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# GMATCLUB VERBAL ATTACK

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MBA Section Director
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GMATCLUB VERBAL ATTACK [#permalink]

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GMATCLUB VERBAL ATTACK

Hello all
I got my first 760 on MGMAT CAT 2 so I am extremely happy.
With that happiness I have decided to take a break, devoting my time entirely into gmatclub.

So here is what we are going to do
Each week On this forum we will discuss one main topic of Verbal and go over as much we can, covering everything we can share, including resources and questions.

Update:

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Joined: 19 Mar 2012
Posts: 3259
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1262

Kudos [?]: 9113 [8] , given: 1842

WEEK 1: CRITICAL REASONING STRENGTHEN/WEAKEN Questions [#permalink]

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WEEK 1: Strengthen/Weaken/Evaluate the Argument

STRATEGY : Strengthen Question

Which of the following strengthens/ supports/ most justifies/ helps…

 Ask to support conclusion/argument in any way- answer can support in a minor or major way!
 Stimulus will always be an argument- since you can only strengthen a conclusion, not a fact set. Identify, isolate and assess the premises and conclusion.
 Focus on conclusion.
 Information in stimulus is suspect. Reasoning errors are present which can be corrected by answer choice.
 Strong prephrases possible
 Answer choices can bring new information which is not present in stimulus.
 While an assumption is necessary to the argument, a strengthen answer might not be essential for the argument to be true.
 The correct answer will , at least somewhat, venture outside the scope of the immediate argument (i.e. introduce something new)

How to strengthen?

• Identify the conclusion – your answer choice should help the author and his conclusion
• Personalize the argument- place yourself inside the situation and think how you will react.
• Look for weaknesses in the argument – any gap, hole- that is tailor made to be eliminated as a correct strengthen answer.
• An answer that highlights an assumption of the author will also strengthen the author’s conclusion
• If the argument stimulus talks of a survey, poll- any answer choice which highlights its soundness or establishes its credibility will be correct.
• Correct answer can strengthen just a little or a lot!

Correct answer will strengthen by:

• Fixing a weakness of the conclusion
• Validate an assumption made by argument
• Introduce additional supporting evidence

Incorrect answer types:

• Opposite answers: Weaken
• Shell Game answers: idea form stimulus altered a little to be wrong
• Out of scope answer: miss the point/conclusion
Whenever a stimulus starts with word ‘Advertisement:’ it will have flawed logic. Be prepared to look out for the gap and address that.

Causality and Strengthen Question

• Eliminate alternate causes
• Show that when the cause occurs, effect occurs
• Show that when the effect is there, cause has occurred
• Show that reverse is not true
• Show that statistical data behind the cause effect conclusion is correct
• Show that when cause doesn’t occur, effect doesn’t occur

In StrnegthenX questions, correct answer choice will mostly have no effect on the argument, or will be out of scope. Be cautious sometimes the answer choice which strengthens the argument is wrongly selected if it strengthens by eliminating an alternate cause which doesn’t occur in stimulus. There is tendency to think that it is out of scope and doesn’t strengthen. E.g. in a question that argues that amphibian population is decreasing because of ozone depletion, an answer choice that their natural habitat is not depleting is not out of scope- but strengthening by eliminating alternate cause of fall in population

BEST APPROACH: SIMPLIFY THE ARGUMENT INTO 1-2 STATEMENTS, and apply choice ONLY to simplified argument. Many choices that seemed relevant otherwise will now not be relevant!

GMATPREP EXAMPLE

Q. Excavation of the ancient city of Kourion on the island of Cyprus revealed a pattern of debris and collapsed buildings typical of towns devestated by earthquakes. Archaeologists have hypothesized that the destruction was due to a major earthquake known to have occured near the island in A.D. 365. Which of the following, if true, most strongly supports the archaeologists' hypothesis?
(A) Bronze ceremonial drinking vessals that are often found in graves dating from years preceding and following A.D. 365 were also found in several graves near Kourion.
(B) No coins minted after A.D. 365 were foundin Kourion, but coins minted before that year were found in abundance
(C) Most modern histories of Cyprus mention that an earthquake occured near the island in A.D. 365.
(D) Several small statues carved in styles current in Cyprus in the century between A.D. 300 and 400 were found in Kourion.
(E) Stone inscriptions in a form of the Greek alphabet that was definitely used in Cyrpus after A.D. 365 were found in Kourion

[Reveal] Spoiler:
Simplified: an earthquake destroyed city. The earthquake happened in year 365. C says that the earthquake happened – that doesn’t strengthen, this is already known to have occurred from the question stem. Reiterate something that is already known – DOES NOT strengthen.

B pinpoints the date at year 365. Correct.

Notes Credit: Vivesomnium, Ron Purewal, Powerscore CR Bible, GMATPrep 2.0

QUESTION SET STRENGTHEN

1. The United States government uses only a household’s cash income before taxes to determine whether that
household falls below the poverty line in a given year; capital gains, non-cash government benefits, and tax credits
are not included. However, yearly cash income is not a fool-proof measure of a given household’s disposable
income. For example, retirees who live off of capital gains from an extensive portfolio could earn hundreds of
thousands of dollars, yet be classified by the government as living in “poverty” because this income is not included
in the calculation. Which of the following, if true, validates the contention that the government’s calculation methods
must be altered in order to provide statistics that measure true poverty?
• For more than 99% of those classified as living in poverty, yearly cash income comprises the vast majority of each
household’s disposable income.
• While the government’s calculation method indicated a 12.5% poverty rate in 2003, the same calculation method
indicated anywhere from a 9% to a 16% poverty rate during the preceding decade.
• Most established research studies conducted by the private sector indicate that the number of people truly living in
poverty in the U.S. is less than that indicated by the government’s calculation method.
• Several prominent economists endorse an alternate calculation method which incorporates all income, not just
cash income, and adjusts for taxes paid and other core expenses.
• The government’s calculation method also erroneously counts those who do not earn income in a given year but
who have substantial assets on which to live during that year.

[Reveal] Spoiler: Question 1 Answer & Explanation
OA: C
The conclusion of the argument is that the government's calculation methods
must be altered in order to provide statistics that measure true poverty. To
support this position, the author first explains how the government’s method
works and then introduces a hypothetical example that would return a "false
positive" - that is, a person who has a large income, yet is classified by the
government as living in poverty. One example, however, is generally not enough
to invalidate an entire method; no method is perfect and there are always a few
results that are not consistent with the overall conclusion. In order to validate, or
strengthen, the conclusion, we need to show that the government’s method is
fundamentally inferior to some alternative that would produce more valid results.

(A) This choice weakens the argument by minimizing the importance of the
author's evidence (the hypothetical retiree with capital gains). According to this
choice, the use of cash income to designate poverty levels is a very sound
method because it provides valid results for more than 99% of those classified as
living in poverty.

(B) This choice shows that the government’s method provided a wide range of
results for the poverty rate over a certain period of time, but it is irrelevant to the
argument at hand. It tells us nothing about whether the method provides relevant
statistics in any given year.

(C) CORRECT. If this statement is true, then the government’s calculation
method seems to overstate the number of people living in poverty, while the
various private sector studies generally agree with each other that the number of
people is lower. Thus, the methods used in the private sector are likely to be
more valid than the government’s method, lending credence to the author's
contention that the government’s method should change.

(D) Although this choice provides an example of people who might agree with the
conclusion (several prominent economists), this choice provides no evidence that
the alternate method they endorse would provide more relevant statistics than
the government’s method.

(E) This choice adds another hypothetical example of how the current method
could include someone in the poverty count who does not actually live in poverty.
It does not, however, address whether there are other calculation methods that
are more accurate than the government’s method.

2. Historically, the drug industry promoted its products to physicians by educating them in their offices or at industry
conferences. In the last 10 years, it has become much more commonplace for drug companies to advertise
prescription drugs directly to consumers, via television advertising and other media. Some public health advocates
have become concerned that patients, encouraged by advertising, may pursue the use of prescription drugs that
may be inappropriate for the individual patient or situation. However, since physicians must prescribe these
medications, there is no reason for such concern. Which of the following pieces of information would be most
helpful in addressing the concern articulated by the public health advocates?
• Certain over-the-counter medications are as effective for many common medical conditions as more powerful
nonprescription medications.
• Prescription medication television advertisements directed at the general public only appear on certain programs
and are not seen by many potential consumers.
• Physicians are also subject to prescription drug advertisements that are directed toward consumers.
• Physicians are not susceptible to pressure from patients in determining appropriate courses of treatment, including
drug prescriptions.
• Prescription medicines have been proven to be safe and effective treatments for many patient conditions.

[Reveal] Spoiler: Question 2 Answer & Explanation
The public health advocates are concerned that patients are subjected to
advertisements about prescription drugs, and may pursue these drugs even
though the drugs may not be clinically appropriate. It is argued that, because
physicians must prescribe the drugs in question, patient pursuit of these
prescription drugs is irrelevant. However, patients who pursue and request
particular prescription drugs may be able to encourage or induce a physician to
prescribe drugs that he or she might not have in the absence of such
encouragement.

(A) The clinical efficacy of certain over-the-counter medications does not address
the public health advocates’ concern regarding patient pursuit of inappropriate
prescription drugs.

(B) The public health advocates’ concern does not rely on every possible
consumer to see the advertisements for prescription medications. It is enough
that some consumers see the advertisements.

(C) This answer choice states the obvious possibility that physicians may also
see the advertisements for prescription drugs directed toward consumers. This is
irrelevant to the concern expressed by the public health advocates.

(D) CORRECT. This answer choice directly addresses the public health
advocates’ concern by establishing that physicians are not susceptible to patient
pressure in prescribing inappropriate drugs. As a result, drugs will be prescribed
according to the objective clinical judgment of the prescribing physician,
mitigating the danger of inappropriate use.

(E) That certain prescription medications are safe and effective treatments for
many conditions does not address the concern of inappropriate use expressed
by the public health advocates. Prescription drugs can be safe and effective
when used for certain conditions by various individuals and still be subject to
unhealthy use by other patients.

3. Studies in restaurants show that the tips left by customers who pay their bill tend to be larger when the bill is
presented with the server’s name hand-written on the bill. Psychologists hypothesize that simply seeing a hand-written name makes many consumers feel more of a personal identification with the server, encouraging larger
tips. Which of the following, if true, most strongly supports the psychologists’ interpretation of the studies?
• The effect noted in the studies applies to patrons paying with either credit cards or cash.
• Nametags for servers have not been shown to have any effect on the size of the bill.
• Greeting card companies have found that charities which send holiday cards with handwritten signatures are more
likely to receive donations than those which send cards with printed signatures.
• The studies indicated much larger average tips if the customer ordered alcoholic beverages with his or her meal.
• Many of the restaurants in which the studies were conducted are located in tourist areas, where people are
traveling for leisure activities.

4. Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline. Which of the following, if true, would best support the analyst’s main assertion?
• New technology often becomes less expensive after an initial surge in sales.
• Media outlets, such as television programs and magazines, often report on the planned introduction of new
devices while the sales of old devices are still strong.
• Many consumers are unable to determine whether new technology is superior to current technology.
• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases.
• Consumers tend to be loyal to technology companies whose products they enjoy using.

5. More and more companies have begun to consume less energy by making themselves more efficient. Over time,
these efforts could place the United States at the forefront of an emerging global market for cleaner technologies.
Such efforts are also essential to tackling the two big energy-related issues of the age: global warming and the
dependence on precarious supplies of oil. The federal government should encourage these efforts by providing the
necessary incentives, whether as loans, direct grants or targeted tax breaks. Which of the following, if true,
provides the most effective support for the argument?
• On the average, Canadian companies are more energy efficient than those in the United States.
• Experts believe that energy efficiency could lower the energy use of the United States to the level of 1995.
• In the past, government incentives have made advances in energy conservation feasible, especially in the auto
industry.
• The dependence on foreign oil is a greater problem in the present than global warming.
• The market for cleaner technologies is currently relatively small because of the infrastructure requirements.

6. State X recently decided to cut state funding for the public library system in County X. To help counteract this cut
in funding, the county library system has increased library late fees from $.10 per day to$.12 per day. Since the
fee increase, library administrators have seen no decline in the number of overdue books. The director of the
county library system concludes that the fee hike has helped to counteract the cut in state funding. Which of the
following statements, if true, most strengthens the director’s claim?
• Since the fee increase, library administrators have noted a significant decrease in the number of books borrowed
each day.
• The library system incurred minor costs to make its visitors aware of the late fee increase.
• Since the fee increase, there has been no significant change in the average number of days that books are
overdue before they are returned.
• The library system in County X tracks its books through a very advanced database system, allowing library
administrators to have access to very accurate statistics on the number of overdue books at any given time.
• Since the reduction in state funding, the library system in County X has eliminated 10% of its staff, creating a 2%
reduction in costs.

7. In the 18th and 19th centuries, it was believed in many coastal American cities that the waterfront was an
undesirable location for residential buildings. As a result, much of the waterfront in these cities was never developed
aesthetically and instead was left to industry and commerce. Today, however, waterfront properties are generally
seen as prestigious, as evidenced by the large sums paid for homes along the beach front. A developer who
wishes to make a large profit would be wise to buy urban waterfront lots and erect residential buildings on them.
Which of the following, if true, most strongly supports the claim made about urban waterfront properties?
• People today have more money, relatively speaking, to spend on real estate than they did in previous centuries.
• Homeowners will be willing to spend large sums on residential properties in traditionally industrial or commercial
districts.
• Many urban waterfront lots are available for purchase.
• Many coastal American cities are encouraging developers to rehabilitate the waterfront through tax incentives.
• Properties in interior residential districts in coastal American cities are significantly more expensive than those
along the waterfront.

8. Charter schools are independent public schools that are given greater autonomy in exchange for increased
accountability. Charter school operators are freed from many of the regulations of the traditional public school
bureaucracy, thereby allowing them to pursue more innovative educational ideas than non-charter public schools
can pursue. At the same time, charter schools are held accountable for achieving specific educational outcomes
and are closed down if those outcomes are not met. Which of the following, if true, best supports the assertion
that students attending charter schools will, on average, perform better on assessments of writing ability than
students attending traditional public schools?
• Students who attend schools that emphasize order and discipline perform worse on assessments of writing ability
than students who attend schools that do not emphasize order and discipline.
• The majority of students who score in the 99th percentile on assessments of writing ability attend charter schools.
• Public schools that operate outside of the traditional public school bureaucracy spend more time teaching students
writing than do traditional public schools.
• Students who attend schools that are allowed to experiment with their writing curricula perform better on
assessments of writing ability than students who attend schools that have less flexible curricula.
• There are far more students attending non-charter public schools than students attending charter schools.

9. Officials of the Youth Hockey League and parents of players in the league have become concerned with the number
of flagrant fouls occurring during league games. This past season, the number of flagrant fouls was double the
number from the season before. League officials plan to reduce the number of such fouls during the coming
season by implementing mandatory suspensions for players who commit flagrant fouls. Which of the following
statements, if true, provides the best evidence that the officials’ plan will be effective?
• Most serious injuries occurring during league games are a direct result of flagrant fouls.
• League referees have been trained to recognize flagrant fouls and to report incidents involving such fouls.
• Parents of players in the league are in support of mandatory suspensions for flagrant fouls.
• A similar league suspends players for committing flagrant fouls; this league has a relatively low incidence of
flagrant fouls when compared with the Youth Hockey League.
• Most players in the league strive to be selected for the All-Star team, and league rules state that no player with a
record of suspension shall be selected for the All-Star team.

10. Almost every modern kitchen today is equipped with a microwave oven, mainly because microwave ovens offer a
fast and convenient way of cooking and reheating food. Indeed, it has become a standard appliance in most
households. Studies have shown, however, that microwave ovens are not completely safe and their use has
occasionally resulted in serious injury. Because of this, some consumer advocates argue that microwave ovens
should not be so readily accepted as a standard appliance until they can be certified to be completely safe. Which
of the following, if true, would most strengthen the argument of the consumer advocates?
• Microwave ovens have taken much of the joy out of cooking.
• There have been many reported incidences of people who have been scalded by liquids superheated in microwave
ovens.
• Absolute safety is the only criterion by which an appliance should be judged to be acceptable as “standard.”
• There is no such thing as a completely safe appliance.
• Stoves and ovens that use natural gas consume energy much more efficiently than microwave ovens.

OAs in 24 Hours followed by a set of 10 700-800 level WEAKEN questions

Please discuss solutions and other questions in this area.
Lets make this our very own verbal workbook
Cheers.

Next Week's Topic

Inference and Boldface
_________________
MBA Section Director
Joined: 19 Mar 2012
Posts: 3259
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1262

Kudos [?]: 9113 [1] , given: 1842

Re: GMATCLUB VERBAL ATTACK [#permalink]

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17 Sep 2012, 11:59
1
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Source: Online forums
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Posts: 2878
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Kudos [?]: 5178 [0], given: 883

Re: GMATCLUB VERBAL ATTACK [#permalink]

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17 Sep 2012, 14:30
Expert's post
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C D A B E D C B D C

I'm here to discuss. Good bank
_________________
MBA Section Director
Joined: 19 Mar 2012
Posts: 3259
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1262

Kudos [?]: 9113 [1] , given: 1842

Re: GMATCLUB VERBAL ATTACK [#permalink]

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17 Sep 2012, 14:39
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You got around 5 wrong
lets see if we have a couple of more answers and then we shall hit the explanations what say?
_________________
Moderator
Joined: 01 Sep 2010
Posts: 2878
Followers: 653

Kudos [?]: 5178 [0], given: 883

Re: GMATCLUB VERBAL ATTACK [#permalink]

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17 Sep 2012, 15:30
Expert's post
Ya

Waiting other responses from members.

In the meantime I would rechek my answers. I'll print it, set a timer and see

They was tough, however

Edit: C D C B C B D C D C
_________________
MBA Section Director
Joined: 19 Mar 2012
Posts: 3259
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1262

Kudos [?]: 9113 [0], given: 1842

Re: GMATCLUB VERBAL ATTACK [#permalink]

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17 Sep 2012, 20:19
Expert's post
Check the edited post above
Included a set of strategies.
Feel free to add something if missed
_________________
Senior Manager
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Posts: 373
Location: US
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Kudos [?]: 82 [0], given: 46

Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 01:23
My answers are listed below. I took 24 min for all of them.
C D C E C C B D E B.
I got 2 of them wrong. One wrong answer is acceptable but other one is not.
Also, we must discuss question 4 because i'm not happy with the explanation floating around for that one.

Cheers!
_________________

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Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 03:07
souvik101990 wrote:

GMATCLUB VERBAL ATTACK

Hello all

I got my first 760 on MGMAT CAT 2 so I am extremely happy.

With that happiness I have decided to take a break, devoting my time entirely into gmatclub.

Good going dude, What resources did you use to get into 750+ zone. You seem to have indicated Thursdays with Ron and e-GMAT.
_________________

The question is not can you rise up to iconic! The real question is will you ?

MBA Section Director
Joined: 19 Mar 2012
Posts: 3259
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1262

Kudos [?]: 9113 [0], given: 1842

Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 03:10
Expert's post
AbhiJ wrote:
souvik101990 wrote:

GMATCLUB VERBAL ATTACK

Hello all

I got my first 760 on MGMAT CAT 2 so I am extremely happy.

With that happiness I have decided to take a break, devoting my time entirely into gmatclub.

Good going dude, What resources did you use to get into 750+ zone. You seem to have indicated Thursdays with Ron and e-GMAT.

Hey Abhi
E-gmat was great but I kind of found it a but mechanical though
Thursdays with Ron, remains to be the BEST free resource out there.
_________________
MBA Section Director
Joined: 19 Mar 2012
Posts: 3259
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1262

Kudos [?]: 9113 [2] , given: 1842

Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 03:16
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STRENGTHEN SET OFFICIAL EXPLANATIONS

Answer KEYS
CDCBCCBDEC

1.
The conclusion of the argument is that the government's calculation methods
must be altered in order to provide statistics that measure true poverty. To
support this position, the author first explains how the government’s method
works and then introduces a hypothetical example that would return a "false
positive" - that is, a person who has a large income, yet is classified by the
government as living in poverty. One example, however, is generally not enough
to invalidate an entire method; no method is perfect and there are always a few
results that are not consistent with the overall conclusion. In order to validate, or
strengthen, the conclusion, we need to show that the government’s method is
fundamentally inferior to some alternative that would produce more valid results.

(A) This choice weakens the argument by minimizing the importance of the
author's evidence (the hypothetical retiree with capital gains). According to this
choice, the use of cash income to designate poverty levels is a very sound
method because it provides valid results for more than 99% of those classified as
living in poverty.

(B) This choice shows that the government’s method provided a wide range of
results for the poverty rate over a certain period of time, but it is irrelevant to the
argument at hand. It tells us nothing about whether the method provides relevant
statistics in any given year.

(C) CORRECT. If this statement is true, then the government’s calculation
method seems to overstate the number of people living in poverty, while the
various private sector studies generally agree with each other that the number of
people is lower. Thus, the methods used in the private sector are likely to be
more valid than the government’s method, lending credence to the author's
contention that the government’s method should change.

(D) Although this choice provides an example of people who might agree with the
conclusion (several prominent economists), this choice provides no evidence that
the alternate method they endorse would provide more relevant statistics than
the government’s method.

(E) This choice adds another hypothetical example of how the current method
could include someone in the poverty count who does not actually live in poverty.
It does not, however, address whether there are other calculation methods that
are more accurate than the government’s method.

2.
The public health advocates are concerned that patients are subjected to
advertisements about prescription drugs, and may pursue these drugs even
though the drugs may not be clinically appropriate. It is argued that, because
physicians must prescribe the drugs in question, patient pursuit of these
prescription drugs is irrelevant. However, patients who pursue and request
particular prescription drugs may be able to encourage or induce a physician to
prescribe drugs that he or she might not have in the absence of such
encouragement.

(A) The clinical efficacy of certain over-the-counter medications does not address
the public health advocates’ concern regarding patient pursuit of inappropriate
prescription drugs.

(B) The public health advocates’ concern does not rely on every possible
consumer to see the advertisements for prescription medications. It is enough
that some consumers see the advertisements.

(C) This answer choice states the obvious possibility that physicians may also
see the advertisements for prescription drugs directed toward consumers. This is
irrelevant to the concern expressed by the public health advocates.

(D) CORRECT. This answer choice directly addresses the public health
advocates’ concern by establishing that physicians are not susceptible to patient
pressure in prescribing inappropriate drugs. As a result, drugs will be prescribed
according to the objective clinical judgment of the prescribing physician,
mitigating the danger of inappropriate use.

(E) That certain prescription medications are safe and effective treatments for
many conditions does not address the concern of inappropriate use expressed
by the public health advocates. Prescription drugs can be safe and effective
when used for certain conditions by various individuals and still be subject to
unhealthy use by other patients.

3.
This argument concerns a potential explanation for larger tips on the part of
restaurant patrons. The explanation provided is that customers are more
generous toward servers that leave their hand-written name on the bill due to a
greater degree of personal identification with the server, which encourages larger
tips. The correct answer will either support the fact that a hand-written name
strengthens personal identification, or that personal identification encourages
larger tips.

(A) The fact that the effect applies equally regardless of the method of payment
is not relevant to the conclusion.

(B) The argument does not address the size of the bill; rather, it addresses the
size of the tip. This choice is irrelevant.

(C) CORRECT. This answer choice provides further evidence that a hand-written name or signature generates a greater form of personalization and
emotional connection among recipients, leading to more donations.

(D) The impact of alcoholic beverages on tipping behavior is irrelevant.

(E) The location of the restaurants and leisure pursuits of the patrons are
irrelevant to the argument.

4.
The conclusion is that a company should wait until purchases of an old device
have begun to decline before announcing a new device. The basis for this claim
is that consumers stop buying the old device. We are asked to strengthen the
argument.

(A) The typical drop in the price of new technology does not influence whether a
company should wait until sales of an old technology begin to decline before
introducing a new one.

(B) CORRECT. This choice states that media outlets such as television and
magazines often report on the planned introduction of new devices while sales of
old devices are still strong. The argument requires that consumers "hear about
the new device"; stories in the media provide a means for consumers to do so.

(C) If many consumers are unable to determine the superiority of new
technology, then they might be less swayed to wait for a new, recently
announced device than otherwise. As a result, this claim may be seen to weaken
the analyst's assertion.

(D) The number of technology purchases per year does not directly relate to this
argument. The argument is about waiting until the consumer demand declines
before announcing a new technology. However frequently consumers typically
purchase technology, some will be ready to buy the old device when news of the
upcoming device gets out -- and according to the argument, this news will cause
some of those consumers to wait.

(E) The passage makes no mention of whether the technologies belong to the
same company or different companies.

5.
The argument claims that federal incentives should be provided to encourage
energy efficiency. The argument also notes that companies are already working
in this direction and that this trend will ease the environmental and energy
pressures that currently trouble the world. Supporting this argument could involve
providing evidence of possible success for these efforts toward their goals.

(A) This choice is an irrelevant comparison. That Canadian companies are more
efficient has no bearing on efforts in the United States or the role of government
incentives.

(B) This choice does not strengthen the claim. Experts' claims are not the same
as reality. Furthermore, the choice does not say whether reducing energy use to
the 1995 level is a significant decrease, nor does it provide any information to
strengthen the link between government incentives and reduced energy use.

(C) CORRECT. This choice provides evidence that government incentives are
effective. Thus, this choice confirms an assumption that the conclusion is
feasible.

(D) This choice is an irrelevant distinction. It does not matter to the argument’s
conclusion if one of these issues is a greater problem than the other in the
present.

(E) The passage asserts that the United States should be at the forefront of an
emerging market for cleaner technologies; i.e., the market will be significant in
the future. The size of the market at present is irrelevant to the argument.

6.
The director concludes that the fee hike has helped to counteract the cut in state
funding. In other words, the director believes that increasing the late fees has led
to increased revenue from late fees. While the size of the fee itself is one
important factor, there are other factors that also have an effect on the amount of
revenue generated from late fees: the number of overdue books and the number
of days that books are overdue before they are returned. It’s very possible that
the fee increase would prompt more borrowers to return their books on time; this
would reduce the number of late fees being paid, reducing revenue from late
fees. Further, it’s possible that the fee increase would prompt more borrowers to
return their already overdue books sooner than they would otherwise. This would
reduce the average amount of each late fee, reducing revenue from late fees.
The argument explicitly states that there has been no decline in the number of
overdue books, but it says nothing about the number of days that books are
overdue before they are returned. A statement that rules out the possibility that
borrowers are returning their already overdue books sooner than they would
have if they were still being charged the original lower overdue fee would
strengthen the director’s claim.

(A) A decrease in the number of borrowed books has no bearing on the revenue
generated from late fees if the number of overdue books remains unchanged.
The question explicitly states that the number of overdue books has not changed.

(B) If anything, this statement weakens the argument. The costs incurred to
implement the new fees would cut into the revenue generated from these new
fees.

(C) CORRECT. This statement rules out the possibility that the library system is
losing revenue as a result of borrowers returning overdue books earlier than they
would otherwise.

(D) The argument has explicitly stated that the number of overdue books has not
changed. This is a stated premise that we must take as factual information,
regardless of the quality of the database being used to track such information.

(E) The elimination of other unrelated costs has no bearing on whether the library
system has successfully increased revenues through late fees.

7.
The conclusion is that a developer who wishes to make a large profit would be
wise to buy urban waterfront lots and erect residential buildings on them. The
basis for that claim is that people pay large sums for beach front homes. We are
asked to strengthen this argument.

(A) This choice states that people have more buying power today than in
previous centuries. This does not strengthen the claim that a developer will make
money on urban waterfront properties.

(B) CORRECT. This choice states that homeowners will be willing to spend large
sums of money on residential properties in traditionally industrial or commercial
districts. Since we know from the argument that urban waterfronts have
traditionally been industrial, this fact strengthens the claim that a developer can
make a profit on urban waterfront properties.

(C) This choice states that many urban waterfront lots are available for purchase.
This does not suggest, however, that a developer will be able to sell them after
he or she builds on them.

(D) This choice states that many coastal cities are giving tax breaks to
developers who rehabilitate the waterfront. But this does not suggest that anyone
will buy the developed properties.

(E) This choice states that properties in the interior of cities are more expensive
than those on the waterfront. Although waterfront properties are therefore
cheaper to acquire, this does not necessarily mean that a developer can make a
profit after buying such properties.

8.
The question asks for information that will support the conclusion that students
attending charter schools will, on average, perform better on assessments of
writing ability than students attending traditional public schools. The passage
specifies that charter schools differ from non-charter public schools in that
charter schools have more freedom to innovate and that they are held
accountable for meeting specific educational outcomes. One way to support the
conclusion is to demonstrate that one of the two differences cited between
charter and non-charter public schools is somehow tied to higher performance on
writing assessments.

(A) While the passage mentions that charter schools themselves are freed from
many regulations, no information is presented about any difference in emphasis
with respect to order and discipline between charter and non-charter public
schools. As such, it is impossible to tell whether this information would support
the conclusion in the question.

(B) This choice presents information only about those students who score at the
very highest level of the writing assessments. However, this presents no
information about the difference, on average, between all charter school students
and non-charter public school students. It is possible, for example, that while the
students who perform at the highest level on writing assessments are those who
attend charter schools, on average non-charter public school students perform
better.

(C) There is no necessary link between the amount of time spent teaching writing
and student performance on writing assessments. For example, a good teacher
who spends one hour teaching writing may have a more positive impact on
student performance than a poor teacher who spends three hours teaching
writing.

(D) CORRECT. The passage specifies that charter schools have more freedom
to pursue innovative educational ideas than non-charter public schools. It follows
that charter schools are allowed to experiment with their curricula to a greater
degree than non-charter public schools. This choice links this difference to higher
student achievement on assessments of writing ability.

(E) The number of students attending charter vs. non-charter schools has no
bearing on the conclusion. The conclusion focused on student performance on
average, thereby eliminating raw numbers of students as relevant to this
measure.

9.
League officials plan to reduce the number of flagrant fouls by implementing
mandatory suspensions for players who commit such fouls. This plan will work
only if the punishment serves to deter players from committing flagrant fouls.

(A) The cause of injuries has no bearing on whether suspensions will deter
players from committing flagrant fouls.

(B) While the referees’ effectiveness in recognizing and reporting flagrant fouls
will surely aid in the implementation of the new policy, this has no bearing on
whether the policy will deter players from committing flagrant fouls.

(C) The parents’ opinion has no bearing on whether the suspensions will deter
players from committing flagrant fouls.

(D) While we might conclude that the other, similar league has a low incidence of
flagrant fouls because it suspends players who commit such fouls, we have no
evidence to show that the suspensions actually deter players from committing
fouls. It is entirely possible that the other league has a low incidence of flagrant
fouls for other reasons. For example, maybe the players in the other league are
just inherently less aggressive.

(E) CORRECT. If players want to make the All-Star team, and if a record of
suspension precludes these players from being selected for the team, then
players are less likely to commit fouls that will lead to suspensions.

10.
The passage makes the premise that microwave ovens are not completely safe.
This is followed by a conclusion by the consumer advocates that microwave
ovens should not be accepted as standard appliances. Since there is nothing in
the passage that provides an explicit link between the safety of microwave ovens
and their acceptability as standard appliances, the consumer advocates’
conclusion is based on an assumption (i.e., an implied premise) that “an
appliance should be accepted as standard only if it is found to be completely
safe.” The most effective way to strengthen such a conclusion is to show that
such an assumption is indeed true.

(A) The strength of the consumer advocates’ argument hinges upon the link
between the level of safety of microwave ovens and the rationale for their
acceptance in the home. Any lack of joy in microwave cooking is not relevant to
the argument.

(B) Providing a specific example of how a person might be injured, even
seriously, by a microwave oven may provide emotional support for the consumer
advocates’ position, but does little to strengthen the argument logically: the
possibility of injury has already been stipulated as a premise.

(C) CORRECT. This choice best strengthens the argument by making explicit the
assumption upon which the consumer advocates’ argument was based.

(D) If no appliance is completely safe, then the consumer advocates’ argument is
absurb: no appliance is, or ever will be, acceptable as “standard” in a modern
kitchen. This choice weakens the conclusion.

(E) The relative energy efficiency of gas vs. microwave cooking is not relevant to
this argument.

Please feel free to post particular question doubts, and I will be happy to clarify as much as I can.
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Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 03:18
Expert's post
Capricorn369 wrote:
My answers are listed below. I took 24 min for all of them.
C D C E C C B D E B.
I got 2 of them wrong. One wrong answer is acceptable but other one is not.
Also, we must discuss question 4 because i'm not happy with the explanation floating around for that one.

Cheers!

Please let me know which OA do you find debatable?
BTW All questions in this set are taken from MGMAT
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Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 03:41
Expert's post
I got 4 wrong :

The level is 700 800 how did you say ??

My errors on 6 and 7 OK, but 8 and 9 are silly

In general MGMAT is more difficult than the exam ??
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Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 03:59
Expert's post
First, I only mentioned the level of difficulty, because I anticipated that a lot of people would ask that question. There should be ABSOLUTELY nothing called level of difficulty, and you should not be bothered about it even if there is.
Second, I have taken 3 MGMAT CATs and 3 GMATPreps
I think GMATPrep quant is not harder than that of MGMAT albeit a bit trickier.
But GMATPrep Verbal is definitely a notch on the higher side.
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Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 12:33
souvik101990 wrote:
Capricorn369 wrote:
My answers are listed below. I took 24 min for all of them.
C D C E C C B D E B.
I got 2 of them wrong. One wrong answer is acceptable but other one is not.
Also, we must discuss question 4 because i'm not happy with the explanation floating around for that one.

Cheers!

Please let me know which OA do you find debatable?
BTW All questions in this set are taken from MGMAT

I would like to discuss question number 4.
I'm not satisfied with the given OA/OE. Can someone illustrate?

Cheers!
_________________

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Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 12:42
Expert's post
Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline.

Which of the following, if true, would best support the analyst’s main assertion?

• New technology often becomes less expensive after an initial surge in sales. irrilevant

• Media outlets, such as television programs and magazines, often report on the planned introduction of new correct
devices while the sales of old devices are still strong.

• Many consumers are unable to determine whether new technology is superior to current technology. we care about the sales not technology

• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases. irrilevant

• Consumers tend to be loyal to technology companies whose products they enjoy using. loyal is not the point

is not good to announce new devices and at the same time sell the old ones, because the latter fall and all customers go to the new devices BUT is media magazine and so on report that new devices are annonce and at the same time the old devices are still sold.
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Re: GMATCLUB VERBAL ATTACK [#permalink]

### Show Tags

18 Sep 2012, 13:12
Expert's post
Capricorn369 wrote:
souvik101990 wrote:
Capricorn369 wrote:
My answers are listed below. I took 24 min for all of them.
C D C E C C B D E B.
I got 2 of them wrong. One wrong answer is acceptable but other one is not.
Also, we must discuss question 4 because i'm not happy with the explanation floating around for that one.

Cheers!

Please let me know which OA do you find debatable?
BTW All questions in this set are taken from MGMAT

I would like to discuss question number 4.
I'm not satisfied with the given OA/OE. Can someone illustrate?
Cheers!

4. Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline. Which of the following, if true, would best support the analyst’s main assertion?
• New technology often becomes less expensive after an initial surge in sales.
• Media outlets, such as television programs and magazines, often report on the planned introduction of new
devices while the sales of old devices are still strong.
• Many consumers are unable to determine whether new technology is superior to current technology.
• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases.
• Consumers tend to be loyal to technology companies whose products they enjoy using.

Conclusion of this argument
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline

A. This has almost nothing to do with the argument as this is talking about the sales after the announcement and the release of the new device.
B. This seems to strengthen because if, according to the author, the company does not announce the new device, the media will have nothing to report and sales of the old device will remain strong.
C. As long as their indecisiveness doesn't hamper their buying tendencies, do we need to care?
D.This means almost everything. It means some people may buy the device while some people wont. In any case, we can draw much from this statement.
E. Loyalty can be proved both by purchasing new stuffs from the same company or by not purchasing anything at all(from that or any other company).

Hope this helps
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Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 13:36
carcass wrote:
Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline.

Which of the following, if true, would best support the analyst’s main assertion?

• New technology often becomes less expensive after an initial surge in sales. irrilevant

• Media outlets, such as television programs and magazines, often report on the planned introduction of new correct
devices while the sales of old devices are still strong.

• Many consumers are unable to determine whether new technology is superior to current technology. we care about the sales not technology

• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases. irrilevant

• Consumers tend to be loyal to technology companies whose products they enjoy using. loyal is not the point

is not good to announce new devices and at the same time sell the old ones, because the latter fall and all customers go to the new devices BUT is media magazine and so on report that new devices are annonce and at the same time the old devices are still sold.

While announcing new technology -> wait until purchases of the old device have begun to decline -> announce the upcoming sale of a new device.

How the aforesaid sequence is aligned with answer option 2, I don't see any correlation.
_________________

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MBA Section Director
Joined: 19 Mar 2012
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Followers: 1262

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Re: GMATCLUB VERBAL ATTACK [#permalink]

### Show Tags

18 Sep 2012, 13:42
Expert's post
Capricorn369 wrote:
carcass wrote:
Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline.

Which of the following, if true, would best support the analyst’s main assertion?

• New technology often becomes less expensive after an initial surge in sales. irrilevant

• Media outlets, such as television programs and magazines, often report on the planned introduction of new correct
devices while the sales of old devices are still strong.

• Many consumers are unable to determine whether new technology is superior to current technology. we care about the sales not technology

• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases. irrilevant

• Consumers tend to be loyal to technology companies whose products they enjoy using. loyal is not the point

is not good to announce new devices and at the same time sell the old ones, because the latter fall and all customers go to the new devices BUT is media magazine and so on report that new devices are annonce and at the same time the old devices are still sold.

While announcing new technology -> wait until purchases of the old device have begun to decline -> announce the upcoming sale of a new device.

How the aforesaid sequence is aligned with answer option 2, I don't see any correlation.

http://gmatclub.com/forum/gmatclub-verbal-attack-139074.html#p1122812
Note that the media CAN ONLY REPORT if the company itself "plans" it
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Re: GMATCLUB VERBAL ATTACK [#permalink]

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18 Sep 2012, 14:54
Expert's post
Capricorn369 wrote:
carcass wrote:
Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline.

Which of the following, if true, would best support the analyst’s main assertion?

• New technology often becomes less expensive after an initial surge in sales. irrilevant

• Media outlets, such as television programs and magazines, often report on the planned introduction of new correct
devices while the sales of old devices are still strong.

• Many consumers are unable to determine whether new technology is superior to current technology. we care about the sales not technology

• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases. irrilevant

• Consumers tend to be loyal to technology companies whose products they enjoy using. loyal is not the point

is not good to announce new devices and at the same time sell the old ones, because the latter fall and all customers go to the new devices BUT is media magazine and so on report that new devices are annonce and at the same time the old devices are still sold.

While announcing new technology -> wait until purchases of the old device have begun to decline -> announce the upcoming sale of a new device.

How the aforesaid sequence is aligned with answer option 2, I don't see any correlation.

Sorry

If the media announce a new plan this come from the company (apple says: we have the new iPhone) then if this is possible, and is possible to have storg sales of old devices the argument is weaken. The plan is not feasible, B say that is feasible because we have reports about this, due to something that the companies say

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Re: GMATCLUB VERBAL ATTACK   [#permalink] 18 Sep 2012, 14:54

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#### Applications of Integration Model Question Paper

12th Standard EM

Reg.No. :
•
•
•
•
•
•

Maths

Time : 01:00:00 Hrs
Total Marks : 45
5 x 1 = 5
1. The value of $\int _{ 0 }^{ \frac { \pi }{ 6 } }{ { cos }^{ 3 }3xdx }$

(a)

$\frac{2}{3}$

(b)

$\frac{2}{9}$

(c)

$\frac{1}{9}$

(d)

$\frac{1}{3}$

2. If f(x)$f(x)=\int _{ 1 }^{ x }{ \frac { { e }^{ { sin }^{ u } } }{ u } } du,x>1\quad and\quad \int _{ 1 }^{ 3 }{ \frac { { e }^{ { sinx }^{ 2 } } }{ x } } dx=\frac { 1 }{ 2 } [f(a)-f(1)]$, then one of the possible value of a is

(a)

3

(b)

6

(c)

9

(d)

5

3. The value of $\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ { sin }^{ 2 }xcosxdx }$ is

(a)

$\frac{3}{2}$

(b)

$\frac{1}{2}$

(c)

0

(d)

$\frac{2}{3}$

4. The area enclosed by the curve y = $\frac { { x }^{ 2 } }{ 2 }$ , the x - axis and the lines x = 1, x = 3 is

(a)

4

(b)

8$\frac23$

(c)

13

(d)

4$\frac{1}{3}$

5. The area enclosed by the curve y2 = 4x, the x-axis and its latus rectum is ............ sq.units.

(a)

$\frac23$

(b)

$\frac43$

(c)

$\frac83$

(d)

$\frac{16}{3}$

6. 2 x 2 = 4
7. The area of the region bounded by the graph of y = sin x and y = cos x between x = 0 and x = $\frac { \pi }{ 4 }$
(1) $\int _{ 0 }^{ \frac { \pi }{ 4 } }{ (cos \ x-sin \ x) } dx$
(2) ${ \left[ sinx+cosx \right] }_{ 0 }^{ \frac { \pi }{ 4 } }$
(3) $\int _{ 0 }^{ \frac { \pi }{ 4 } }{ (sinx-cosx) } dx$
(4) $\sqrt { 2 } -1$

8. $\int _{ a }^{ b }{ f(x) } dx=$
(1) $\int _{ a }^{ b }{ f(y) } dy$
(2) $-\int _{ a }^{ b }{ f(x) } dx$
(3) $\int _{ a }^{ b }{ f(a+b-x) } dx$
(4) $\int _{ 0 }^{ a }{ f(a-x) } dx$

9. 3 x 2 = 6
10. Evaluate:  $\int ^{\frac{\pi}{2}}_{\frac{\pi}{2}}$x cox x dx.

11. Evaluate the following definite integrals:
$\int _{ 3 }^{ 4 }{ \frac { dx }{ { x }^{ 2 }-4 } }$

12. Find the area of the region enclosed by the curve y = $\sqrt x$ + 1, the axis of x and the lines x=0, x=4.

13. 5 x 3 = 15
14. Evaluate $\int _{ 1 }^{ 2 }{ \frac { x }{ (x+1)(x+2) } dx }$

15. Evaluate the following definite integrals:
$\int _{ -1 }^{ 1 }{ \frac { dx }{ { x }^{ 2 }+2x+5 } }$

16. Evaluate $\int _{ 0 }^{ \infty }{ \frac { { x }^{ n } }{ { x }^{ x } } } dx$, where n is positive integer $\ge$2

17. Find, by integration, the volume of the solid generated by revolving about y-axis the region bounded between the curve y=$\frac{3}{4} \sqrt {x^2 -16}, x\ge4$the y-axis, and the lines y =1 and y = 6.

18. Evaluate $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x }{ 9+{ cos }^{ 2 } } dx }$

19. 3 x 5 = 15
20. Show that $\int ^\frac{\pi}{2}_0$ $\frac {dx}{4+5 sin x}$ = $\frac {1}{3}$ log2

21. Show that $\int ^{1}_{0} (tan ^{-1} x + tan ^{-1}(1-x))$ dx = $\frac {\pi}{2}$ - loge

22. Show that the area under the curve y = sin x and y = sin 2x between x = 0 and x = $\frac { \pi }{ 3 }$ and x axis are as 2:3

format: plain


text:
# zone mechanical command

Syntax

zone mechanical keyword

Primary keywords:

Sets parameters for a static mechanical analysis, that are specific to zones. The following keywords apply:

active b

Sets mechanical calculation off/on (default is on). The mechanical calculation may be turned off for a thermal-only calculation or a fluid flow-only calculation. Note that in general it is preferable to set mechanical calculations off for the entire model with the model mechanical active command.

damping keyword <range>

Select the damping type for the static, mechanical process (the default damping is local).

combined <f >

combined local damping (default is 0.8).

local <f ><alternate>

local damping (default is 0.8). If the alternate keyword is specified, an experimental alternate implementation of local damping is used that produces less sensitivity to small changes in the model.

energy keyword

allows elastic strain energy and dissipated plastic energy to be calculated (see Energy Calculation in FLAC3D).

active b

Turns the calculations off/on in the stress-strain loop

clear <range>

will set the four zone energy values in every zone back to zero. The zone mechanical active command does not clear these values. This allows you to stop accumulating plastic work over any interval you wish, and resume accumulating at any time from where it left off.

list

shows a summary of current zone mechanical settings in the console.


text:
# $11.99 Estes Viking Bulk Pack-ONE BUILD ### Help Support The Rocketry Forum: #### DMehalko ##### Well-Known Member Hobby Lobby clearance continues to be great,$12 Viking box for 12 Vikings!

Anyone else get one? Who’s up for building one rocket out of this? Must use all body tubes and all nose cones.

#### Attachments

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#### Attachments

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#### Cape Byron

##### The BAR formerly known as Skippy-2
TRF Supporter
$12 for 12 kits! Stuff like this is hard for us Aussies to see on the forum. Lets see... for$12 I could buy... maybe a couple of BT-20 nose cones.

#### SharkWhisperer

##### Well-Known Member
Wow, that is dirt cheap if still available. Going to look right now...

Nope, 2 hours after first post and I can't find it anywhere online at Hobby Lobby...

Good snatch!

Last edited:

#### GlenP

##### Well-Known Member
Could build something with several pods, to use up tubes and cones, like a Trident or Astron Explorer, for example. Will be interesting to see what you come up with. Are you restricting your build to use only parts included in the 12 kits, or will you take the liberty to add anything, like larger fins, if needed?

#### DMehalko

##### Well-Known Member
$12 for 12 kits! Stuff like this is hard for us Aussies to see on the forum. Lets see... for$12 I could buy... maybe a couple of BT-20 nose cones.
haha this stuff isn’t normally this cheap, our hobby lobby’s are clearance crazy right now for Estes stuff

Wow, that is dirt cheap if still available. Going to look right now...

Nope, 2 hours after first post and I can't find it anywhere online at Hobby Lobby...

Good snatch!
I know there were several bulk Boxes there when I got this, should of bought them all up but now they are gone, I know a couple other club members found some too however

Could build something with several pods, to use up tubes and cones, like a Trident or Astron Explorer, for example. Will be interesting to see what you come up with. Are you restricting your build to use only parts included in the 12 kits, or will you take the liberty to add anything, like larger fins, if needed?
yep exactly! Getting concerned about stability and weight haha. And only using what’s in the box for fins (60 of them ), so far I’m 12 fins in, doubt I’ll be able to use them all. The ’all the tubes and all the cones‘ is already a tough one.

#### GlenP

##### Well-Known Member
If you can build it light enough a Super C5-3 might be able to handle it, otherwise you can cluster 18mm motors. But if you allow yourself to add a 24 mm engine mount... should be a fun project, thanks for sharing it here!

Can also extend the fins with tube fins cut from the body tubes, like the Super Neon XL... I will try to refrain from more ideas to see what you come up with.

#### DMehalko

##### Well-Known Member
If you can build it light enough a Super C5-3 might be able to handle it, otherwise you can cluster 18mm motors. But if you allow yourself to add a 24 mm engine mount... should be a fun project, thanks for sharing it here!

Can also extend the fins with tube fins cut from the body tubes, like the Super Neon XL... I will try to refrain from more ideas to see what you come up with.
Ha right! Have that in the works, ill share one more picture then ill get a completed build and hopefully a 3 engine cluster flight video shortly

#### Attachments

• 59.7 KB Views: 28

#### OC-Patrick

##### Well-Known Member
went to a couple of Hobby Lobby stores here, didn't find the Viking bulk packs - bummer!

#### nosecone

##### Well-Known Member
Great idea. I'm going to check out my local HobbLobb

TRF Supporter

#### mo2872

##### Well-Known Member
Scored a bulk pack at my local HL. Donating it to the club for give-aways. Thanks for the heads-up!

#### Attachments

• 135.5 KB Views: 9

#### Woody's Workshop

##### Well-Known Member
TRF Supporter
I feel like Hobby Lobby ripped me off, now!
A while back I ordered online a 12 pack of vikings for $29, thought it was a great deal. But would have thought they put them on sale for$12? Certainly not I.
I'll check online, but I doubt any is left. If so, I'll order another one.
Kids in the apartment complex will love them.
EDIT: No Vikings, not even a single....

#### nosecone

##### Well-Known Member
I just went to my Hobby Lobby and the rocket section is kind of cleared out. I am sad now.

#### mo2872

##### Well-Known Member
I went to the local chain hobby store, and they had the bulk pack for $89, and a single Viking for$13!!!! Yikes!!!!!

#### SharkWhisperer

##### Well-Known Member
US$33 on Amazon just now. More at the usual online rocket shops.$85 from Estes...

#### DMehalko

$30 still isn’t too bad for 12 rocket kits! Who else is up for the fun challenge? Getting there, planning to paint tomorrow and fly Saturday . Going to put together a fun time lapse video on my new YouTube channel ‘Almost Space’ #### Attachments • 90.9 KB Views: 44 #### SharkWhisperer ##### Well-Known Member$30 still isn’t too bad for 12 rocket kits! Who else is up for the fun challenge?

Getting there, planning to paint tomorrow and fly Saturday . Going to put together a fun time lapse video on my new YouTube channel ‘Almost Space’
Bwaaah, that build is ridiculously entertaining--almost as much as your maiden flight video will be!! Can't wait.

How many motors and what impulse are you planning to use?

Your CP/CG relationship is the stuff of rocketry nightmares! Wear kevlar and eye protection, please. But this will definitely be interesting!

#### SecondRow

##### Well-Known Member
How many fins, so far? I was thinking, you don’t need to get all 60 on to be a true 12-Viking rocket. I believe the instructions allow you to choose any configuration between 3 to 5 fins, right? Technically, it’ll be a Dodeca-Viking with a minimum of 36 fins. At least in my mind.

##### Well-Known Member
TRF Supporter
My bulk pack showed up. Not going to bash them all together; but that looks fun. Going to let the kid build a few and two will be merged into a mini D-Region Tomahawk.

#### DMehalko

##### Well-Known Member
Bwaaah, that build is ridiculously entertaining--almost as much as your maiden flight video will be!! Can't wait.

How many motors and what impulse are you planning to use?

Your CP/CG relationship is the stuff of rocketry nightmares! Wear kevlar and eye protection, please. But this will definitely be interesting!
Hahaha, ya going to be interesting! planning 3x C6-3’s

How many fins, so far? I was thinking, you don’t need to get all 60 on to be a true 12-Viking rocket. I believe the instructions allow you to choose any configuration between 3 to 5 fins, right? Technically, it’ll be a Dodeca-Viking with a minimum of 36 fins. At least in my mind.
I got 16 fins on it, I think that’s going to be my stop, the challenge was to use all 102” of bt20 tube and all 12 nose cones which i did!

My bulk pack showed up. Not going to bash them all together; but that looks fun. Going to let the kid build a few and two will be merged into a mini D-Region Tomahawk.

ahh common, I want to see some contenders/others approach to this challenge lol

#### mo2872

##### Well-Known Member
Straight as an arrow on the up!!! Nice!

#### GlenP

##### Well-Known Member
That thing went to Valhalla and back! Great job.

##### Well-Known Member
TRF Supporter
Really excellent video and flight! Great job! And, it looks damn good too!!

#### neil_w

##### Yum yum rockety goodness
TRF Supporter
Very well done, and great flight!


text:
How to get the area of the triangle embedded in the unit circle when it makes an inner reflection?

The problem is as follows:

The figure represents the unit circle which has a radius of one unit. Find the value of the angle $$\alpha$$ such that the largest edge of the cherry shaded region is equal to $$\sqrt{2+\sqrt{3}}$$.

The choices given in my book are as follows:

$$\begin{array}{ll} 1.&\frac{2\pi}{3}\\ 2.&\frac{5\pi}{6}\\ 3.&\frac{11\pi}{12}\\ 4.&\frac{3\pi}{4}\\ \end{array}$$

I'm not sure exactly how to solve this problem, but I belive that the given angle alpha is referred that begins on $$A$$ and ends in the other end from the vertex of the triangle which appears to be isosceles.

I think the approach here is that to get the value of alpha I must make a trigonometric equation and use the larger edge in terms of alpha and equate this with what I was given and this may give the desired result.

The distance from the $$\textrm{x-axis}$$ to any of the vertex of the base of the triangle with those parallel to $$\textrm{y-axis}$$ is the same, hence this is an isosceles triangle and this may help or ease the solution a bit.

Since those internal angles in the circle which make up the triangle are $$\frac{\alpha}{2}$$ because it is an iscribed angle, then I'm getting:

I'm naming the end point of the angle alpha as $$P$$:

Thus $$\angle OAP=90-\alpha/2$$ and the intersection of lines where is the second little square looking from the left would be point $$R$$.

Thus:

$$\angle ROP=180-\alpha$$

Therefore:

$$OR=1\cdot \cos (180-\alpha)$$

$$AO=1$$

Thus:

$$AR=1-\cos\alpha$$

$$AR\sec \left(90-\frac{\alpha}{2}\right)= \sqrt{2+\sqrt{3}}$$

From which I believe the equation to be solved would be as follows:

$$(1-\cos\alpha)\cdot \sec \left(90-\frac{\alpha}{2}\right)= \sqrt{2+\sqrt{3}}$$

Using the necessary algebra I'm getting this into:

$$\cos\alpha=0$$

$$2\cos^2\alpha-(6+3)\cos \alpha=0$$

$$\cos\alpha=\frac{6+\sqrt{3}}{2}$$

But from looking at these expressions none of these seem to help me much into the solution.

Was my strategy wrong or what?. Can someone help me here?. I honestly don't think I'm far off from the answer, so I need a helping hand which can guide me to the right path.

First notice that the longest side of the cherry triangle (the hypotenuse) is congruent to its reflection above the $$x$$-axis: the segment connecting the initial $$(1, 0)$$ and terminal $$(\cos \alpha, \sin \alpha)$$ points of the angle $$\alpha$$ in standard position. Let's call this length $$\ell$$. Then, Pythagoras give us $$\ell^2 = (1 - \cos \alpha)^2 + (\sin \alpha)^2 = 1 - 2\cos \alpha + \cos^2 \alpha + \sin^2 \alpha = 2(1 - \cos \alpha).$$ So we need to solve the equation $$2(1 - \cos \alpha) = 2 + \sqrt{3}$$ for $$\alpha$$, i.e. $$\cos \alpha = -\frac{\sqrt{3}}{2}.$$
The diagram suggest that the terminal point is above the $$x$$-axis (can we assume this?), in which case $$0 \leq \alpha \leq \pi$$. Then, there is a unique angle $$\alpha = \arccos \biggl(\! -\frac{\sqrt{3}\,}{2} \biggr) = \frac{5\pi}{6}.$$


text:
This post was also published on Future Processing - Technical Blog

I bet that all of us, developers, at least once started thinking about a domain model from designing data structures. This way of modelling applied to the complex domain almost always leads us to the solution that is not really effective in dealing with business cases. Moreover it is far from representing the real business domain - it represents a projection that is focused on our data store. The classical way of “producing” models for business domains treats events as a side effects of technical flows, not as a domain’s first class citizens. In the “event storming” domain modelling starts from events, which are assumed to be key points of business workflows. The rest of the domain is built to support events.

# TL;DR

1. Define events in the system
2. Define sources (commands, process managers) and actors
3. Group commands around aggregates
4. Implement…

Post-it, long piece of paper and people…

# Let’s play

Generally speaking “event storming” is about extracting domain from events which describe it. In most of the complex domains there are events that represent important changes in the state of our domain, simply begin with them. We’ll need the following things:

• Unlimited modelling space - sounds impossible, but in most cases very long piece of paper will be more than enough. White board is also OK, but it is hard to “serialize” it after the meeting.
• Post-its in various colours - one colour represents one class of objects.
• People who know the questions, and those who know the answers - in fact, in most cases, stakeholders will be assumed here, but the guy that is doing an actual work in the company may be useful too.
• A room without chairs - sitting = sleeping, it’s hard to go asleep during a meeting without chairs :). The key point here is to engage everyone into the work.

I’m assuming that there will be at least one person in the room who knows what event storming is, and this person will be the moderator. It’s a good practice for moderator to place the first event on the modelling space. Simply put one post-it with the event name, a chosen colour will represent events. The modelling space represented by a long piece of paper should have a direction which will represent the time, so we can arrange events chronologically.

But what event actually is? There is a “simple” definition:

Domain event is something that happened that domain experts care about.

Let business experts put events that are in their region of interest on the paper, and let them argue about how the business works (but don’t let them kill each other)! They should work out the clean description of the business flow. The value here is to clarify complex workflows by finding common points. If they are not approaching common point, they must have found the misconception in their business - it is an opportunity to improve. Or maybe they are simply talking about the same thing from completely different perspectives. If one expert is responsible for invoicing and another one for delivery - they can talk about the same thing, but in two separated subdomains, so that thing looks completely different for each of them.

When all events are in place we can go to the next phase.

# Reverse engineering

Starting from the events we want to get to the point in which we have all important structures clearly visible on the modelling space. When we will think about events that are happening all the time around us everything has a more or less obvious cause. Similarly, in the domain, nothing happens without cause. We need to find all causes for events.

Event can be triggered by a command, by time or even by another event - so basically every event has the source. Obviously, event may also have more than one source i.e.: AssessmentCompletedEvent may be triggered by time when Assessment’s end date expires or by user which manually completes it in the application. Our task is to discover sources of events. In this phase we need to put on the modelling space all commands, process managers and actors that are involved in generating events.

Command is a well-known pattern and even with a bunch of rules of thumb that comes from DDD there is no reason to define it again.

Process Manager is a simple creature that executes commands when event is raised, so if we need to execute command in reaction to event we need the Process Manager to do this work for us.

Actor is an external source of activity - users, external systems and even time (here are some controversies) may be treated as an actor.

The moment we have defined all sources for our events, we can group commands around aggregates changed by them. Basically that should be iterative process where we are deciding which command modifies which aggregate. From my perspective this might be the most difficult part of the modelling as designing good aggregate is always hard & tricky!

# Implement!

The process described above should generate something :) that theoretically should be easy to express as a code. We have domain aggregates, commands that operates on them and events that represents state changes in aggregates. Every artefact that we generate before can be easily represented by building block from DDD and match to CQRS/ES architecture. There is nothing better to do than implement this model.

# Is Event Storming good for my project?

From my point of view any domain can be modelled in this way.


text:
# zbMATH — the first resource for mathematics

Partial sums of biased random multiplicative functions. (English) Zbl 1414.11115
Summary: Let $$\mathcal{P}$$ be the set of the primes. We consider a class of random multiplicative functions $$f$$ supported on the squarefree integers, such that $$\{f(p) \}_{p \in \mathcal{P}}$$ form a sequence of $$\pm$$1 valued independent random variables with $$\mathbb{E} f(p) < 0$$, $$\text{for all } p \in \mathcal{P}$$. The function $$f$$ is called strongly biased (towards classical Möbius function), if $$\sum_{p \in \mathcal{P}} \frac{f(p)}{p} = - \infty$$ a.s., and it is weakly biased if $$\sum_{p \in \mathcal{P}} \frac{f(p)}{p}$$ converges a.s. Let $$M_f(x) : = \sum_{n \leq x} f(n)$$. We establish a number of necessary and sufficient conditions for $$M_f(x) = o(x^{1 - \alpha})$$ for some $$\alpha > 0$$, a.s., when $$f$$ is strongly or weakly biased, and prove that the Riemann Hypothesis holds if and only if $$M_{f_\alpha}(x) = o(x^{1 / 2 + \varepsilon})$$ for all $$\varepsilon > 0$$ a.s., for each $$\alpha > 0$$, where $$\{f_\alpha \}_\alpha$$ is a certain family of weakly biased random multiplicative functions.
##### MSC:
 11N37 Asymptotic results on arithmetic functions 11A25 Arithmetic functions; related numbers; inversion formulas 11K65 Arithmetic functions in probabilistic number theory
Full Text:
##### References:
 [1] Apostol, T. M., Introduction to analytic number theory, Undergrad. Texts Math., (1976), Springer-Verlag New York · Zbl 0335.10001 [2] Basquin, J., Sommes friables de fonctions multiplicatives aléatoires, Acta Arith., 152, 243-266, (2012) · Zbl 1304.11103 [3] Bradley, R. C., Every “lower psi-mixing“ Markov chain is “interlaced rho-mixing”, Stochastic Process. Appl., 72, 221-239, (1997) · Zbl 0948.60064 [4] Bradley, R. C., Basic properties of strong mixing conditions. A survey and some open questions, Probab. Surv., 2, 107-144, (2005), update of, and a supplement to, the 1986 original · Zbl 1189.60077 [5] Bryc, W.; Smoleński, W., Moment conditions for almost sure convergence of weakly correlated random variables, Proc. Amer. Math. Soc., 119, 629-635, (1993) · Zbl 0785.60018 [6] Carlson, F., Contributions à la théorie des séries de Dirichlet. III, Ark. Mat. Astr. Fys., 23A, 19, (1933) · JFM 48.0338.02 [7] Chatterjee, S.; Soundararajan, K., Random multiplicative functions in short intervals, Int. Math. Res. Not. IMRN, 479-492, (2012) · Zbl 1248.11056 [8] Chow, Y. S.; Teicher, H., Probability theory: independence, interchangeability, martingales, Springer Texts Statist., (1997), Springer-Verlag New York · Zbl 0891.60002 [9] Conway, J. B., Functions of one complex variable, Grad. Texts in Math., vol. 11, (1978), Springer-Verlag New York [10] Erdős, P., Some unsolved problems, Magyar Tud. Akad. Mat. Kutató Int. Közl., 6, 221-254, (1961) · Zbl 0100.02001 [11] Granville, A.; Soundararajan, K., Pretentious multiplicative functions and an inequality for the zeta-function, (Anatomy of Integers, CRM Proc. Lecture Notes, vol. 46, (2008), Amer. Math. Soc. Providence, RI), 191-197 · Zbl 1187.11032 [12] Häggström, O., Finite Markov chains and algorithmic applications, London Math. Soc. Stud. Texts, vol. 52, (2002), Cambridge University Press Cambridge · Zbl 0999.60001 [13] Halász, G., On random multiplicative functions, (Hubert Delange Colloquium, Orsay, 1982, Publ. Math. Orsay, vol. 83, (1983), Univ. Paris XI Orsay), 74-96 [14] Harper, A. J., Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function, Ann. Appl. Probab., 23, 584-616, (2013) · Zbl 1268.60075 [15] Harper, A. J., On the limit distributions of some sums of a random multiplicative function, J. Reine Angew. Math., 678, 95-124, (2013) · Zbl 1274.60067 [16] Hough, B., Summation of a random multiplicative function on numbers having few prime factors, Math. Proc. Cambridge Philos. Soc., 150, 193-214, (2011) · Zbl 1231.11117 [17] Koukoulopoulos, D., On multiplicative functions which are small on average, Geom. Funct. Anal., 23, 1569-1630, (2013) · Zbl 1335.11082 [18] Lau, Y.-K.; Tenenbaum, G.; Wu, J., On mean values of random multiplicative functions, Proc. Amer. Math. Soc., 141, 409-420, (2013) · Zbl 1294.11167 [19] Littlewood, J. E., Quelques conséquences de l’hypothèse que la fonction $$\zeta(s)$$ de Riemann n’a pas de zéros dans le demi-plan $$\mathfrak{R}(s) > \frac{1}{2}$$, C. R. Acad. Sci., 154, 263-266, (1912) · JFM 43.0329.02 [20] Meaney, C., Remarks on the Rademacher-menshov theorem, (CMA/AMSI Research Symposium “Asymptotic Geometric Analysis, Harmonic Analysis, and Related Topics”, Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 42, (2007), Austral. Nat. Univ. Canberra), 100-110 · Zbl 1213.42122 [21] Newman, D. J., Simple analytic proof of the prime number theorem, Amer. Math. Monthly, 87, 693-696, (1980) · Zbl 0444.10033 [22] Royden, H. L., Real analysis, (1988), Macmillan Publishing Company New York · Zbl 0704.26006 [23] Shiryaev, A. N., Probability, Grad. Texts in Math., vol. 95, (1996), Springer-Verlag New York, translated from the first (1980) Russian edition by R.P. Boas · Zbl 0909.01009 [24] Tenenbaum, G., Introduction to analytic and probabilistic number theory, Cambridge Stud. Adv. Math., vol. 46, (1995), Cambridge University Press Cambridge, translated from the second French edition (1995), by C.B. Thomas · Zbl 0788.11001 [25] Titchmarsh, E. C., The theory of the Riemann zeta-function, (1986), The Clarendon Press, Oxford University Press New York, edited and with a preface by D.R. Heath-Brown · Zbl 0601.10026 [26] Viana, M., Ergodic theory of interval exchange maps, Rev. Mat. Complut., 19, 7-100, (2006) · Zbl 1112.37003 [27] Wintner, A., Random factorizations and Riemann’s hypothesis, Duke Math. J., 11, 267-275, (1944) · Zbl 0060.10510
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# Greedy Graph Coloring in Python

Graph Coloring Algorithm (Greedy/ Welsh Powell)

I am trying to learn graphs, and I couldn't find a Python implementation of the Welsh Powell algorithm online, so I tried to write my own. Here are the steps.

1. Order the nodes in descending degree. (Most neighbors ... Least neighbors)
2. For each node, check the colors of neighbor nodes and mark them as unavailable.
3. Choose the lowest available color. (from [0, 1, 2, ..., len(graph) -1])

def color_nodes(graph):
# Order nodes in descending degree
nodes = sorted(list(graph.keys()), key=lambda x: len(graph[x]), reverse=True)
color_map = {}

for node in nodes:
available_colors = [True] * len(nodes)
for neighbor in graph[node]:
if neighbor in color_map:
color = color_map[neighbor]
available_colors[color] = False
for color, available in enumerate(available_colors):
if available:
color_map[node] = color
break

return color_map

if __name__ == '__main__':
graph = {
'a': list('bcd'),
'b': list('ac'),
'c': list('abdef'),
'd': list('ace'),
'e': list('cdf'),
'f': list('ce')
}
print(color_nodes(graph))
# {'c': 0, 'a': 1, 'd': 2, 'e': 1, 'b': 2, 'f': 2}

For the input graph, it produced the above result. Is the implementation correct?

## 1 Answer

PEP 8, the official Python style guide, says that indentation should be 4 spaces per level. Since whitespace is significant in Python, that is a pretty strong convention.

The implementation could be less verbose:

• sorted(list(graph.keys()), …) could be shortened to sorted(graph, …).
• Instead of defining available_colors as a list of booleans, you could define taken_colors as a set, ideally using a generator expression.
• The loop that assigns color_map[node] can be simplified down to next(generator expression with a condition).
def color_nodes(graph):
color_map = {}
# Consider nodes in descending degree
for node in sorted(graph, key=lambda x: len(graph[x]), reverse=True):
neighbor_colors = set(color_map.get(neigh) for neigh in graph[node])
color_map[node] = next(
color for color in range(len(graph)) if color not in neighbor_colors
)
return color_map

• Thank you for your solid feedback! Concise and elegant! I especially like the idea of using a set rather than an array of booleans. – Thawsitt Sep 8 '18 at 13:34


text:
2 added 788 characters in body

Your sequence $p_n (u,v)$ can be defined by $p_n (u,v) = vp_{n - 1} (u,v) - up_{n - 2} (u,v) + p_{n - 3} (u,v)$ with initial values $p_0 (u,v) = 1,p_1 (u,v) = v,p_2 (u,v) = v^2 - u.$ In my above remark I have overlooked a term in the fifth polynomial. This is now the same as the formula given by ARupinski.

Added later: Extend the sequence $p_n (u,v)$ to negative indices by $p_{ - 1} (u,v) = p_{ - 2} (u,v) = 0$ and $p_{ - n} (u,v) = p_{ n - 3} (v,u)$ for $n >2 .$ Define a new sequence of polynomials $r_n (u,v)$ by the same recurrence and initial values $r_{ - 1} (u,v) = 1,r_0 (u,v) = 0,r_1 (u,v) = - u.$ Extend it to negative values by $r_{ - n} (u,v) = r_{n - 2} (v,u).$

Let $A$ be the matrix with rows $(0,1,0),(0,0,1),(1, - u,v).$

Then $A^n$ is the matrix with the following rows: $\left( {p_{n - 3 + j} (u,v),r_{n - 2 + j} (u,v),p_{n - 2 + j} (u,v} \right)$ for $0 \le j \le 2.$

It seems that the sequence $r_n (u,v)$ or the sequence $r_{2n} (u,v)/(1 - uv)$ has analogous properties with respect to the zeroes. Is it also related to the group representation?

1

Your sequence $p_n (u,v)$ can be defined by $p_n (u,v) = vp_{n - 1} (u,v) - up_{n - 2} (u,v) + p_{n - 3} (u,v)$ with initial values $p_0 (u,v) = 1,p_1 (u,v) = v,p_2 (u,v) = v^2 - u.$ In my above remark I have overlooked a term in the fifth polynomial. This is now the same as the formula given by ARupinski.


text:
# FA2

(i) Let $X=C[0,1]\,$ with maximum metric $d(f,g)=\max\{|f(t)-g(t)|:t\in [0,1]\}\,$. Prove that $C[0,1]\,$ is separable.

(ii) Use (i) to prove that $X=C[0,1]\,$ is also separable with respect to the metric $\rho (f,g)=\left(\int _{0}^{1}|f(t)-g(t)|^{p}dt\right)^{{1/p}}\,$.

## (i)

Let $X=C[0,1]\,$ have the maximum metric $d(f,g)=\max\{|f(t)-g(t)|:t\in [0,1]\}\,$. Let $Y\,$ be the set of all polynomials with rational coefficients on $[0,1]\,$. Let $Z\,$ be the set of all real polynomials on $[0,1]\,$. Since $Z\,$ is dense in $X\,$, ${\bar {Z}}=X\,$.

$Y\,$ is countable. Proof: Let $Y_{n}\,$ be the set of all polynomials of degree $n\,$ with rational coefficients. Then $|P_{n}|={\mathbb {Q}}\times {\mathbb {Q}}\times ...\times {\mathbb {Q}}\,$, where there are $(n+1)\,$ ${\mathbb {Q}}\,$'s. Now define $Y=\bigcup _{{n=1}}^{\infty }P_{n}\,$. $Y\,$ is countable because it is a countable union of countable sets.

Let $f\in Z\,$ such that $f(t)=\sum _{{j=0}}^{n}a_{j}t^{j},a_{j}\in {\mathbb {R}}\,$. Let $\epsilon >0\,$. Since ${\bar {{\mathbb {Q}}}}={\mathbb {R}}\,$, there exists $q_{0},q_{1},q_{2},...,q_{n}\in {\mathbb {Q}}\,$ such that $|q_{i}-a_{i}|<{\frac {\epsilon }{n+1}}\,$ for $i=0,...,n\,$. Let $g(t)=\sum _{{i=0}}^{n}q_{i}t^{i}\in Y\,$.

Notice $d(g,f)=\max _{{t\in [0,1]}}|g(t)-f(t)|\,$

$=\max _{{t\in [0,1]}}|\sum _{{i=0}}^{n}(q_{i}-a_{i})t^{i}|\,$

$\leq \max _{{t\in [0,1]}}\sum _{{i=0}}^{n}|q_{i}-a_{i}|t^{i}\,$ by the triangle inequality.

$=\sum _{{i=0}}^{n}|q_{i}-a_{i}|\,$

$\leq {\frac {\epsilon }{n+1}}(n+1)=\epsilon \,$.

$g\in B(f,\epsilon )\,$, making $f\in {\bar {Y}},Z\subseteq {\bar {Y}}\,$. We have $X={\bar {Z}}\subseteq {\bar {{\bar {Y}}}}={\bar {Y}}\,$. Furthermore, ${\bar {Y}}\subseteq X\,$, so ${\bar {Y}}=X\,$. Since $Y\,$ is countable, $X\,$ is separable.

## (ii)

Let $X,Y,\,$ and $Z\,$ be defined as above with the metric $d(f,g)=\left(\int _{0}^{1}|f(t)-g(t)|^{p}dt\right)^{{1/p}}\,$. We still have ${\bar {Z}}=X\,$and $Y\,$ is countable. Let $f\in Z\,$ such that $f(t)=\sum _{{i=0}}^{n}a_{i}t^{i},a_{i}\in {\mathbb {R}}\,$. Let $\epsilon >0\,$. Since ${\bar {{\mathbb {Q}}}}\subseteq {\mathbb {R}}\,$, there exists $q_{0},q_{1},...,q_{n}\,$ such that $|q_{i}-a_{i}|<{\frac {\epsilon }{n+1}}\,$. Notice $g(t)=\sum _{{i=0}}^{n}q_{i}t^{i}\in Y\,$. From (i), we have $d(g,f)<\epsilon \,$. Now notice, $\rho (f,g)=\left(\int _{0}^{1}|f(t)-g(t)|^{p}dt\right)^{{1/p}}\,$. $\leq \left(\max _{{t\in [0,1]}}|f(t)-g(t)|^{p}\right)^{{1/p}}\,$ $=\max _{{t\in [0,1]}}|f(t)-g(t)|\,$ $=d(f,g)<\epsilon \,$

$g\in B_{\rho }(f,\epsilon )\,$, and by the same argument as in (i), $X\,$ is separable.