898]

For AC (D) I felt like the answer was saying that the number of new cars purchased last year by residents of Blomenvile was greater than the number of new cars sold by Regis Motors (and since it didn't say "sold by Regis Motor LAST YEAR it threw me off). Because it could mean all of the previous years combined. Any suggestions?

Thanks

[atierney]

Yeah, when faced with a question like that if a reasonable interpretation yields the only rendering of an AC that must-be-true, then you should definitely use that as your answer. Here, where there is a question of interpretation, it's important to interpret in the most applicable way. Every other sales quantity refers to the previous year, thus it's very reasonable to assume that this one will as well. As you recognized, there is a question of how interpret, so it would be wise to interpret in both ways, or at least recognize the different ways in which it may be interpreted, and consider how each would affect the truthfulness of the AC.

Let me know if you have further questions.