Logical Reasoning

PT123 · S2 · Q13 Standard aluminum soft-drink cans

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Standard aluminum soft-drink cans do not vary in the amount of aluminum that they contain.

Conclusion (it follows that)

M contains twice as many cans as L.

Evidence (since / and)

All cans have the same aluminum content, and they're basically nothing but aluminum.

All the cans from group L were recycled into cans in group M (all the same standard size).

50% of the aluminum in M came from L. (i.e. M has twice as much aluminum as L does)

Evaluate

This is definitely a dense argument to process. It fundamentally comes down to a mathematical equivalence.

If X is 50% of Y, then Y is twice as large as X.

A lot of Math-y argument play off of complementary percentages; an author might say . We know that 40% of people are not-X, but the author would be assuming "if you're not-X, then you're Y".

So this argument is essentially saying, if M has twice as much aluminum as L, then M is twice as many cans as L.

Let's that 10 kg of aluminum are used to make M. 5 kg (50% ) came from L.

If M is 100 cans, does that mean that L was 50 cans?

Apparently not! It seems like a tempting inference, but if were a logically guaranteed one, then they wouldn't be able to ask a Sufficient Assumption question. So we would probably want to go into Anti-Conclusion mode (very rare for Sufficient Assumption), and think to ourselves,

Given that ... M is twice as much aluminum as L How could we argue that ... M is NOT twice as many cans as L?

Goal

We might just have to live with being stumped by this paradox and head over to answers, seeking some hint about how we could possibly make this counterargument. (the correct answer would rule out such an objection)

Overall, we want an answer to convince us that .

13.

The conclusion of the argument follows logically if which one of the following is assumed?

The aluminum in the cans
Out of Scope
The argument does not address what might happen with the aluminum in the cans of M. This does nothing to convince us that "twice as much aluminum in M = twice as many cans in M".
7% picked this
Recycled aluminum is of poorer
Out of Scope
The quality of aluminum is not relevant to this argument. We only care about the relationship between amount of aluminum and number of cans.
4% picked this
Correct
All of the aluminum in
Why this is right
This ensures that fifty percent of the aluminum in M is equivalent to one hundred percent of the aluminum in L. If it weren't true that all the aluminum in a can is recovered, then we would have our objection. We could argue that, "Yes, M is 10 kg of aluminum spread out over 100 cans. And yes, L supplied 5 kg of that aluminum. But that doesn't mean that L was 50 cans. After all, not all the aluminum is recovered in the recycling process. If we recycled 50 cans from L, we wouldn't recover all 5 kg of aluminum in there. Some of it is lost in the recycling process. We might only get 4 kg of aluminum from those 50 cans." Thus, if some of the aluminum is lost in the process, then you might need to recycle 60 cans worth of L in order to get 50 cans worth of recycled aluminum. It might be that L was 60 cans, comprised of 6 kg of aluminum, but when we recycled it, we only recovered 5 kg of aluminum. We used that 5 kg to help make 100 cans (10 kg) of M. But it isn't true to say M has twice as many cans as L, if M is 100 cans and L was 60 cans. This answer rules out that sort of objection and makes the math all work. If everything from L gets transferred over in the recycling process, then "half as much aluminum as M = half as many cans as M".
Skill tested: Sufficient Assumption · how this choice captures the argument's function is the move to repeat next time.
72% picked this
None of the soft-drink cans
Out of Scope
Whether the aluminum in the cans of L had been used in previously is not relevant to the argument. We are told that L is pretty much 100% aluminum (the non-aluminum parts are negligible). So whether the aluminum in L is a "first pressing" or the result of recycling previous aluminum containers doesn't change the fact that the cans in group L were basically 100% aluminum.
14% picked this
Aluminum soft-drink cans are more
Out of Scope
Soft-drink cans made from other materials are not relevant to this argument. We only care about the relationship between amount of aluminum recycled and number of cans used to make that recycled aluminum.
4% picked this

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