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After evidence was obtained in the 1920s that the universe is expandin

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After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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After evidence was obtained in the 1920s that the universe is expanding, it became reasonable to ask: Will the universe continue to expand indefinitely, or is there enough mass in it for the mutual attraction of its constituents to bring this expansion to a halt? It can be calculated that the critical density of matter needed to brake the expansion and “close” the universe is equivalent to three hydrogen atoms per cubic meter. But the density of the observable universe—luminous matter in the form of galaxies—comes to only a fraction of this. If the expansion of the universe is to stop, there must be enough invisible matter in the universe to exceed the luminous matter in density by a factor of roughly 70.

Our contribution to the search for this “missing matter” has been to study the rotational velocity of galaxies at various distances from their center of rotation. It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center. If luminosity were a true indicator of mass, most of the mass would be concentrated toward the center. Outside the nucleus the rotational velocity would decrease geometrically with distance from the center, in conformity with Kepler’s law. Instead we have found that the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly. This unexpected result indicates that the falloff in luminous mass with distance from the center is balanced by an increase in nonluminous mass.

Our findings suggest that as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth. Such dark matter could be in the form of extremely dim stars of low mass, of large planets like Jupiter, or of black holes, either small or massive. While it has not yet been determined whether this mass is sufficient to close the universe, some physicists consider it significant that estimates are converging on the critical value.
115. The passage is primarily concerned with

(A) defending a controversial approach
(B) criticizing an accepted view
(C) summarizing research findings
(D) contrasting competing theories
(E) describing an innovative technique

[Reveal] Spoiler:
C


116. The authors’ study indicates that, in comparison with the outermost regions of a typical spiral galaxy, the region just outside the nucleus can be characterized as having

(A) higher rotational velocity and higher luminosity
(B) lower rotational velocity and higher luminosity
(C) lower rotational velocity and lower luminosity
(D) similar rotational velocity and higher luminosity
(E) similar rotational velocity and similar luminosity

[Reveal] Spoiler:
D


117. The authors’ suggestion that “as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth” (lines 34–37) would be most weakened if which of the following were discovered to be true?

(A) Spiral galaxies are less common than types of galaxies that contain little nonluminous matter.
(B) Luminous and nonluminous matter are composed of the same basic elements.
(C) The bright nucleus of a typical spiral galaxy also contains some nonluminous matter.
(D) The density of the observable universe is greater than most previous estimates have suggested.
(E) Some galaxies do not rotate or rotate too slowly for their rotational velocity to be measured.

[Reveal] Spoiler:
A


118. It can be inferred from information presented in the passage that if the density of the universe were equivalent to significantly less than three hydrogen atoms per cubic meter, which of the following would be true as a consequence?

(A) Luminosity would be a true indicator of mass.
(B) Different regions in spiral galaxies would rotate at the same velocity.
(C) The universe would continue to expand indefinitely.
(D) The density of the invisible matter in the universe would have to be more than 70 times the density of the luminous matter.
(E) More of the invisible matter in spiral galaxies would have to be located in their nuclei than in their outer regions.

[Reveal] Spoiler:
C


119. The authors propose all of the following as possibly contributing to the “missing matter” in spiral galaxies EXCEPT

(A) massive black holes
(B) small black holes
(C) small, dim stars
(D) massive stars
(E) large planets

[Reveal] Spoiler:
D

[Reveal] Spoiler: Question #1 OA
[Reveal] Spoiler: Question #2 OA
[Reveal] Spoiler: Question #3 OA
[Reveal] Spoiler: Question #4 OA
[Reveal] Spoiler: Question #5 OA

Last edited by hazelnut on 06 Oct 2017, 08:07, edited 5 times in total.
Edited the question.

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New post 04 Oct 2009, 11:16
This OG RC passage has the first two questions on which I don't agree with the OA.

116.
Passage says: Velocity either remains constant with increasing distance from the center or increases slightly.
Question: compare "outermost regions" vs "region just outside the nucleus".
=> "region just outside the nucleus" could have either similar or lower velocity.
=> Both B and D could be right; a case for D has strong foundations given that we are comparing the "region just outside the nucleus" with the "outermost region" -> greatest possible distance withing the galaxy.

117.
OA is A. I believe A is wrong. Explanation:
"Galaxies that contain little nonluminous matter" = dark matter (in the form of either dim stars, black holes or large planets). Thus, spiral galaxies being less common than "obscure" galaxies does not weaken the suggestion that "as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth".
D is the best answer. If the density of the observable universe (small fraction) is increased, that 90% would be lower; increase the fraction significantly, and you can have an observable reduction in that 90%.
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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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akankshasoneja wrote:
Couldn't get Q117..Can some give a detailed explanation please


hi

117. The authors’ suggestion that “as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth” (lines 34–37) would be most weakened if which of the following were discovered to be true?
(A) Spiral galaxies are less common than types of galaxies that contain little nonluminous matter.
(B) Luminous and nonluminous matter are composed of the same basic elements.
(C) The bright nucleus of a typical spiral galaxy also contains some nonluminous matter.
(D) The density of the observable universe is greater than most previous estimates have suggested.
(E) Some galaxies do not rotate or rotate too slowly for their rotational velocity to be measured.

see the author is concluding:
Our findings suggest that as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth.
(last para 1st line)
what is the basis of this conclusion:

It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center. If luminosity were a true indicator of mass, most of the mass would be concentrated toward the center. Outside the nucleus the rotational velocity would decrease geometrically with distance from the center, in conformity with Kepler’s law. Instead we have found thatthe rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly.This unexpected result indicates that the falloff in luminous mass with distance from the center is balanced by an increase in nonluminous mass.

so author experiment is onTYPICAL galaxy ==>some results came==>then he concluded.
see the flaw is he is considering only a limited source of galaxy and generalising for whole universe.

so the ultimate weakener that is option B:
Spiral galaxies are less common than types of galaxies that contain little nonluminous matter.
SO this is saying that typical spiral galaxy are less number hence whatever conclusion author is trying to make can be wrong.

hope it helps
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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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This can be done within 10 mins. I goofed up in 117 but then realized my mistake. 116 is tricky :)
115. The passage is primarily concerned with
(A) defending a controversial approach
(B) criticizing an accepted view
(C) summarizing research findings
>>
P1: Problem is introduced.
P2: A Research is introduced in this regard.
P3: Closes the discussion with a final note on the research.
So overall its summarizing the research.

(D) contrasting competing theories
(E) describing an innovative technique

116. The authors’ study indicates that, in comparison with the outermost regions of a typical spiral galaxy, the region just outside the nucleus can be characterized as having
(A) higher rotational velocity and higher luminosity
(B) lower rotational velocity and higher luminosity
(C) lower rotational velocity and lower luminosity
(D) similar rotational velocity and higher luminosity
>> Instead we have found that the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly.

(E) similar rotational velocity and similar luminosity

117. The authors’ suggestion that “as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth” (lines 34–37) would be most weakened if which of the following were discovered to be true?
(A) Spiral galaxies are less common than types of galaxies that contain little nonluminous matter.
>> Author concludes that its the low intensity wavelength of NLM because of which it cant be detected on earth. so assumption is, spiral galaxy is full of NLM. But what if there is not ample or very little NLM in spiral galaxy.Then it weakens the conclusion as its the scarcity and not the WL of the NLM which is resulting in this behavior.

(B) Luminous and nonluminous matter are composed of the same basic elements.
(C) The bright nucleus of a typical spiral galaxy also contains some nonluminous matter.
(D) The density of the observable universe is greater than most previous estimates have suggested.
(E) Some galaxies do not rotate or rotate too slowly for their rotational velocity to be measured.

118. It can be inferred from information presented in the passage that if the density of the universe were equivalent to significantly less than three hydrogen atoms per cubic meter, which of the following would be true as a consequence?
(A) Luminosity would be a true indicator of mass.
(B) Different regions in spiral galaxies would rotate at the same velocity.
(C) The universe would continue to expand indefinitely.
(D) The density of the invisible matter in the universe would have to be more than 70 times the density of the luminous matter.
(E) More of the invisible matter in spiral galaxies would have to be located in their nuclei than in their outer regions.

119. The authors propose all of the following as possibly contributing to the “missing matter” in spiral galaxies EXCEPT
(A) massive black holes
(B) small black holes
(C) small, dim stars
(D) massive stars
(E) large planets
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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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New post 29 Jan 2016, 09:41
I still do not understand Q 117
mikemcgarry please clear my doubt here.

In option A) Spiral galaxies are less common than types of galaxies that contain little nonluminous matter.
It could be very possible that the researchers already took this into account. The passage states that the researchers studied typical spiral galaxies and through their studies concluded that 90% percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth.

Researchers line of reasoning - spiral galaxies are less common --- spiral galaxies research suggest that there's x amount of non-luminous mass --- considering everything, this accounts to 90%.
The passage never mentions that the researchers assumed that spiral galaxies were very common. How can we assume that they wrongly estimated the proportion of spiral galaxies.

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New post 31 Jan 2016, 00:02
vabhs192003 wrote:
Completed within 10mins with 1 wrong. :x :x

Though I got 117 correct using POE :!: I would like to know the definite rationale to eliminate option D.:?:


Notice that the author's assertion is not very precise: "as much as 90 percent of the mass . . . " So if we find that the observable universe is denser than we thought, it wouldn't really undermine this vague assertion. We would just adjust the maximum down by some unknown amount. Furthermore, the author's team is not basing their assertion on current estimates of the density of the observable universe, but on the observation of galaxies. This is why (A) presents a problem for this view. If it turned out that spiral galaxies like ours, which are rich in nonluminous matter, were uncommon, this would undermine the entire basis of the author's idea.
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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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New post 17 Feb 2016, 23:24
vabhs192003 wrote:
Completed within 10mins with 1 wrong. :x :x

Though I got 117 correct using POE :!: I would like to know the definite rationale to eliminate option D.:?:



Hi,

The author wants to imply that almost 90% of the Universe doesn't have luminous mass.

If D) Was correct

It implies that there is even more invisible mass than that was thought, which strengthens the statement rather than weakening it. It's a classic CR question.
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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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New post 18 Sep 2016, 15:46
kunwardeep25 wrote:
Can someone please explain 116?


Hello friend, it is a combination of this two parts:

Quote:
Instead we have found that the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly.


and...

Quote:
It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center.

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New post 26 Oct 2016, 11:09
JarvisR wrote:
This can be done within 10 mins. I goofed up in 117 but then realized my mistake. 116 is tricky :)
115. The passage is primarily concerned with
(A) defending a controversial approach
(B) criticizing an accepted view
(C) summarizing research findings
>>
P1: Problem is introduced.
P2: A Research is introduced in this regard.
P3: Closes the discussion with a final note on the research.
So overall its summarizing the research.

(D) contrasting competing theories
(E) describing an innovative technique

116. The authors’ study indicates that, in comparison with the outermost regions of a typical spiral galaxy, the region just outside the nucleus can be characterized as having
(A) higher rotational velocity and higher luminosity
(B) lower rotational velocity and higher luminosity
(C) lower rotational velocity and lower luminosity
(D) similar rotational velocity and higher luminosity
>> Instead we have found that the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly.

(E) similar rotational velocity and similar luminosity

117. The authors’ suggestion that “as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth” (lines 34–37) would be most weakened if which of the following were discovered to be true?
(A) Spiral galaxies are less common than types of galaxies that contain little nonluminous matter.
>> Author concludes that its the low intensity wavelength of NLM because of which it cant be detected on earth. so assumption is, spiral galaxy is full of NLM. But what if there is not ample or very little NLM in spiral galaxy.Then it weakens the conclusion as its the scarcity and not the WL of the NLM which is resulting in this behavior.

(B) Luminous and nonluminous matter are composed of the same basic elements.
(C) The bright nucleus of a typical spiral galaxy also contains some nonluminous matter.
(D) The density of the observable universe is greater than most previous estimates have suggested.
(E) Some galaxies do not rotate or rotate too slowly for their rotational velocity to be measured.

118. It can be inferred from information presented in the passage that if the density of the universe were equivalent to significantly less than three hydrogen atoms per cubic meter, which of the following would be true as a consequence?
(A) Luminosity would be a true indicator of mass.
(B) Different regions in spiral galaxies would rotate at the same velocity.
(C) The universe would continue to expand indefinitely.
(D) The density of the invisible matter in the universe would have to be more than 70 times the density of the luminous matter.
(E) More of the invisible matter in spiral galaxies would have to be located in their nuclei than in their outer regions.

119. The authors propose all of the following as possibly contributing to the “missing matter” in spiral galaxies EXCEPT
(A) massive black holes
(B) small black holes
(C) small, dim stars
(D) massive stars
(E) large planets


For Q-116, Can you explain how it is higher luminosity???
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New post 29 Oct 2016, 02:22
@emmafoaster, check out this sentence in paragraph 2: "It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center."

This implies that the luminosity is highest in the nucleus, a bit lower outside the nucleus, and a whole lot lower as you get toward the edge.
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New post 22 Dec 2016, 12:09
nitya34 wrote:
[box_out]
After evidence was obtained in the 1920s that the universe is expanding, it became reasonable
to ask: Will the universe continue to expand indefinitely, or is there enough mass in it for the mutual attraction of its constituents to bring this expansion to a halt? It can be calculated that the critical density of matter needed to brake the expansion and “close” the universe is equivalent to three hydrogen atoms per cubic meter. But the density of the observable universe—luminous matter in the form of galaxies—comes to only a fraction of this. If the expansion of the universe is to stop, there must be enough invisible matter in the universe to exceed the luminous matter in density by a factor of roughly 70.

Our contribution to the search for this “missing matter” has been to study the rotational velocity of galaxies at various distances from their center
of rotation. It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center. If luminosity were a true indicator of mass, most of the mass would be concentrated toward the center. Outside the nucleus the rotational velocity would decrease geometrically with distance from the center, in conformity with Kepler’s law. Instead we have found that the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly. This unexpected result indicates that the falloff in luminous mass with distance from the center is balanced by an increase in nonluminous mass.

Our findings suggest that as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth. Such dark matter could be in the form of extremely dim stars of low mass, of large planets like Jupiter, or of black holes, either small or massive. While it has not yet been determined whether this mass is sufficient to close the universe, some physicists consider it significant that estimates are converging on the critical value.
[box_in]115. The

118. It can be inferred from information presented in the passage that if the density of the universe were equivalent to significantly less than three hydrogen atoms per cubic meter, which of the following would be true as a consequence?
(A) Luminosity would be a true indicator of mass.
(B) Different regions in spiral galaxies would rotate at the same velocity.
(C) The universe would continue to expand indefinitely.
(D) The density of the invisible matter in the universe would have to be more than 70 times the density of the luminous matter.
(E) More of the invisible matter in spiral galaxies would have to be located in their nuclei than in their outer regions.

Hi sayantanc2k,
Hope you're well brother. I've stuck with question# 118. The passage says that if the density is equivalent to 3 hydrogen atoms per cubic meter, then the expansion of the universe will be stop. That means: if the density is LESS than 3 hydrogen atoms per cubic meter, then expansion will be be continued, WHICH is answer option C (the correct choice). But, my question is: if the density is MORE THAN 3 hydrogen atoms per cubic meter, then the expansion of the universe will STILL be continued?
Thanks...
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New post 29 Dec 2016, 03:14
iMyself, there's no support for the conclusion that expansion would continue if the density were higher than the needed amount. If I said that you needed $10,000 to open an investment account or that you needed a 3.0 GPA to apply to a program, you wouldn't assume that you were out of luck if you had $50,000 and a 4.0, right?

If the intended meaning were that the density needed to be exactly three hydrogen atoms per cubic meter, the passage would need to say that.
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New post 26 Apr 2017, 02:55
It took me 12 min 20 sec to complete the passage with only one question wrong.

Am I taking a lot of time to read? Need some feedback.

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New post 28 Apr 2017, 18:46
That's a bit too long, but it depends in part on how your time was allocated. Keep in mind that the GMAT will only give you 3-4 questions per passage, so doing 5 as a timed set is not realistic. Aim to read the passage & do 3-4 questions in 6-8 minutes. Then time the other questions separately, aiming to average 1 minute per question.
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New post 24 Jun 2017, 23:46
Hi Experts / GMATNinjaTwo

Q116:
As per passage:
It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center
which implies: as distance increases form center / nucleus, luminosity decreases.

Then why OA is D, I am clear about rotational velocity
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New post 29 Jun 2017, 12:23
adkikani wrote:
Hi Experts / GMATNinjaTwo

Q116:
As per passage:
It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center
which implies: as distance increases form center / nucleus, luminosity decreases.

Then why OA is D, I am clear about rotational velocity

Yes, as distance from the center increases, luminosity decreases. This is consistent with choice (D): In comparison with the outermost regions of a typical spiral galaxy, the region just outside the nucleus can be characterized as having higher luminosity. In other words, the luminosity is lower in the outermost regions than the luminosity just outside the nucleus.

We also know "that the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly." This is also consistent with choice (D): In comparison with the outermost regions of a typical spiral galaxy, the region just outside the nucleus can be characterized as having similar rotational velocity.

I hope that helps!
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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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New post 02 Aug 2017, 09:35
Regarding question 117 this is my 10 cents.

(A) Spiral galaxies are less common than types of galaxies that contain little nonluminous matter.

Little nonluminous=No Nonluminous= Luminous

So it says Spiral galaxies are less common than galaxies that contain luminous matter.

As per the passage spiral galaxies contain dark matter and A says those galexies are less in number than those galexies which contain no dark matter. So as per this logic a can be considered as a weakener.



(B) Luminous and nonluminous matter are composed of the same basic elements.- Density does not matter. We are talking about percentage of space occupied by luminous or nonluminous matter. So B is out.

(C) The bright nucleus of a typical spiral galaxy also contains some nonluminous matter. -Does not matter


(D) The density of the observable universe is greater than most previous estimates have suggested. -Again density. Density does not matter.We are talking about percentage of space occupied



(E) Some galaxies do not rotate or rotate too slowly for their rotational velocity to be measured.-Does not matter

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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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New post 03 Aug 2017, 15:10
Could someone please comment on 117 regarding answer D ?

if the density of the "observable universe" (defined in the passage as "luminous matter in the form of galaxies") com[ing] to a small fraction of the [necessary 3 hydrogen atoms/cubic meter] forms the basis for the assertion that "there must be enough INVISIBLE (nonluminous) matter in the universe to exceed the luminous matter by a density by a factor of roughly 70", then wouldn't this density estimate of the observable universe being understated (as answer D states) imply without room for refute that the assertion that nonluminous matter makes up 90% of the mass in the universe is weakened ???

Thanks for addressing this run on sentence. Seriously, this question (and the OG explanation) are quite off-target IMO - the official answer makes a much less airtight argument.

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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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New post 17 Aug 2017, 07:54
boobymiles wrote:
Could someone please comment on 117 regarding answer D ?

if the density of the "observable universe" (defined in the passage as "luminous matter in the form of galaxies") com[ing] to a small fraction of the [necessary 3 hydrogen atoms/cubic meter] forms the basis for the assertion that "there must be enough INVISIBLE (nonluminous) matter in the universe to exceed the luminous matter by a density by a factor of roughly 70", then wouldn't this density estimate of the observable universe being understated (as answer D states) imply without room for refute that the assertion that nonluminous matter makes up 90% of the mass in the universe is weakened ???

Thanks for addressing this run on sentence. Seriously, this question (and the OG explanation) are quite off-target IMO - the official answer makes a much less airtight argument.

Quote:
if the density of the "observable universe"... com[ing] to a small fraction of the [necessary 3 hydrogen atoms/cubic meter] forms the basis for the assertion that "there must be enough INVISIBLE (nonluminous) matter in the universe to exceed the luminous matter by a density by a factor of roughly 70"

The author does not argue that nonluminous matter must exceed luminous matter by a density factor of 70 BECAUSE that is what would be necessary to stop the expansion of the universe. Rather, the author merely comments that nonluminous matter would have to exceed luminous matter by a density factor of 70 IN ORDER TO stop the expansion of the universe.

Choice (D) would certainly affect the factor of 70 cited in the first paragraph; if there is more luminous matter than had been previously estimated, that would suggest that it would take less invisible matter to stop the expansion of the universe.

However, the author's suggestion mentioned in question #117 is based on the findings described in the second paragraph: "the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly. This unexpected result indicates that the falloff in luminous mass with distance from the center is balanced by an increase in nonluminous mass."

The author believes that those findings "suggest that as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth." Choice (D) does not affect the author's reasoning at all. The author is using observations of spiral galaxies to draw conclusions about the universe. Choice (A) suggests that, even if the findings are true, they do not accurately reflect what's going on in most galaxies.

I hope that helps!
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Re: After evidence was obtained in the 1920s that the universe is expandin [#permalink]

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New post 29 Sep 2017, 07:37
Q. 118 - if the density of the universe were equivalent to significantly less than 3 HA/CM
For this I referred 1st paragraph of the passage. If mentions that "is there enough mass in it for the mutual attraction of its constituents to bring this expansion to a halt"? God knows what it means - mutual attraction of.. enough mass..! Whoa!
Okay - so does this mean that in order to halt the universe expansion, we need mutual attraction of (some of) its constituents, and this needs enough mass in the universe?? Who would want what? I am confused
Now rightaway, critical density of the matter needed to brake the expansion and close the universe is equivalent to 3HA/cm. But the density of the observable universe is only a fraction.
Here, first of all, I understand mass = density. Now, is the mass (density) referring to the density of the universe or the constituents (matter)? And why would the author talk about the density of the constituents when he himself talks about the density of the universe in the previous sentence? Or both are same?
Then, as the density of observable universe is only a fraction of 3HA/cm, we need 70 times of that fraction for the density of the invisible (inobservable) mass/matter to be. Observable + inobservable = mass needed to halt expansion.

Now, if the mass of universe is less than 3HA/cm, this means that we would need less of inobservable density, i.e., <70. Thus, why would it keep expanding indefinitely?

I apologize if I have confused my peers or senior members. Grateful if someone can help me here. Is my approach faulty? Or do I need to really work hard on my comprehension skills? Can someone advise me what approach I must take to improve in such circumstances. The mind goes blank and stuck.

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Re: After evidence was obtained in the 1920s that the universe is expandin   [#permalink] 29 Sep 2017, 07:37

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