Logical Reasoning

PT107 · S1 · Q20 The price of a full-fare coach

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The price of a full-fare coach ticket from Toronto to Dallas on Breezeway Airlines is the same today as it was a year ago, if inflation is taken into account by calculating prices in constant dollars.

Conclusion

On average, people pay less today (in adjusted dollars) for a Breezeway T->D coach ticket than they did a year ago.

Evidence

Today A Year Ago

price of full-fare = price of full-fare coach T->D coach T->D

90% discount vs. 50% discount 10% full-fare 50% full-fare

Evaluate

Since we're trying to prove a very mathematical conclusion, we just need all the relevant mathematical data.

We don't need to know anything about raw numbers of tickets, because we're only concerned with averages. We know that a higher proportion of people today buy "discount" rather than full-fare tickets, but that doesn't immediately prove they're spending less money per ticket.

What if the price for a Full-Fare and/or Discount ticket has gone up?

The argument reassures us . But it doesn't tell us whether the price of a discount ticket has stayed the same. If the price of a discount ticket has gone up, then even though a higher proportion of people are buying discount tickets, they might be spending more on average than a year ago.

If you want some math to make sense of it, let's say there were 10 tickets bought each year (so that it's easy to take 90%, 50%, 10% of it).

Last year, 5 full-fare and 5 discount tickets. This year, 1 full-fare and 9 discount tickets.

So in which year did people spend more money? We'd have to know the costs of the tickets. Full-fare stayed the same, but discount could have changed.

Let's pretend that last year, full = $100, discount = $50 5 full + 5 discount = 5(100) + 5(50) = 750 $75 per ticket average.

Let's pretend that this year, full = $100, discount = $90 1 full + 9 discount = 1(100) + 9(90) = 910 $91 per ticket average.

Goal

Since our only way to mathematically object to the argument is to say, , the way to prove this conclusion true is to shut down that objection.

We either want to hear that the price of a discount coach T->D ticket is the same, or that it's cheaper than before.

20.

Which one of the following, if assumed, would allow the conclusion above to be properly drawn?

  1. A Toronto-to-Dallas full-fare coach ticket

    Out of Scope: Service

    We don't care about any qualitative comparison of now vs. last year. We're just here to try to prove a mathematical claim about dollars and cents.

    1% picked this

  2. Correct

    A Toronto-to-Dallas discount coach ticket

    Why this is right

    If full-fare costs the same (as we were told) and discount costs the same (as this answer is telling us), and this year people are buying more discount than full-fare, then it's mathematically certain that the average ticket price is lower this year. Note: we are, correctly, adding our own dictionary-based assumption that "a discount ticket costs less than a full-fare ticket"

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

    65% picked this

  3. All full-fare coach tickets on

    Unrelated to Goal

    We already knew that full-fare coach price was unchanged when it came to the Toronto to Dallas flight, and the conclusion is only about the price of the Toronto to Dallas flight. This answer is only providing information about the cost of other flights, which are totally out of scope.

    18% picked this

  4. The average number of coach

    Unrelated to Goal

    We don't care about the number of passengers per flight. That could be mathematically relevant if we were interested in the revenue or profit per flight that Breezeway Airlines was making, but this conclusion only cares about the price per ticket that passengers are paying. They paid what they paid, regardless of how many people are on the flight. The only mathematical variable we care about is the price of a discount coach T->D ticket this year vs. last year.

    11% picked this

  5. The criteria that Breezeway Airlines

    Unrelated to Goal

    We're trying to prove a mathematical claim about dollars and cents, and this is talking about a non-mathematical idea: criteria for who gets to buy a discount ticket If it ain't a fact about the price of a discount coach ticket from T to D, we ain't interested. Because that math fact is the only thing left that affects whether the conclusion is true or false.

    5% picked this

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