This question is also a sufficient assumption question. There's another one in the same section earlier that's also a sufficient assumption.

What we're doing is the question is saying if which one of the following is assumed, the argument, the conclusion of the argument, follows logically.

In other words, that means the argument becomes valid. So currently we have an argument. It's not a valid argument.

It might be a very good argument, but it's not valid. And there's a very specific definition of what valid means, which is covered in a later lesson.

But here, they're telling us that we need to assume one of these things in order to make the conclusion valid.

And to do that, the definition of validity is just that if the premises are true, then the conclusion must be true.

So here, without the correct answer choice, if the premises are true, the conclusion could still be false.

But with the correct answer choice, whichever one it is, then when the premises are true, plus the correct answer choice, then the conclusion must be true.

That's what sufficient assumption questions will force us to do.

So they all have like 30 grams of aluminum per can.

And 50% of the aluminum cans contain a certain group M. So this is called group M cans.

Each one is a can. And then we're saying of each of the cans,

50% of the aluminum was recycled from another group.

So let's say this whole thing represents a can. This is 50%.

This is aluminum recycled. This is aluminum new.

That's aluminum recycled. That's 50%. It doesn't look like 50%.

But anyway, we're saying this used to be L.

So let's think about this for a little bit. They just told us that the amount of aluminum in any given soft drink can is fixed.

It's a fixed amount. It doesn't vary very much. So we just randomly said 30 grams.

It's some fixed amount. And they're telling us that group M has all these cans.

But half of the aluminum in group M came from group L.

And they're telling us now that all the cans in L were recycled into cans in M.

And since the amount of material other than aluminum in aluminum cans is negligible, essentially there's nothing else in aluminum cans.

And all of the cans in L were melted down into aluminum and then put into M.

They say it follows that M contains twice as many cans. Well, it must, right?

It must because it's got 50% of the cans from L.

50% of the cans from L and all the cans in L were melted down to aluminum and used for cans in M.

And then each new can is drawing upon the same amount of aluminum, then it must be that M has twice the amount of cans as L.

Well, no. See, we're assuming something. We're assuming there's no loss in the production.

But what if I started out with, let's say 30 grams is in, let's say this whole thing has 600 grams.

Let's say this whole thing has 600 grams is what's in here.

So it goes 300 over here and 300 over here.

So which means this over here is 10 cans and this over here is 10 cans.

So you're thinking, oh, well, then group L once had 10 cans and this whole group now has 20 cans.

Well, you are already presuming that in the melting down process, we didn't lose anything.

What if group, I don't know, what if group L started out with 400 grams?

400 is probably not a good number. It's not round.

Let's say what if group L also started with 600 grams?

That means it's 20 cans.

And then in the melting down process, 300 grams became unusable.

So really when we said we used all the cans were recycled into group M, only half of the aluminum,

all the cans were recycled but only half the aluminum survived.

In which case we get 300 grams of aluminum, but it no longer means that M contains twice as many cans as L

because now M only has 20 cans and L started out with 20 cans as well.

It just lost half its aluminum in the melting process.

That's something that we need to make sure doesn't happen.

So the answer is that the aluminum in cans of M cannot be recycled further.

If we stipulate that once you become an M can, you cannot recycle aluminum any further,

how does that force this conclusion to be true?

How does it force M to have twice as many cans as L?

It doesn't. Who cares what you do with aluminum in M?

Again, what does that matter? Who cares if it's poor quality?

Who cares if it crumbles apart in your hand?

It might not be helpful for drinking your soft drink, but that has nothing to do with this argument.

Just the fact that recycled aluminum is of poor quality, that just doesn't matter.

It doesn't help us establish the number of cans that M has.

There you go.

See, they're trying to be tricky here with this word recover, but they just mean you don't lose anything.

It's all recovered.

All the aluminum in an aluminum can is recovered, which this is perfect

because this means that 50% of the aluminum in M, here we stipulated 300 grams,

300 grams of L, that's all the L there ever was.

So it prevents what I said from being possible.

It prevents for any loss.

How many grams of aluminum was in the group L before we started the melting process?

Well, now we know. Now it's exactly 50%.

Well, now it's exactly 50%, then see, originally L had to have had 10 cans,

which means M now has 20 cans.

20 is twice 10, so now our argument becomes valid.

You see how that works? When all these statements are true and this statement is true,

the conclusion now has no choice but to be true.

Okay, but see, we really – I mean, how does that help?

I don't really care where the aluminum in group L came from.

It could have been recycled. It could have been brand new.

That's not going to help us establish this numerical relationship.

See, this in essence is just a math question.

It's just a math question disguised in – well, not disguised really,

but delivered to you via English.

than are soft drink cans made from other materials.

I mean, the ease of recycling aluminum versus the ease of recycling other materials

is entirely irrelevant to this argument.

It doesn't hurt this argument. It doesn't help this argument.

It certainly doesn't mean that it establishes this 2 to 1 ratio for the argument.

It just does nothing.