Q19 - Spectroscopic analysis has revealed the

[meredith.segal]

I would actually also really appreciate an explanation of this question... thanks!

[bbirdwell]

Well, let's see...

Since it's an "assumption" question, we'll need to analyze the argument in terms of conclusion and premises, and try to anticipate possible gaps.

The argument proceeds as follows:

1. on the surface of Pluto, there is frozen N, M, and Cm.
2. these ices tend to vaporize and produce an atmosphere
3. the amount of a gas in the atmosphere is proportionate to how readily that gas vaporizes

C: Thus, Pluto's atmosphere is composed of N, Cm, and M in decreasing order of abundance

Note that the conclusion is about Pluto's atmosphere while the evidence is about the ices on Pluto's surface. The argument does not state HOW MUCH of each ice is on Pluto's surface, nor does the argument state that they are the ONLY frozen gases on Pluto's surface. Therefore, these are possible gaps in the logic.

(A) is close, but ultimately backwards. The author assumes that there IS more frozen N on the surface.
(B) is clearly out of scope.
(C) is right on target. The author does assume that there is no substance that vaporizes "MORE readily than M but LESS readily than Cm." This statement is not unlike some constraints on LSAT Logic Games. "More than X but less than Y" means BETWEEN X and Y.
If you negate this choice, it essentially reads "there IS a substance between M and
CM," which makes the conclusion invalid. This is one way to recognize the answer.
(D) is close, but misses the mark. We don't know that this is the ONLY way N is found in the atmosphere, just that it's one way.
(E) is out of scope.

[meredith.segal]

Well, let's see...

Since it's an "assumption" question, we'll need to analyze the argument in terms of conclusion and premises, and try to anticipate possible gaps.

The argument proceeds as follows:

1. on the surface of Pluto, there is frozen N, M, and Cm.
2. these ices tend to vaporize and produce an atmosphere
3. the amount of a gas in the atmosphere is proportionate to how readily that gas vaporizes

C: Thus, Pluto's atmosphere is composed of N, Cm, and M in decreasing order of abundance

Note that the conclusion is about Pluto's atmosphere while the evidence is about the ices on Pluto's surface. The argument does not state HOW MUCH of each ice is on Pluto's surface, nor does the argument state that they are the ONLY frozen gases on Pluto's surface. Therefore, these are possible gaps in the logic.

(A) is close, but ultimately backwards. The author assumes that there IS more frozen N on the surface.
(B) is clearly out of scope.
(C) is right on target. The author does assume that there is no substance that vaporizes "MORE readily than M but LESS readily than Cm." This statement is not unlike some constraints on LSAT Logic Games. "More than X but less than Y" means BETWEEN X and Y.
If you negate this choice, it essentially reads "there IS a substance between M and
CM," which makes the conclusion invalid. This is one way to recognize the answer.
(D) is close, but misses the mark. We don't know that this is the ONLY way N is found in the atmosphere, just that it's one way.
(E) is out of scope.

Thanks so much for the quick, comprehensive, and clear explanation! One question: the stem does not state "astronomers have concluded that the ONLY components of Pluto's atmosphere are..." Why could there not be some additional gas without negating the stem? Thanks.

[bbirdwell]

Here's a crisper analysis of this one, and a simple analogy:

N, M, and Cm exist on Pluto.
They vaporize.
Amt of gas is proportional to how readily it vaporizes.

Therefore, the components of Pluto's atmosphere are N, Cm, and M, with N being most abundant.

Compare this argument to the following hypothetical.
Observation has revealed that squirrels, deer, and elephants exist on Earth.
The population of a mammal is proportional to its size.

Therefore, the mammals on Earth are Squirrels, Deer, and Elephants, Elephants being the most abundant.

What's missing here? Just because we've seen squirrels, deer, and elephants, does that mean there are no other mammals? Isn't it possible that there's a mammal somewhere between deer and elephants in size and population?

This is what (C) does.

Notice what happens if you negate (C): "There are MANY frozen substances on Pluto that vaporize more readily than M and less than Cm." Now the conclusion is stupid. This is how you know you've found the correct assumption!

[perng.yan]

That is the reason why I chose (A).. because "the proportion of any gas in such an atmosphere depends directly on how readily the corresponding ice vaporizes..." and the author concludes that the most abundant of the three is nitrogen. That would mean that ice nitrogen vaporizes most readily, and therefore, there would be LESS nitrogen ice than the other ices because it's vaporized.

Can you please clarify for me? thank you.

[bbirdwell]

That is the reason why I chose (A).. because "the proportion of any gas in such an atmosphere depends directly on how readily the corresponding ice vaporizes..." and the author concludes that the most abundant of the three is nitrogen. That would mean that ice nitrogen vaporizes most readily, and therefore, there would be LESS nitrogen ice than the other ices because it's vaporized.

The argument says this:

amt in atmosphere is proportionate to readiness to vaporize

And I think you may be confusing this with:

amt in atmosphere is proportionate to amount on surface

[dean.won]

someone mentioned it above but just to clarify, when it says THE components is it saying that they are the ONLY components?

[LSATeater]

someone mentioned it above but just to clarify, when it says THE components is it saying that they are the ONLY components?

I have this exact same gripe with this question. After spending over ten minutes working on this problem, I decided that none of the choices presents a necessary assumption. I eliminated choices A, B, D, and E for the reasons posted above.

I also eliminated C precisely because I thought that even if there was another frozen substance, say lithium, that vaporized more readily than methane but less so than carbon monoxide, it would still be the case that carbon monoxide gas was more abundant in Pluto's atmosphere (and also more readily vaporizing whilst frozen on Pluto's surface)than methane; after all, if i initially tell you I have 10 apples and 8 oranges, my subsequent revelation of also having 9 kiwis will do nothing to disrupt that relative hierarchy of apples to oranges.

Ultimately, this problem has revealed itself to be an exercise in LSAC language usage more so than an exercise in logic. But now I'm wondering if this use of "the components" is unique to the LSAT (and other similar vile creations).

Out of curiosity, for those who were not totally frustrated by this problem, did you naturally process "the components" as "the ONLY components" and is that specifically what the word components actually means? So if I were to tell a judge that the components of my wallet are a credit card and a penny, would I necessarily be committing perjury if I also kept mum about my expired driver's license?

[tommywallach]

Hey Guys,

A quick note on "definite" versus "indefinite" articles.

A -- indefinite pronoun -- implies an indefinite example

Example: "I have a problem."
Meaning: This is not my only problem, but I still have it.

Example: "Sugar is an ingredient in this cake."
Meaning: Sugar is one of multiple ingredients in this cake.

THE -- definite pronoun -- implies a definite example

Example: "That's exactly the problem."
Meaning: There is one problem we are discussing, and that's it.

Example: "The ingredients in this cake are pears, sugar, and flour."
Meaning: The only ingredients in this cake are pears, sugar, and flour.

OUR QUESTION: "...the components of Pluto's atmosphere are nitrogen, carbon monoxide, and methane..."
Meaning: The only components are those listed.

You can hate it, but that's the way it works. : )

-t

[redcobra21]

Thanks for the great responses. Just a quick clarification question: shouldn't answer choice (C) say "less readily than NITROGEN" instead of "less readily than CARBON MONOOXIDE"? If nitrogen has greater abundance than carbon , doesn't that mean that nitrogen vaporizes less readily than carbon monoxide?

Thanks

[tommywallach]

Hey Red Cobra,

The passage says they are in order of "Decreasing abundance," so the list would go:

Nitrogen
Carbon Monoxide
Methane

Something that vaporizes more readily (vaporizing meaning that it goes INTO the atmosphere) than methane but less readily than Carbon Monoxide would go right here:

Nitrogen
Carbon Monoxide
THINGY THINGY
Methane

Hope that helps!

-t

[aznriceboi17]

When I took this as a practice test I guessed (C) but was not happy with it as an answer, because it seems like another huge factor (that was actually mentioned earlier by bbirdwell) is the amount of ice (measured by mass). Suppose there is a frozen substance on the surface that vaporizes more readily than methane but less readily than carbon monoxide: what if its mass was orders of magnitude less than that of the named gases? Even if we assume ALL of it vaporized, it's possible that it'd still represent a tiny proportion of the atmosphere compared to the others.

To be precise, for gas g let p_g denote the proportion of g in the atmosphere (so 0<=p_g<=1), let m_g denote the mass of the frozen gas g on the surface, and let v_g denote its tendency to vaporize. Suppose that p_g is given by the equation:

p_g = m_g * v_g

Whether or not it makes physical sense doesn't matter, but the point is that p_g is proportional to v_g (which is what all of us seem to have interpreted 'p_g depends directly on v_g' as), so we have a relationship that matches what we're told.

For two gases r and s then, it is certainly possible that p_r > p_s even though v_r < v_r (just need m_r > m_s to compensate), which would seem to show that (C) isn't actually a necessary assumption.

Can someone explain where I'm going wrong? The only thing I can think of to save it is if the whole 'depends directly on' condition means that the relative proportion of the gases in the atmosphere is entirely determined by their tendency to vaporize. That is given two gases r and s, if v_r > v_s then p_r > p_s. However, this is clearly a much stronger statement than p_r is proportional to v_r, and to me doesn't seem like a reasonable interpretation.

[rinagoldfield]

Hi aznriceboi17,

Great sharp question; I had to think about this one for a while. However, I don’t think mass can be an additional factor. Someone gave me a science-y explanation for this, but since I’m not a scientist, I won’t try to recapture that explanation. Instead I’ll try to explain this via analogy.

First, though, the problem:

The stimulus tells us that the ratio of a gas in the atmosphere is directly proportional to how readily the ice vaporizes. To put this in terms of an equation, since you seem to like equations:

RG = VG*k

RG= ratio of the gas in the atmosphere
VG=the vaporizing of the gas
k=some constant

(^this is the definition of direct proportionality.)

Note that the VG isn’t directly proportional to the AMOUNT of gas generated, it’s related to the RATIO of that gas in relation to other gases in the atmosphere.

Here’s my analogy:

Let’s say hours worked are directly proportional to the AMOUNT of money you make. The more hours you work, the more money you make. In this scenario, hourly wage can also affect how much money you make without messing up the direct proportionality.

However, let’s say I told you that workers together are making a total of one billion dollars. That one billion dollars is the "pie" and workers take slices of varying sizes of that "pie." Now let’s say hours worked are directly proportional to the size of your pie slice. The more hours you work, the bigger your slice.

In this scenario, no other factor could affect the size of the pie slice. For example, hourly wage: What if a guy making a billion dollars an hour went from working 1 hour per day to 10 hours per day? Everyone else’s pie slices (remember, we have an unchanging total of one billion dollars) would get smaller, even if the number of hours they worked stayed the same. This would destroy the direct proportionality between hours worked and the size of your money-pie slice.

Similarly, in the problem, we’re comparing the vaporizing-ness of a gas to the ratio of that gas in a whole atmosphere. That's like the size of the money-pie slice above. The vaporizing-ness of the gas must be the only factor affecting that ratio. If any other factor (like mass) affected the ratio, then the VG could no longer be directly proportional to that ratio.

Maybe someone with a science background can weigh in as well?

[aznriceboi17]

Hi Rina, thank you for your response! It's helped clear up some things for me, but also raised some other questions.

The point you made about the slice of a fixed pie makes sense to me, but then it seems that if we use the definition of 'proportional' here http://en.wikipedia.org/wiki/Proportion ... athematics), in saying A is directly proportional to B, then the quantity represented by A cannot have an upper bound if B does not have an upper bound.

As an example, we could look at the one you gave of a person's slice of the pie being directly proportional to the the number hours he worked:

PS = k * HOURS

(PS=pie slice, with 0 <= PS <= 1, k is some constant). This relationship wouldn't be able to hold, because as soon as we have HOURS > 1/k, that equation would result in a value greater than 1 for PS, which would be meaningless. But to say that PS is proportional to HOURS means that the above equation must be true for any given value of HOURS. Since it's not, PS and HOURS cannot be proportional.

The equation

PG = VG * k

would face the same problem since PG again represents a proportion. Now I guess one could argue that VG could be measured on a finite scale (perhaps scientists use a 1 to 100 scale to measure tendency to vaporize), so the above equation only has to be true for the values of VG in that range, but that seems to stretch things too much.

All this leads me back to the stimulus wording:

Since the proportion of any gas in such an atmosphere depends directly on how readily the corresponding ice vaporizes...

If we use some shorthand: A = 'proportion of gas in atmosphere' and B = 'how readily the corresponding ice vaporizes', then the stimulus can be rewritten as

Since A directly depends on B...

However, it seems everyone has interpreted it as saying

Since A is directly proportional to B...

How did we go from the bolded phrase to the italicized phrase? I'm worried that we've taken the word 'proportion' in A and incorrectly transferred its meaning into the phrase 'directly depends on'.

Because of the earlier point, I don't think the 'directly proportional' interpretation of 'directly depends on' can be defended in this case, but I'd really like to hear what you or anyone else thinks.

[zhan941]

Thank you all for clarifying all the confusion. But I still have one question. Isn't (C) out of scope?
(C) says "there is no frozen substance on the surface of Pluto that vaporizes more readily than methane but less readily than carbon monoxide."
So, if we negate (C), that is there were such gases, then this destroy our conclusion, which says "the component".
But are we taking one step further to ASSUME "whatever frozen substance on the surface of Pluto that vaporizes WILL be included the components of Pluto"?
I eliminated C and here is my thinking process.
Even if there is some in-between frozen substance that could vaporize, say Lithium, what do we care about it when we are not explicitly told that Lithium will become the component after vaporizing? We could even say there are unlimited frozen substances that vaporizes more readily than methane but less readily than carbon monoxide. As long as we have no information of how these extra "things" will do to our atmosphere, we don't get to make that unwarranted assumption. Please clarify. Thank you very much.

[maryadkins]

Because of the earlier point, I don't think the 'directly proportional' interpretation of 'directly depends on' can be defended in this case, but I'd really like to hear what you or anyone else thinks.

Sure, I see what you mean. The language isn't super precise here. But (C) is the only one that works, so we fudge it.

[poppyyjm]

Hi, I am still really confused here, since the author says that proportion of gas directly depends on how readily the ice vaporizes, isn't it saying that how easily it turns into gas? Then the astronauts conclude that there's more nitrogen that the other two substances. Here the astronauts are taking about the amount of each substance. Since the author is saying the proportion, meaning the amount of certain gas compared to the total amount, is directly related to how easily certain ice vaporizes, then isn't he assuming that the amount of each substance in the ice form should be the same? Since the amount of corresponding gas in the atmosphere is purely proportional to their respective readiness of vaporization, then if the amount of each substance in the ice form is not the same, then how can the author reach such a conclusion? For example, if there's 1000 ton of nitrogen, 2000 ton of CO and 3000 ton of methane originally in the form of ice, and their readiness of vaporization respectively are 10%, 9% and 8%(by which I mean under the same circumstance this much of each substance vaporizes). Since the amount of gas in the atmosphere is proportional to readiness to vaporize, then according to this theory there should be N>CO>methane in the atmosphere. However the reality is completely the opposite, since there will be 100 ton of nitrogen, 180 ton of CO and 240 ton of methane in the atmosphere. Since it's the opposite of the astronauts' conclusion, and we know mass of each substance doesn't play a part in any of this, then we know there's an assumption saying the amount of the substances are the same. Then since Nitrogen is the most ready to vaporize, then the astronauts reach the conclusion that there's more nitrogen in the atmosphere than the other two substances, and since more of nitrogen escapes, then there is at least no more frozen nitrogen on the surface than the other two substances. So A is correct. Can someone help me find out the what's wrong with my reasoning above? Thanks!

That is the reason why I chose (A).. because "the proportion of any gas in such an atmosphere depends directly on how readily the corresponding ice vaporizes..." and the author concludes that the most abundant of the three is nitrogen. That would mean that ice nitrogen vaporizes most readily, and therefore, there would be LESS nitrogen ice than the other ices because it's vaporized.

The argument says this:

amt in atmosphere is proportionate to readiness to vaporize

And I think you may be confusing this with:

amt in atmosphere is proportionate to amount on surface

[jiangziou]

Here are my thoughts.

For assumption questions, right answers should either close the gap between the premise and the conclusion or eliminate an alternate explanation. Typical wrong answers are premise boosters, conclusion redundancy, opposites, out of scope and reversed logic.

Answer (A) is right, but it is a "premise booster". This is not a Must be true question. It doesn't connect the premise and the conclusion. The conclusion is about the components of Pluto's atmosphere, while (A) is about the surface of Pluto, which just try to convince us that the premise is true.

Hi, I am still really confused here, since the author says that proportion of gas directly depends on how readily the ice vaporizes, isn't it saying that how easily it turns into gas? Then the astronauts conclude that there's more nitrogen that the other two substances. Here the astronauts are taking about the amount of each substance. Since the author is saying the proportion, meaning the amount of certain gas compared to the total amount, is directly related to how easily certain ice vaporizes, then isn't he assuming that the amount of each substance in the ice form should be the same? Since the amount of corresponding gas in the atmosphere is purely proportional to their respective readiness of vaporization, then if the amount of each substance in the ice form is not the same, then how can the author reach such a conclusion? For example, if there's 1000 ton of nitrogen, 2000 ton of CO and 3000 ton of methane originally in the form of ice, and their readiness of vaporization respectively are 10%, 9% and 8%(by which I mean under the same circumstance this much of each substance vaporizes). Since the amount of gas in the atmosphere is proportional to readiness to vaporize, then according to this theory there should be N>CO>methane in the atmosphere. However the reality is completely the opposite, since there will be 100 ton of nitrogen, 180 ton of CO and 240 ton of methane in the atmosphere. Since it's the opposite of the astronauts' conclusion, and we know mass of each substance doesn't play a part in any of this, then we know there's an assumption saying the amount of the substances are the same. Then since Nitrogen is the most ready to vaporize, then the astronauts reach the conclusion that there's more nitrogen in the atmosphere than the other two substances, and since more of nitrogen escapes, then there is at least no more frozen nitrogen on the surface than the other two substances. So A is correct. Can someone help me find out the what's wrong with my reasoning above? Thanks!

That is the reason why I chose (A).. because "the proportion of any gas in such an atmosphere depends directly on how readily the corresponding ice vaporizes..." and the author concludes that the most abundant of the three is nitrogen. That would mean that ice nitrogen vaporizes most readily, and therefore, there would be LESS nitrogen ice than the other ices because it's vaporized.

The argument says this:

amt in atmosphere is proportionate to readiness to vaporize

And I think you may be confusing this with:

amt in atmosphere is proportionate to amount on surface

[aaronwfrank]

(D) is close, but misses the mark. We don't know that this is the ONLY way N is found in the atmosphere, just that it's one way.

So if I understand correctly (D) is wrong because it suggests that nitrogen could exist in the atmosphere without vaporizing from ice on the surface?

I'm curious how that doesn't affect the conclusion since it specifically states: "components of Pluto's atmosphere are...in order of decreasing abundance." If the nitrogen isn't necessarily emanating from the ice, how would they be able to quantify abundance using the method in the premise?

Are we to assume that regardless of the method used to reach the conclusion, the possibility of nitrogen existing without ice will not affect the argument?