Logical Reasoning

PT149 · S3 · Q23 Each new car in the lot

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Each new car in the lot at Rollway Motors costs more than $18,000.

Conclusion

Costs $5 - $18 → used < 10 yrs. old

Evidence

New → costs > $18

≥ 10 yrs old → costs < $5

Evaluate

This conclusion takes the contrapositive of each rule to derive the upper and lower boundary of its conclusion.

If it costs < $18, then it's not new (i.e. Used). If it costs > $5, then it's less than 10 yrs old.

Thus, if it's between $5 - 18, then it's got to be Used and less than 10 yrs. old.

Goal

The argument needs to give us two conditional premises. The conclusion's trigger should be the net effect of being "Not outcome 1 + Not outcome 2".

The premises' outcomes were → more than $18. → less than $5

And the conclusion's trigger was between $5 and $18.

The outcome of the conclusion should combine the negation of the two triggers. The premises' triggers were New → 10 or more yrs old →

So the conclusion's outcome was Used and less than 10 yrs old

23.

The pattern of reasoning in which one of the following arguments is most similar to that in the argument above?

  1. Each apartment above the fourth

    Reversed Conclusion

    Given these premises ... Above 4th → more than 2 bedrooms Below 4th → fewer than 2 bedrooms ... the trigger for the conclusion should be contradicting both outcomes. The only idea that contradicts both is "exactly 2 bedrooms". It's not more than 2, it's not fewer than 2. And the outcome for the conclusion should be contradicting both triggers, which would be "4th floor". So the proper conclusion would be "if exactly 2 bedrooms, then 4th floor". Instead, we get the reversal: "if 4th floor, exactly 2 bedrooms"

    13% picked this

  2. Each apartment above the fourth

    Bad Conclusion Match

    Given these premises ... Above 4th → 2 or 3 bedrooms Below 4th → not more than 2 bedrooms ... the trigger for the conclusion should be contradicting both outcomes. The only idea that contradicts "2 or 3" and "not more than 2" would be 0 or 1. If it's 0 or 1 bedrooms, then it's not 2 or 3 and it's not more than 2. And the outcome for the conclusion should be contradicting both triggers, which would be "4th floor". So the proper conclusion would be "if exactly 1 or none bedrooms, then 4th floor". Instead, we get: "if 3 bedrooms, then 4th or higher"

    12% picked this

  3. Correct

    No apartment above the fourth

    Why this is right

    Given these premises ... Above 4th → 3 or more bedrooms Below 4th → fewer than 2 bedrooms ... the trigger for the conclusion should be contradicting both outcomes. The idea that contradicts both is "exactly 2 bedrooms". If there are exactly 2, then there aren't 3 or more and there aren't fewer than 2. And the outcome for the conclusion should be contradicting both triggers, which would be "4th floor". So the proper conclusion would be "if exactly 2 bedrooms, then 4th floor". And that's the conclusion we get!

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

    51% picked this

  4. No apartment above the fourth

    Bad Conclusion Match

    Given these premises ... Above 4th → 2 or fewer bedrooms Balcony → 3 bedrooms ... the trigger for the conclusion should be contradicting both outcomes. The only idea that contradicts both is "4 or more bedrooms". If it's got 4 or more, then it isn't 2 or fewer and it isn't a 3 bedroom. The outcome for the conclusion should be contradicting both triggers, which would be "4th floor or below without a balcony". So the proper conclusion would be "if an apartment on the 4th floor or lower lacks a balcony, then it has 4 or more bedrooms". Instead, we get "if balcony, then 4th or lower"

    11% picked this

  5. Each apartment above the fourth

    Bad Premise Match

    Given these premises ... Above 4th → more than 2 bedrooms 4th or lower → not vacant ... the trigger for the conclusion should be contradicting both outcomes, but this would be a weird blend of ideas that aren't quantitatively related, like all the other options were. The only idea that contradicts both is "1 or 0 bedrooms and occupied". And the outcome for the conclusion should be contradicting both triggers, which is impossible. The two triggers (above 4) and (4 or lower) account for all possible numbers. So it would be impossible to derive a conclusion like that of the original.

    13% picked this

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