Logical Reasoning

PT157 · S2 · Q7 The mu mesons generated by

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The mu mesons generated by cosmic rays just outside Earth’s atmosphere travel to Earth at speeds approaching the speed of light.

Facts

contrast Mm's generated by cosmic rays just outside Earth’s atmosphere travel at speeds approaching the speed of light, whereas mm's in the lab are nearly at rest.

math-y contrast lab-mm to decay < space mm to reach detection TIME

conditional + implicit fact that triggers contrapositive If mm's traveling through the atmosphere at speeds approaching the speed of light typically decay as fast as lab-mm's, then we should detect only about one one-hundredth of the number we actually do detect.

Evaluate

We know that space Mm's are fast (near speed of light) while lab Mm's are slow (nearly at rest).

And we know that lab Mm's decay in less time than it takes for a space Mm to be detected on Earth.

Is there anything we can get by combining those ideas? Nothing obvious.

Meanwhile, the final sentence gives us a conditional statement as well as an implicit fact that triggers that conditional idea. That sounds fancy, but it just means that the sentence with the rule is also triggering its own contrapositive.

Suppose you heard, What can you infer? Diana is not a good dancer.

The sentence conveys that Diana has not placed as high as would be required for a good dancer, so we can apply the rule to her and derive that she's not a good dancer.

Similarly,

This statement is already telling us that the necessary condition—the "then" part—is not true. We are not detecting one one-hundredth of the number we actually do detect. We are detecting the number that we actually do detect.

So this allows us to infer that

Goal

If we can look past the scientific terms and get a handle on the essence of what these statements are telling us, we can make a very good prediction. We expect a correct answer to indicate that MMs traveling through the atmosphere decay more slowly that ones created in the lab.

7.

Which one of the following most logically completes the argument?

  1. take longer to reach Earth

    Opposite (if anything)

    There aren't any ideas in the stimulus about us revising any previously held beliefs. The inference we're looking for is about decay rates, not about travel time.

    5% picked this

  2. are quite difficult to detect

    Out of Scope: difficult

    The information makes it sound like we're detecting 100x as many Mm's are we might have guessed ("if space Mm's decayed like lab Mm's, then we shouldn't only be detecting 1/100 of what we detect"). So we have no grounds for saying it's difficult to detect Mm's with our current equipment.

    7% picked this

  3. are much less numerous than

    Opposite (if anything)

    There aren't any ideas in the stimulus about us revising any previously held beliefs. The inference we're looking for is about decay rates, not about overall quantity of Mm's.

    9% picked this

  4. Correct

    decay more slowly than mu

    Why this is right

    Our prediction (from applying the contrapositive of the conditional) was that space Mm's don't decay as fast as lab Mm's. That's all this answer is saying, except we're term-swapping "near lightspeed Mm's" for space Mm's and "nearly at rest Mm's" for lab Mm's, which is fair since the first two sentences told us as much.

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

    77% picked this

  5. are probably not generated by

    Contradicted

    The very first sentence of the stimulus states that mu mesons are "generated by cosmic rays just outside Earth's atmosphere." Nothing in the subsequent evidence undermines this statement.

    2% picked this

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