Logical Reasoning

PT103 · S3 · Q19 Over the past 20 years, skiing

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Over the past 20 years, skiing has become a relatively safe sport due to improvements in ski equipment.

Conclusion (clearly)

There have not been decreases in the number of injuries in all categories.

rephrase: there are more knee injuries than before.

Evidence (for)

Knee injuries used to be 11% of all ski injuries whereas now they represent 16% of all ski injuries.

Evaluate

The fact that a percentage goes up (which is what the evidence is saying) doesn't mean that a raw number goes up (which is what the conclusion is saying).

This is a classic Percent vs. # flaw.

Say there's a room full of 10 people, 5 men and 5 women. Then 2 men leave and so there's 3 men and 5 women.

The percentage of women increased from 50% (5/10) to 62.5% (5/8), but there weren't any women added to the room. The raw number of women stayed the same.

A percentage can increase without the raw number increasing, if other things get smaller. The same raw number is divided by a smaller denominator, and so it looks like a bigger percentage.

In this argument we actually know that the total number of ski injuries (the denominator) has gotten smaller. There's has been a 50% drop in the number of ski injuries. Let's make up a real number to demonstrate this math.

20 yrs. ago Now

total # of 2,000 1,000 ski injuries

% of ski injuries 11% 16% knee-related

total # of 220 160 knee injuries

There are actually fewer knee injuries today, because taking 16% of 1,000 is a smaller number than taking 11% of 2,000.

Goal

Let's look for an answer addressing the author's confusion between an increasing % (knee injuries went from 11% to 16%) and an increasing # (knee injuries actually decreased in number).

19.

The reasoning in the argument is flawed because the argument does which one of the following?

  1. It fails to allow for

    Doesn't Fail to Allow

    Just because the argument only mentions broken legs, ankle injuries, and knee injuries doesn't mean that it's thinking that those are the only injuries there are. We're never allowed to think "the only X's mentioned = the only X's there are".

    3% picked this

  2. It infers disparate effects from

    Bad Conclusion/Evidence Match

    The only causality in the paragraph is background fact that ski injuries have lessened due to better equipment. But the author's conclusion and evidence have no causality in them. It's just numbers and percents. The conclusion is that there are more knee injuries than before. The evidence is that knee injuries went from 11% to 16% of all ski injuries. That isn't inferring the effect of any cause. That's just stating a quantitative idea. Also, there's nothing inherently wrong with inferring differing effects from the same single cause. It's possible that a single cause (like more CO2 in the atmosphere) could cause damage to some ecosystems while also making plants photosynthesize more efficiently elsewhere.

    4% picked this

  3. It ignores the possibility that

    Not an Objection

    Since this answer starts with fails to consider / ignores the possibility, we can ask ourselves if the idea that follows would Weaken. Could we object to this argument by saying, "Hey, author -- the total number of skiers has increased!" No, that would just lend support to her conclusion. She thinks there are more knee injuries than before, so if there are more skiers than before that would help her case.

    16% picked this

  4. Correct

    It assumes that an increase

    Why this is right

    The author is assuming that "because the percentage of knee injuries went up from 11% to 16%, that means that the number of knee injuries went up". Technically, the conclusion is "there have no been decreases in all categories", so the author is concluding that "the number of knee injuries didn't decrease". Thus, this answer perfectly matches the author's reasoning move: "If there has been an increase in the proportion (i.e. percentage) of knee injuries, then there hasn't been a decrease in the number of knee injuries".

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

    67% picked this

  5. It proceeds as though there

    Bad Description

    This answer accuses the author of making an argument she never made. It's saying the author was arguing something like this: "Our store sells only products X, Y, and Z. Last month we sold 30% more X than usual, 40% more Y, and 50% more Z. Thus, last month we sold 25% more than we usually do." The overall uptick in sales would have to be somewhere between 30%-50%, since all the constituent parts moved by that degree. This answer accuses our author of thinking that even though the overall decrease in injuries was 50%, the decrease in each category was greater than 50%. The author does think in the category of leg/ankle injuries, the decrease was greater than 50% (it was 90%). But the author isn't thinking that all other categories decreased by more than 50%; in fact knee injuries is a category that our author thinks has increased.

    10% picked this

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