Logical Reasoning

PT148 · S1 · Q22 Most of the new cars that Regis

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Most of the new cars that Regis Motors sold last year were purchased by residents of Blomenville.

Statements

quantifiers (most)

Most new cars sold were purchased by Regis Motors residents of last year Blomenville

Most new purchased by were not sold residents of by Blomenville Regis Motors

math-y comparison

Regis Motors sold more new cars last year than in any previous year.

Evaluate

On Must Be True questions, we're primarily scanning for Conditional, Quantified, or Causal ideas.

When we see Quantifiers, we know there are a couple different types of quantity overlap / relationship inferences that LSAT likes to test:

All A's are B Most A's are B Some A's are C Most A's are C ------------------- ------------------- infer: some B's are C some B's are C

Since we were given two Most claims, we should be thinking about that second one, the "Most + Most" inference. However, for that inference to work, we need both Most claims to be about the same group.

This question is actually testing a more obscure "Most + Most" inference, that has only shown up a couple times (both tests are in the 70s / 80s).

Most A's are B Most B's are ~A ------------------- infer: more B's than A's

Take any two qualities, say "likes cake" and "likes ballet".

Most people who like ballet like cake, but most people who like cake do not like ballet.

Let's pretend we're in some ballroom that contains people who just like ballet, just like cake, like both, or like neither.

Let's pretend we have 15 people who like ballet. Most of them like cake, so a minimum of 8. So we'll say 15 people who like ballet, 8 of them like cake, 7 of them don't.

Now let's think about the second fact, "Most people who like cake don't like ballet", What's the minimum number of cake lovers?

We already know there are 8 people who like cake and ballet. So 8 of the people who like cake also like ballet. But we know most of the people who like cake do not like ballet, so there would have to be at least 9 of them.

Thus the minimum number of cake lovers in 17.

We've proven that when we hear Most people who like ballet like cake, but most people who like cake do not like ballet. it tells us that there are more cake lovers than ballet lovers.

I know it's confusing to make it click. Remember, you'll have an easy form you can memorize. You're just trying to understand it so that it's easier to remember and process.

Here's one more way to talk about it. There is some number of people in the world that like both cake and ballet. Let's use the variable 'x'. There are x people in the world who like both cake and ballet.

When we say, "Most people who like ballet also like cake", we're saying that those people who like both are a majority of ballet lovers.

When we say, , it means that people who like both cake and ballet (x) are a minority of cake lovers.

If x is a majority of the ballet group (more than 50%), but a minority of the cake group (less than 50%), then that mathematically proves that the cake group is a bigger number.

x > 0.50 B x < 0.50 C

0.50 B < x < 0.50 C

B < x < C

Goal

They seem to be handing us the ingredients for this inference, Most A's are B Most B's are ~A ------------------- infer: more B's than A's

Most [sold by Regis Motors] are [bought by Blomenville's], but Most [bought by Blomenville's] are [not sold by Regis Motors]

infer: [bought by Blomenville's] > [sold by Regis Motors]

In other words, more new cars were bought by Blomenville residents than were sold by Regis Motors.

22.

If the statements above are true, which one of the following must also be true?

  1. Regis Motors sold more new

    Out of Scope

    Out of Scope: record # of new to Blomenville's We know that Regis sold a record number of new cars last year, but we don't know that Regis sold a record number of new cars to Blomenville residents last year. They may have achieved their record by selling the same / fewer new cars to Blomenville's residents and selling way more new cars to nonresidents of Blomenville.

    7% picked this

  2. The total number of new

    Out of Scope

    Out of Scope: record # bought by Blomenville's We know that Regis sold a record number of new cars last year, but we don't know that residents of Blomenville bought a record number of new cars last year. The "most" fact we get in the final sentence doesn't combine with anything else to derive that residents of Blomenville set an all time record for how many new cars they bought, because we have no way to judge whether their car-buying behavior from other dealerships is higher/lower than in years past.

    5% picked this

  3. A car retailer other than

    Out of Scope

    Out of Scope: other than Regis Motors We don't know about any other dealers besides Regis Motors, so it would be hard to prove a must be true about any of them. Given the last sentence, we know that there were lots of new cars bought by residents of Blomenville that came from retailers other than Regis Motors, but we wouldn't be able to say that any one retailer outsold Regis Motors. Maybe Regis Motors sold residents of Blomenville 20,000 new cars last year, while three other dealerships each sold B's residents 10,000 new cars last year. Of the 50,000 new cars bought by Blomenville's residents, most of them were not purchased from Regis, even though "no car retailer other than Regis Motors sold the most new cars to Blomenville's residents". We just showed how even given the facts in the stimulus, this answer choice could be false.

    19% picked this

  4. Correct

    The number of new cars

    Why this is right

    As we detailed (painfully) in the write-up of the paragraph, this is the thing we can infer when we have Most A's are B Most B's are ~A ------------------- infer: more B's than A's Most [sold by Regis Motors] are [bought by Blomenville's], but Most [bought by Blomenville's] are [not sold by Regis Motors] infer: [bought by Blomenville's] > [sold by Regis Motors] Let's say Regis sold 100 new cars last year. At least 51 of them went to residents of Blomenville. So if 51 new cars purchased by Blomenville residents were purchased from Regis, but "most new cars purchased by Blomenville residents were not purchased from Regis Motors", then there must have been at least 52 new cars bought by Blomenville's residents that didn't come from Regis Motors. That means that there would be a minimum of 103 new cars bought by Blomenville's residents.

    Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.

    66% picked this

  5. Regis Motors' share of the

    Out of Scope: market share

    We could only speculate about market share, since we haven't received any data relating to that.

    4% picked this

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