# The Rule of 72 and the GMAT

The rule of 72 is quite important in the GMAT for the fast estimation of an investment doubling time. I am proud to discover it was an Italian mathematician, Luca Pacioli (1445-1514), a Franciscan friar, to publish it for the first time in Summa de Arithmetica (Venice, 1494. Fol. 181, n. 44).

” A voler sapere ogni quantita a tanto per 100 l’anno, in quanti anni sarà tornata doppia tra utile e capitale, tieni per regola 72, a mente, il quale sempre partirai per l’interesse, e quello che ne viene, in tanti anni sarà raddoppiato. Esempio: Quando l’interesse è a 6 per 100 l’anno, dico che si parta 72 per 6; ne vien 12, e in 12 anni sarà raddoppiato il capitale.”

A few provisions shall be mentioned about the applicability of this rule:

1. The rule of 72 applies to one-time investments: It can’t be applied if money is invested on a regular basis, such as monthly or yearly.

2. The rule of 72 assumes a constant annual return: it’s not applicable to stocks, mutual funds, or bonds with inherent variable return.

3. The rule of 72 is an approximation: the rule gives the best results for interest rates between 4% and 18%; outside this range, other approximations, e.g. 70 or 69, work better (e.g., to the limit of continuous compounding, 69 gives the best result at any rate)

Beware of the power and the limits of the Rule of 72, especially when you sit for a GMAT test session! A good source of information is the Wikipedia’s page on the Rule of 72.

# Mind Maps for GMAT AWA

Here is some Mind Maps that I created while preparing for the GMAT AWA Essay. You are free to make whatever use you like of them. These maps are a collection of stuff that I found on many online resources. Please forgive me if I don’t mention the sources, but I did not keep any record.

# Practicing 1st Paragraphs for the GMAT AWA Essay

The last thing you wanna do at the AWA GMAT Essay is to get stuck in drafting the first paragraph of the essay. Don’t undervalue the Art of a Good Start. Failing at quickly drafting the first paragraph of the essay may indeed not only put at risk the AWA part of the GMAT, but also kill your morale for the rest of the test.

A good exercise that I recommend to everybody is to read all AWA sample topics that you can find on the official guide or on the GMAT website as downloadable pdf and identify the one you feel most unfamiliar with. The take a few hours to write the starting paragraph of each of them. You don’t need to complete the whole essay. Just write down the starter and then move on on the next one.

Here are the essay I decided to practice. In some cases, along with my version of the starting paragraph I also added a version that I found online.

The following appeared in the health section of a magazine on trends and lifestyles.

“People who use the artificial sweetener aspartame are better off consuming sugar, since aspartame can actually contribute to weight gain rather than weight loss. For example, high levels of aspartame have been shown to trigger a craving for food by depleting the brain of a chemical that registers satiety, or the sense of being full. Furthermore, studies suggest that sugars, if consumed after at least 45 minutes of continuous exercise, actually enhance the body’s ability to burn fat. Consequently, those who drink aspartame-sweetened juices after exercise will also lose this calorie-burning benefit. Thus it appears that people consuming aspartame rather than sugar are unlikely to achieve their dietary goals.”

The argument states that people willing to lose weight are better of sugar then the artificial sweetener aspartame, because aspartame can induce weight gain by depleting the brain of chemicals associated with the sensation of satiety and sugar helps the body to burn fat after physical exercise.

However, the author of the argument relies on weak evidence and unfounded assumptions; as a result, the argument is seriously flawed.

The following appeared in the editorial section of a local newspaper.

“In the first four years that Montoya has served as mayor of the city of San Perdito, the population has decreased and the unemployment rate has increased. Two businesses have closed for each new business that has opened. Under Varro, who served as mayor for four years before Montoya, the unemployment rate decreased and the population increased. Clearly, the residents of San Perdito would be best served if they voted Montoya out of office and reelected Varro.”

Discuss how well reasoned… etc.

The argument the local newspaper’s editorial recommends the citizens of San Perdito to reelect former mayor Varro and vote current mayor Montoya our of office. The recommendation is based on the fact that under Varro, the unemployment rased decreased and the population increased, while opposite effect have been obtained during the last mandate of Montoya.

The argument bases its conclusion on weak evidence and unfounded assumptions; therefore, the argument is unconvincing.

The following appeared as a part of an advertisement for Adams, who is seeking reelection as governor.

“Re-elect Adams, and you will be voting for proven leadership in improving the state’s economy. Over the past year alone, seventy percent of the state’s workers have had increases in their wages, five thousand new jobs have been created, and six corporations have located their headquarters here. Most of the respondents in a recent poll said they believed that the economy is likely to continue to improve if Adams is reelected. Adams’s opponent, Zebulon, would lead our state in the wrong direction, because Zebulon disagrees with many of Adams’s economic policies.”

Discuss how well reasoned… etc.

The argument, however, is based on weak evidence and unfounded assumptions; as a result, it is seriously flawed and unconvincing.

The following appeared as part of an article in the education section of a Waymarsh City newspaper.

“Throughout the last two decades, those who earned graduate degrees found it very difficult to get jobs teaching their academic specialties at the college level. Those with graduate degrees from Waymarsh University had an especially hard time finding such jobs. But better times are coming in the next decade for all academic job seekers, including those from Waymarsh. Demographic trends indicate that an increasing number of people will be reaching college age over the next ten years; consequently, we can expect that the job market will improve dramatically for people seeking college-level teaching positions in their fields.”

The argument in the educational section of a Waymarsh City newspaper states that the job market will dramatically improved for people seeking college-level teaching positions in their fields because of positive demographic trends in the next ten years. The argument, however, relies on unfounded assumptions and fails to demonstrate a causal relationship between the evidence and the conclusion; therefore, it us unconvincing.

The following is an excerpt from a memo written by the head of a governmental department.

“Neither stronger ethics regulations nor stronger enforcement mechanisms are necessary to ensure ethical behavior by companies doing business with this department. We already have a code of ethics that companies doing business with this department are urged to abide by, and virtually all of these companies have agreed to follow it. We also know that the code is relevant to the current business environment because it was approved within the last year, and in direct response to specific violations committed by companies with which we were then working—not in abstract anticipation of potential violations, as so many such codes are.”

Discuss how well reasoned… etc.

The memo written by the head of governmental department argues that neither stronger ethic nor stronger enforcement mechanisms are necessary to ensure ethical behaviour by company doing business with his department. The first reason given is that a code of ethic and agreed to by the companies doing business is already in force. The second reason is that the code is relevant to the current business environment. Yet, the argument fails to prove that the existing code of ethic is effective in preventing future violations, thus the argument is unconvincing and seriously flawed.

The following appeared as part of an article in the travel section of a newspaper.

“Over the past decade, the restaurant industry in the country of Spiessa has experienced unprecedented growth. This surge can be expected to continue in the coming years, fueled by recent social changes: personal incomes are rising, more leisure time is available, single-person households are more common, and people have a greater interest in gourmet food, as evidenced by a proliferation of publications on the subject.”

The article appeared within the travel section of a newspaper argues that a surge in the restaurant industry of Spiessa will continue in the coming years following a positive trend fuelled by recent social changes.

Even though the mentioned social changes, comprising increasing personal income, availability of more leisure time, higher frequency of single-person households and great interest in gourmet food, appear as reasonable factors in promoting the growth of restaurant industry, the argument relies on assumption for which there is no clear evidence. Hence, the argument is unconvincing and has several flaws.

The following appeared as part of an editorial in an industry newsletter.

“While trucking companies that deliver goods pay only a portion of highway maintenance costs and no property tax on the highways they use, railways spend billions per year maintaining and upgrading their facilities. The government should lower the railroad companies’ property taxes, since sending goods by rail is clearly a more appropriate mode of ground transportation than highway shipping. For one thing, trains consume only a third of the fuel a truck would use to carry the same load, making them a more cost-effective and environmentally sound mode of transport. Furthermore, since rail lines already exist, increases in rail traffic would not require building new lines at the expense of taxpaying citizens.”

The author of the editorial of an industry newsletter endorses a lowering of taxes for railroad companies’ property taxes, claiming that taxes should be reduced because rail is a more appropriate ground transportation that highway shipping which, in turn, is unfairly competing with railroads because trucking companies do not pay enough maintenance and property tax on the highway the use.

Even though the argument seems appealing at a first sight, the conclusion of the argument relies on unfounded assumptions based on weak evidence. Hence, the argument is seriously flawed and unconvincing.

The following appeared in a memo from the customer service division to the manager of Mammon Savings and Loan.

“We believe that improved customer service is the best way for us to differentiate ourselves from competitors and attract new customers. We can offer our customers better service by reducing waiting time in teller lines from an average of six minutes to an average of three. By opening for business at 8:30 instead of 9:00, and by remaining open for an additional hour beyond our current closing time, we will be better able to accommodate the busy schedules of our customers. These changes will enhance our bank’s image as the most customer-friendly bank in town and give us the edge over our competition.”

Discuss how well reasoned… etc.

The customers service division of Mammon Savings and Load claims that changes in the customer service will enhance the bank’s image and, consequently, give the bank an edge over its competitors. The argument assumes that reduced waiting time in teller lines and extended opening hours will meet the busy schedule of the customers which, in turn, will rate the bank as the most customer-friendly bank in town.

The conclusion of the argument, however, relies on assumptions for which there is no clear evidence. Hence, the argument is weak and has several flaws.

The following appeared as part of an article in a magazine on lifestyles.

“Two years ago, City L was listed 14th in an annual survey that ranks cities according to the quality of life that can be enjoyed by those living in them. This information will enable people who are moving to the state in which City L is located to confidently identify one place, at least, where schools are good, housing is affordable, people are friendly, the environment is safe, and the arts flourish.”

The argument claims that City L, which ranked 14th in a recent survey on cities’ quality of life, can be confidently identified as a place where schools are good, people are friendly, the environment is safe and arts flourish. Even though the city ranking might considered an indicator of an overall good quality of life, the argument does not provide enough evidence to support its conclusion. Moreover, it relies on assumptions for which there is no clear evidence. Hence, the argument is unconvincing and has several flaws.

Sample found online: The author concludes that City L has good schools, affordable housing, friendly people, flourishing arts and a safe environment. To support this claim the author cites an annual survey that ranks cities according to quality of life. Two years ago City L was listed 14th in this survey. As it stands this argument is unconvincing.

The following appeared in an article in a college departmental newsletter

“Professor Taylor of Jones University is promoting a model of foreign language instruction in which students receive ten weeks of intensive training, then go abroad to live with families for ten weeks. The superiority of the model, Professor Taylor contends, is proved by the results of a study in which foreign language tests given to students at 25 other colleges show that first-year foreign language students at Jones speak more fluently after only ten to twenty weeks in the program than do nine out of ten foreign language majors elsewhere at the time of their graduation.”

The argument supports a method of language teaching promoted by Professor Taylor of Jones University that, through a combination of intensive training and family stay abroad, purportedly gives students using this method an advantage compared with other foreign language majors elsewhere. To support its conclusion, the argument mentions the result of a study based on a foreign language test focused on speaking skills.

The argument is flawed because it relies on unsupported assumptions to reach a conclusion that is not supported by the evidence.

Sample found online: This newsletter article claims that Professor Taylor’s foreign-language program at Jones University is a model of foreign language instruction. This conclusion is based on a study in which foreign language tests were given to students at 25 other universities. The study shows that first-year language students at Jones speak more fluently after just 10 to 20 weeks in the program than do 90 percent of foreign-language majors at other colleges at graduation. Despite these impressive statistics, I am unconvinced by this argument for two reasons.

The following appeared as part of an article in the business section of a local newspaper.

“Motorcycle X has been manufactured in the United States for over 70 years. Although one foreign company has copied the motorcycle and is selling it for less, the company has failed to attract motorcycle X customers—some say because its product lacks the exceptionally loud noise made by motorcycle X. But there must be some other explanation. After all, foreign cars tend to be quieter than similar American-made cars, but they sell at least as well. Also, television advertisements for motorcycle X highlight its durability and sleek lines, not its noisiness, and the ads typically have voice-overs or rock music rather than engine-roar on the sound track.”

The article claims that a foreign company that copied the motorcycled manufactured by Motorcycle X failed to attract X’s customers for reasons that go beyond the lack of the exceptionally loud noise made by motorcycle X. The argument bases its conclusion on parallelism with the car industry and on the nature of television advertisements of motorcycle X. However, to reach its conclusion the argument relies on weak evidence and unfounded assumptions. Hence, the argument is seriously flawed and unconvincing.

Sample found online: The author rejects the claim that the loud engine noise of American-made Motorcycle X appeals to the manufacturer’s customers and explains why they are not attracted to quieter, foreign-made imitations. The author’s rejection is based on two reasons. First, the author points out that foreign cars tend to be quieter than similar American-made cars, yet they sell just as well. Secondly, the author claims that ads for Motorcycle X do not emphasize its engine noise; instead, the ads highlight its durability and sleek lines, and employ voice-overs of rock music rather than engine roar. In my view, these reasons do not establish that the quieter engines of the foreign imitations fail to account for their lack of appeal.

The following appeared as part of an article in a trade publication.

“Stronger laws are needed to protect new kinds of home-security systems from being copied and sold by imitators. With such protection, manufacturers will naturally invest in the development of new home-security products and production technologies. Without stronger laws, therefore, manufacturers will cut back on investment. From this will follow a corresponding decline not only in product quality and marketability, but also in production efficiency, and thus ultimately a loss of manufacturing jobs in the industry.”

The argument supports the introduction of stronger laws to protect new kinds of home-security systems from being copied and sold by imitators. The first reason given in support of the conclusion is that is that such protection will foster investment in technology development, thus keeping a high product quality and marketability and, as a result, a solid base of manufacturing jobs in this industry. Despite the arguments seems sound at a first sight, a deeper analysis shows that it relies on weak evidence to support its assumptions. Hence, the argument is flawed and unconvincing.

# GMAT Essays, third attempt: family-friendly program

The following appeared in a memorandum sent by a vice-president of the Nadir Company to the company’s human  resources department:

“Nadir does not need to adopt the costly ‘family-friendly’ programs that have been proposed, such as part-time work, work at home, and jobsharing. When these programs were made available at the Summit Company, the leader in its industry, only a small percentage of employees participated in them. Rather than adversely affecting our profitability by offering these programs, we should concentrate on offering extensive training that will enable employees to increase their productivity.”

Discuss how well reasoned . . . etc.

The memorandum of the vice-president of the Nadir Company argues that the Company should not implement ‘family-friendly’ programs because they are too expensive and are not successful. Instead, the Company should offer training courses to increase the productivity of the employees. The argument, however, relies on weak evidence and unsupported assumptions to reach this conclusion; therefore, it is seriously flawed.

First, the fact that only a small percentage of employees participated in a ‘family-friendly’ program at the Summit Company does not imply that such program was unsuccessful. Indeed, a predominant piece of information is missing to interpret this evidence, that is the percentage of employees with family over the total of employees. This evidence would support the conclusion of the argument only if the ratio between the number of employees with family that adopted the ‘family-friendly’ program and the total number of employees with family would be very low.

Besides the fact that the evidence does not prove that the program was unsuccessful at the Summit Company, the argument assumes that the same low success rate would be obtained at the Nadir Company without supporting this assumption. For example, it is possible that the Summit Company is based in a city where there are good services for employees with family, such as cheap and reliable kindergarten and schools offering afternoon service for working families. On the contrary, the Nadir Company might be based in a different city where services to support families with working parents are not as good as in Summit Company’s area. As a result, a ‘family-friendly’ program could be of much higher interest for Nadir’s employees than for Summit’s employees, resulting in a higher success rate.

Finally, even assuming that only a low fraction of Nadir’s employees would take advantage of part-time work, work at home and jobsharing, this does not mean that the program would result in a loss of profit for the company. It is indeed demonstrated that when parents are allowed to have flexible work conditions, they are more productive on the work that in absence of flexibility. Therefore, the costs of a ‘family-friendly’ program would be offset by the higher productivity of the employees.  It is not clear why training would make the employees with family more productive than they are now.

In conclusion, the argument fails to demonstrate that ‘family-friendly’ program constitute only a cost for the Company that does not result in an increased productivity of its employee. The argument would be more thorough by showing that training is more effective than flexibility on the work to increased the productivity of employees with family.

# GMAT Essays, second attempt: Apathy about Management

“The common notion that workers are generally apathetic about management issues is false, or at least outdated: a recently published survey indicates that 79 percent of the nearly 1,200 workers who responded to survey questionnaires expressed a high level of interest int he topics of corporate restructuring and redesign of benefits program”

Discuss how well reasoned …etc.

This argument challenges the general notion that workers are apathetic about management issues, by mentioning the results of a recent surveys that showed a high interest in certain management topics among the respondents. However, the evidence mentioned in the argument appears to be too specific to make any general statement. Moreover, the representativeness of the sample cannot be assessed based on what the argument states. Therefore, this alone does not allow to make a general claim applicable to all workers and comprehensive of all management issues.

A convincing argument would have to consider at least the following three elements: a statistically sound survey, a comprehensive list of questions on management topics and the segmentation of the surveyed sample.

First, a survey should consider not only the total number of respondents, but also the total number of non respondents. This information is not given in the argument, which explicitly mentioned that the results are based only on the workers who responded to the questionnaire; therefore, it is not possible to determine to what percentage of the total surveyed people corresponds the mentioned 79 percent figure. Without this element, it is only possible to conclude that those who answered are (not surprisingly) highly interested in the two topics above.

Second, the expressions of high interest concern only the topics of corporate restructuring and the redesign of benefits program. Both topics are clearly the subject of high interest for most of the workers: the former because it is directly related to major changes in the organization with the potential to affect one’s career, the latter because it has an impact on every employees benefits such as retirement plans, healthcare assurance etc. This does not prove that the workers are concerned about other management issues that involve the rest of the organization, for example those related to the efficient management of the company or to the effective communication of decisions and strategies throughout the organization’s hierarchy.

Finally, no information is given on the composition of the surveyed sample. Do the 1,200 surveyed workers who responded to the questionnaire belong to the higher or lower spheres of the respective companies? It is clear that those with more responsibilities – coordinators, managers and executives – most likely are very much concerned about management issues, while those with less responsibilities – line workers, clerks and support staff – are more likely to be apathetic towards the same issues. In the former case, the reported figures may be not surprising, while in the latter case a high percentage would constitute a really significant, perhaps unexpected and noteworthy, result.

In conclusion, despite the argument shows that within a rather unidentified part of the body of workforce (the respondent), and on certain specific topics (corporate restructuring and benefits program) there seems to be a high sensitivity, the evidence is not enough to falsify the general belief that most of the workers are generally apathetic about management issues.

# GMAT Practice Essays for the Analytical Writing Assessment

Practicing for the  Analytical Writing Assessment is probably one of the most time-consuming and demanding part of the GMAT test preparation. There are several reasons why studying for this section of the test risks to be very time consuming or ineffective, above all: the limited knowledge of GMAT’s expectations for this section, the difficulty of an easy assessment of one’s AWA level and the self-confidence in one’s own writing skills.

It has to be considered that the GMAT AWA essay is rated on a 1.0 to 6.0 scale according to certain standards, which lack of knowledge can seriously harm the possibility of obtaining a high mark even if the essay is, in principle, well-written. The GMAT AWA optimal essays characteristics can be summarized as follows: length comprised between 300 and 500 words, 5 paragraph structure (Introduction, three paragraphs and conclusion) and the presence all over the essay of the so called “structural words” (i.e., supporting examples, contrasts, Ying-Yang etc.). Knowing in details these few guidelines for the AWA section, and constantly practicing accordingly, is of outmost importance to obtain a high score.

While practicing for GMAT AWA is important to learn how to write an essay in a perfect GMAT Style, assessing one’s own initial AWA level and quantifying the progress during the preparation for the test, is very difficult due to the lack of an automatic rating system that can fully substitute the role of the human grader.

# GMAT Essays, first attempt: Olympic Foods

Learning Journal

This is my first GMAT essay that I am publishing on this website. My overall impression is that I didn’t score that well here, but I made a commitment to publish my essays online and I have to honor that commitment to keep motivation high. However poor the result is, what matters is what I learned through this first exercise:

• The optimal length of a GMAT essay seems to be about 600 words. Writing a text of this length in only 30 minutes doesn’t leave much time to hesitate on the content of each paragraph
• The first paragraph of an essay typically recalls the argument, in its essence, and introduces the view of the writer. I think it is very important to start right away drafting these few lines, to help the mind assimilate the essence of the topic, before thinking about “how well reasoned etc.” the argument is.
• The following 2-3 paragraphs shall be used to express the writer’s view. It is important to take a minute, before starting to write, to think exactly what is really important and strongest from the logical point of view, to be addressed. I found indeed that I came up when I was almost overtime with ideas that I could have given higher importance, and could have been easier to describe early on in the text.

My final realization is that much more exercise is needed to get a good performance within the time constrains. So I cut it short now, and go on with the next assignment 🙂

The following appeared as part of an annual report sent to stockholders by Olympic Foods, a processor of frozen foods: “Over time, the costs of processing go down because as organizations learn how to do things better, they become more efficient. In color film processing, for example, the cost of a 3-by-5-inch print fell from 50 cents for five-day service in 1970 to 20 cents for one-day service in 1984. The same principle applies to the processing of food. And since Olympic Foods will soon celebrate its 25th birthday, we can expect that our long experience will enable us to minimize costs and thus maximize profits.” Discuss how well reasoned . . . etc.

This argument presented into an Olympic Foods’ annual report states that the company will reduce its operating costs and increase its profits as it approaches its 25 th birthday, because  the long term experience in the field will allow increased efficiency. A comparison with what happened over almost 15 years in the film processing industry is brought as evidence to support this claim.

Although it is true that usually experience translates into optimization of processes and direct costs, there are several elements that could possibly lead to a different outcome, that is stable or reduced process efficiency.

For example, increase efficiency is often achieved by the implementation of new manufacturing equipment. This is particularly true for companies on the market since a long time, such as the 25-years old Olympic Food. In this case, the implementation of more modern manufacturing lines will most likely require a significant investment. As a result, profits in the years immediately following this investment might be lower for the need to pay-back the investment.

The argument is also supported by the analogy with the film processing industry, an industry that heavily dependent on the rapid appearance of new technologies to improve its manufacturing techniques. The appearance of these new technologies – for example the digital print replacing the traditional optical print – has played a major role in the cost reduction of the film processing. On the other side, the frozen food industry has not seen many breakthrough innovation in the last decades; therefore, unless a significantly new and more efficient way of processing frozen food is in sight, it is unlikely that the costs will drop down in a similar fashion.

Finally, the impressive drop in price of the film processing industry, might not be originated at all by increased process efficiency. It is indeed possible that the fierce competition has forced the company to lower the price by reducing the margins on the selling price of the prints. Considering most of the traditional photography processing companies are in deep financial troubles nowadays (e.g., Ilford, Kodak etc.) this could be a plausible scenario, and certainly not a desirable one for Olympic foods.

In conclusion, even though in some cases it is observed a price drop of certain services over time, this is not necessarily due to the improved process efficiency by experience, nor it is a pattern that can be considered of general validity across very different industrial fields. Additional and stronger evidence should be brought to the attention of the stockholders to support this statement.

# Enjoying practicing for GMAT AWA

Have you ever considered than practicing for the GMAT AWA can be funny and also a rewarding activity? I do believe it is possible to kill two birds with one stone by creating blog posts on interesting topics and writing them in a perfect GMAT style.

WordPress post editor already includes a word counter, so what you need to simulate as much as possible the GMAT writing experience, is to set up a timer (30 minutes).

From the next post on, I will try to proceed on these lines to improve my AWA skills, startup my personal blog, and learn something 😉