LR Drill Set 8, Question 11

Necessary AssumptionDifficulty3 of 5
The question

Each car rental company in a certain country(38 more words not shown)

Which one of the following(7 more words not shown)

Reading the argument

What if some of the cities have no car rental company?

At first, the counting argument can sound right: more cities than companies, so somebody must operate in more than one city. But slow down over the first sentence. It says every company operates in at least one major city. It doesn't say every major city has a company.

Try three companies—X, Y, and Z—and five cities—A, B, C, D, and E. X could operate only in A, Y only in B, and Z only in C. Then every company operates in a major city, and there are more cities than companies. Both stated facts are satisfied.

What about cities D and E? They could have no car rental company. We don't have to send X, Y, or Z there just because the cities exist. In this example, no company operates in two cities, so the conclusion fails.

What we’re looking for

For the required assumption, I want the coverage claim the argument has quietly relied on: every major city has a rental company. If all five cities must be served by only three companies, then at least one company has to serve more than one of them.

Working the answers

  • A

    This limits each city to one company, but that isn't needed to get a company into two cities. Several companies could compete in the same city while also operating elsewhere. And the limit wouldn't fix our empty-city example: X in A, Y in B, and Z in C already obeys it. The missing issue is whether every city has any company at all.

  • B

    Operations outside the country don't establish where a company operates inside it. X could operate in one domestic city and ten foreign cities while the conclusion about two of this country's major cities still fails. The argument doesn't need foreign operations and gets no help from this claim.

  • C
    Correct

    Every major city has at least one car rental company operating in it. That is the missing coverage assumption behind the counting argument. Once every city must be covered, having more cities than companies forces some company to appear in more than one city. Without that coverage assumption, our example with empty cities remains possible, and the stated counts alone don't justify the conclusion. Don't swap “every company has a city” for “every city has a company.” They make different promises.

  • D

    The argument doesn't need to rule out a company operating in every major city. Such a company would itself establish the conclusion, since operating in all the major cities would include operating in at least two. Whether any company covers them all is a different question from whether at least one covers two.

  • E

    This concerns where companies do most of their business, not whether they operate in particular cities. A company could make most of its money in small towns and still operate in two major cities. Or it could make all its money in one major city and operate nowhere else. The share of business doesn't supply the missing geographic coverage.

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