Author Archive

An Update…

Posted: September 22, 2010 by kdawgz in Uncategorized

After having disappeared for a month, I’m back!

I had the wonderful opportunity to go down to Mexico City from the last week of August into the first week of September on a missions trip with an organization known as Fusion. It was another amazing experience as this was my third time going down there. I won’t go into too much detail as it would take me a few days to account for everything that happened. But I’ll leave a few pictures on here.

Universidad Nacional Autónoma de México

Otomie Child

Meet Jessica

I learned a lot from this trip, both intellectually and personally about myself. If anything it was about not taking anything we have here in Canada for granted. We have so much. As such we have so much that we can give. Unfortunately, the thinking usually stops after we realize we have so much.

I also had the opportunity to lead English conversation groups with Mexican university students. It was very interesting to hear what they had to say about their own country and city. Mexican people are a lot friendlier and open to new experiences than the majority of North Americans. You can be walking along the street downtown and someone passing by would say “Bueno” (hello) and smile back at you. You’d probably never see this person again. Smiling is contagious nonetheless.

A bit of Mexican culture. It’s important to say hello to everyone when attending events; moreover, it is important to say goodbye to everyone when you leave. That’s not shouting “GOODBYE!”, it’s actually going up to each person individually and saying goodbye. Guys would give other guys a handshake and hug during a greeting or departing. Girls and guys would give other girls a right cheek to right cheek kiss and hug when greeting or departing. That’s something I liked about their culture. Very warm.

Anyway. I’ll leave it at that.

I think someone else needs to write an update on their life. **Cough** Relationship **Cough**

GMAT Questions #3

Posted: August 13, 2010 by kdawgz in GMAT

So here are some more essays for your enjoyment. Feel free to rip them up. These were written over the past week. I feel that some essays are stronger than others due to my knowledge in particular areas. It was also a bit distracting to write these at work at times since my colleagues are professional procrastinators. I’ve also started using outlines for the argument essays to aid in structure and general focus. These are the numbered assumptions or points after each given passage.

Essay #1

Analysis of an argument:

The following appeared in the health section of a magazine:

“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 exercise will 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.”

Discuss how well reasoned you find this argument. In your discussion be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative explanations or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate the conclusion.

The author concludes that aspartame does not reap the same health benefits as compared to its counterpart, sugar, as an artificial sweetener. The author’s line of argument is through the presentation of assumptions and general findings that direct attention towards aspartame’s ability to apparently cause insatiable hunger and the inability to enhance the body’s ability to burn fat as sugar would. This argument is unconvincing for several reasons.

First of all, the initial argument is based on the questionable assumption that aspartame has the negative tendency to contribute to weight gain instead of weight loss. However, the author fails to provide enough support for this claim. A simple point that would refute the argument is showing that the consumption of aspartame is not correlated to weight gain nor weight loss. This can be supported by the fact that aspartame is present in most chewing gum as an artificial sweetener. It is highly unlikely that individuals will become overtly obese through chewing one piece of gum on a daily basis; and consumed by all types of individuals of varying body mass. Therefore, more information is required to support the argument.

Secondly, the argument that aspartame negatively affects a chemical within the brain to enact satiety is based on the assumption that, after consuming aspartame, individuals will have an insatiable appetite and gain weight likewise. However, this assumption fails to support the argument because such a chemical imbalance within the brain might be easily thwarted by simply eating a cracker – aspartame will not empty an individual’s stomach. Moreover, in terms of chewing gum, it is a well known fact that chewing gum tricks the mind into thinking that it is constantly eating; which in turn, causes an individual to believe that they are, in fact, not hungry, and will likely not participate in heavy food bingeing. Therefore, once again, it is not likely that individuals will gain weight upon the consumption of aspartame.

Finally, the author fails to consider the negative aspects of sugar. For example, sugar is considered a simple carbohydrate, and will therefore be used very quickly by the body; which in turn, can cause an individual, upon consumption, to have a sudden spike in energy and lapse into a tired state soon after. Although, the consumption of sugar may actually enhance the body’s ability to metabolize after exercise, the author fails to provide the amount that must be consumed to provide optimal metabolic results. Any sugar that is not consumed by the human body is easily converted into body fat; and that, in the case of exercise, would actually be the opposite of the desired result. Because the author lacks an ample examination of the costs and benefits of both consuming aspartame and sugar, the argument is incomplete.

In conclusion, to convince me that the consumption of sugar is more beneficial than the consumption of aspartame, the author will have to provide evidence that aspartame causes an insatiable appetite in individuals which ultimately causes them to be overcome with the need to consume excessive amounts of food. Furthermore, the author would have to provide evidence that sugar does not have any impact on the human body after consumption. Without this additional evidence, I am not convinced that sugar should be substituted for aspartame for individuals who desire to achieve their dietary goals.

35 Minutes.

Essay #2:

Analysis of an argument:

The following appeared in a report presented for discussion at a meeting of the directors of a company that manufactures parts for heavy machinery.

“The failing revenues that the company is experiencing coincide with delays in manufacturing. These delays, in turn, are due in large part of poor planning in purchasing metals. Consider further that the manager of the department that handles purchasing of raw materials has an excellent background in general business, psychology, and sociology, but knows little about the properties of metals. The company should, therefore, move the purchasing manager to the sales department and bring in a scientist from the research division to be manager of the purchasing department.”

1: Assumption that technical expertise overrides management expertise.

2: Assumption poor planning is the result of poor technical expertise

3: Assumption that technical expertise will result in better management of the purchasing department and; therefore, increased revenues.

The author concludes that, in order to rectify the current delay in manufacturing as a result of poor purchase planning, the purchasing manager should be moved to the sales department and the scientist from the research division should become the manager of the purchasing department. The author’s line of reasoning is that the technical expertise of the scientist of the research department will hopefully garner better planning in the purchase of metals; and therefore, thwart the delays in manufacturing to rectify failing revenues. This argument is unconvincing for several reasons.

First of all, the author assumes that the technical expertise of the scientist is far greater than any management expertise in solving the planning involved for the purchase of metals. However, it is equally valid to assume that the poor planning in purchasing metals is not caused by management malpractice, but the lack of infrastructure for adequate communication of what materials are being requested by scientists in the research department to managers in the purchasing department. Therefore, the poor planning in the purchase of metals as a result of poor communication between divisions appears to be the more accurate argument.

Secondly, the author assumes that the manager’s lack of technical expertise is the reason for the poor planning in the purchase of metals – arguing that the manager does not know the properties of the metals. However, if information is properly communicated, a manager need not be knowledgeable in the properties of metals including their melting points, boiling points, hardness, colour, and texture. The name and an identification number from the supplier of these metals should be sufficient to make a purchase. Admittedly, if a research scientist possessed equal qualifications as the manager or vice-versa, this individual would be most suitable for the task of purchase management.

Finally, the author makes the questionable assumption that technical expertise equates to better management. Although the research scientist with technical expertise may be able to aid, to some degree, in the purchase of metals, the purchase manager is not only in charge of the purchase of such metals, but all raw materials acquired by the purchasing division. Therefore, the technical expertise of the research scientist is limited to a fraction of the responsibilities of the purchase manager. As such, it is inadequate to assume that the situation will be rectified through the replacement of the purchase manager with the research scientist.

In conclusion, in order for the argument to be more convincing, the author must present evidence that the purchase of raw materials is, in fact, highly technical in nature, and will not require the expertise of the manager in the areas of psychology, sociology, and general business to effectively carry out purchasing activities. Without the addition of such evidence, I remain unconvinced that a research scientist will be the panacea to the problem.

30 minutes.

Essay #3:

Analysis of an argument:

The following appeared as part of a promotional campaign to sell advertising space in the Daily Gazette to grocery stores in the Marston area.

“Advertising the reduced price of selected grocery items in the Daily Gazette will help increase your sales. Consider the results of a study conducted last month. Thirty sale items from a store in downtown Marston were advertised in the Gazette for four days. Each time one or more of the 30 items was purchased; clerks asked whether the shopper had read the ad. Twothirds of the 200 shoppers asked answered in the affirmative. Furthermore, more than half of the customers who answered in the affirmative spent over $100 at the store.”

  1. Assumption that customers will increase spending based on ads
  2. Assumption that advertising causes people to shop at the store; perhaps the 200 shoppers are the one solely reading the Daily Gazette to look for sale items in the store
  3. Assumption that ads will produce new customers and retain them specifically to the store

The author concludes that advertising the reduced price of selected grocery items in the Daily Gazette will help increase a store’s sales. The author’s line of reasoning is that shoppers are likely to shop at the store after seeing the ad in the Daily Gazette. The form of reasoning is questionable on many levels.

The first of all, the author’s argument is based on the questionable assumption that customers will increase spending based on ads. Although this may be true for some individuals, it is unlikely that customers would increase spending up to more than $100 if their household does not require that many groceries The argument would be seriously weakened if it was proven that the portion of shoppers that spent over $100 on groceries required to spend that much on groceries on a regular basis; and, therefore, it can be concluded that the ads did not directly affect consumer spending.

Secondly, the author’s argument is based on the assumption that advertising causes people to shop at the store. An equal and opposite assumption can be made that the customers who read the Daily Gazette solely read it for the purposes of seeking out advertisements in that store. The argument can be strengthened with an additional question to customers of whether or not they are a returning customer or a brand new customer based on seeing the ad. By using this method, the store will be able to identify the percentage of new customers who have been influenced by the ad and directly relate that data to increased sales – assuming that the number of returning customers remains constant.

Finally, the argument fails to consider the notion of customer retention. Admittedly, sales may increase upon new advertisements of popular products to incur increases in short-term sales; however, it is in the best interest of the store to advertise in such a manner that customers will feel comfortable in returning to the store on a regular basis. This would aid in increasing sales gradually over in the long-run. It becomes obvious that the author’s argument lacks any analysis in determining whether the advice is for short-term or long-term goals. The latter would be most profitable for the store.

In conclusion, to convince me that increasing the number of advertisements in the Daily Gazette will increase sales, the author must provide information including the ratio of new customers to regular customers, a comparison of the number of sales acquired during the period of advertising and two months after, and if possible, a count of the number of customers per week. Without this additional evidence, I am not convinced that increasing the advertisements in the Daily Gazette will increase sales.

30 minutes.

Essay #4:

Analysis of an argument:

The following appeared as part of a campaign to sell advertising time on a local radio station to local businesses.

“The Cumquat Café began advertising on our local radio station this year and was delighted to see its business increase by 10% over last year’s totals. Their success shows you how you can use radio advertising to make your business more profitable.”

  1. Assumption: Success is not based on new products? New services? Simply advertising?
  2. Assumption: Radio advertising is good for ALL types of products and services

The author concludes that Cumquat Café’s 10% increase in business is solely based on the abilities of radio advertising. The author’s line of reasoning is that since radio advertising has helped to increase Cumquat Café’s business by 10%, then radio advertising will increase revenues for all types of businesses. This argument is questionable on several levels.

First of all, the author makes the questionable assumption that since radio advertising increased business for one company, a café; it will help increase revenues for all businesses. However, the author neglects to recall that a business that advertises false products and services will most definitely not be successful. Therefore, it is likely that Cumquat Café has the products and services that meet the business niche in their area in order for the café to be successful. Finally, it is therefore also important for companies to have legitimate products and services before they decide to attempt radio advertising – or any form of advertising.

Secondly, the author makes the questionable assumption that radio advertising is the ideal form of advertising for all types of products and services. However, it is unlikely that radio advertising will be successful for such tangible products and services including equipment, real estate, insurance, and others that require visual cues such as name brands, logos, and designs to support their claims. For example, it will be almost impossible to determine the difference between two different cellular phones without being shown at least a picture of each.

Finally, the author fails to describe the products and services that Cumquat Café actually provides. For example, the sale of tickets through radio advertising is known to both be popular and successful; especially for celebrity events, citywide events, and movie tickets.  Therefore, it can be concluded that Cumquat Café’s success is simply because they deal with the sale of tickets to various events around their area. Since the author lacks a description of the products and services offered by Cumquat Café, it is almost impossible for those hopeful in radio advertising to ascertain if using this form of advertising will increase revenues.

In conclusion, in order to convince me that radio advertising will help increase revenues for all businesses, the author needs to provide more information on the products and services offered by Cumquat Café and a comparison of products and services and whether achieved gains in revenues through the use of radio advertising. Without this information, it will be impossible for me to determine whether radio advertising is profitable for all businesses.

30 Minutes.

Essay #5:

Analysis of an argument:

“Historically, most of this country’s engineers have come from our universities; recently, however, our university-age population has begun to shrink, and decreasing enrolments in our high schools clearly show that this drop in numbers will continue throughout the remainder of the decade. Consequently, our nation will soon be facing a shortage of trained engineers. If we are to remain economically competitive in the world marketplace, then, we must increase funding for education – and quickly.”

  1. Assumption that engineers create increase economic competency
  2. Assumption that people who do not enrol in universities cannot contribute to a country
  3. Assumption that increasing funding for education will help increase the competency of a country in the world market place

The author concludes that in order for a country to remain competitive in the world market place, funding for education must be increased. The author’s line of reasoning is that because of the lack of university students, namely engineering students, a country’s economy will shift toward a decline due to the lack of trained professionals: engineers. The author’s argument is questionable on several levels.

First of all, the author makes the questionable assumption that only engineers are able to contribute to the economic competency of a country. However, this is clearly not the case. Outside of engineering, there are many other professions and employment opportunities that contribute to a country’s economy including the procurement of natural resources, investment banking, farming, accounting firms, law firms, and the government itself. Moreover, individuals within a country contribute to the economy by simply being consumers; as such, they perpetuate the flow of goods and services throughout a country.

Secondly, the author makes the questionable assumption that individuals who do not enrol into universities cannot contribute to a country’s economic competency. Admittedly, it is true that university studies provide more choices and a greater ability for an individual to contribute to a country; however, that does not equate to those who do not attend university being unable to contribute. There are a vast number of individuals who do not have post-secondary education who are employed. Employment equates to economic contribution whether it is through the provision of a service, administration, or being a custodian; these occupations along with those fortunate enough who are employed upon post-secondary graduation, work together to promote the economic stability and maturity of a country.

Finally, the author fails to understand that it is not simply funding that will aid a country in increasing its ability to compete in the world marketplace. For example, if teacher salaries are increased due to large endowments but their quality of teaching does not increase; funding incentives have not achieved their purpose. In addition to funding, teachers must be trained to instil the value of a proper education to their students such that they may intrinsically become motivated to seek higher education – not for money – but for the sake of learning how they can best contribute to their country whether through art, science, technology, or language.

In conclusion, in order for the author to convince me that engineers are the limiting factor towards improving a country’s economy, the author must provide evidence that the betterment of a country’s economy is initiated through the innovation brought by engineers. I otherwise remain unconvinced that engineers are the only individuals who can contribute to a country’s economic competitiveness in the world marketplace.

30 minutes.

Essay #6:

Note: I feel that this essay is a bit shaky

Analysis of an issue:

“You can tell the ideas of a nation by its advertisements”

Explain what you think this quotation means and discuss the extent to which you agree or disagree with it. Develop your position with reasons and/or specific examples draw from history, current events, or your own experience, observations, or reading.

Whether the ideas of nation can be demonstrated through its advertisements is dependent on the individuals involved in the creation of such media. In my view, there is a difference between commercial advertising and propaganda; therefore, if the term “advertisements” in the statement encompasses both forms, then I disagree with the statement for several reasons.

The main reason for my view is simply due to the fact that most commercial advertising is not intentionally instilling any ideologies into the individuals that view them. For example, advertisements from stores such as BestBuy, Futureshop, Loblaws, and Wal-Mart simply display products, potential sale items, and new product arrivals. Moreover, there are hardly any statements on the flyers from these stores that attempt to initiate any form of alternative agenda in terms of society. Finally, such advertisements are simply used as an information resource for consumers to make better financial decisions in purchasing products or services that suit their personal preferences.

The second reason for my view is that perhaps the only form of advertising that initiates any form of ideology into individuals is propaganda. In a semantic argument, it can be proposed that the terms “advertisement” and “propaganda” are not interchangeable, but rather mutually exclusive. This is because propaganda is generally derived from politicians within the government that are interested in gaining support for personal political agendas. For example, a flyer encouraging young men to join the military ranks by stating that masculinity is only achievable through registration is propaganda. Another example would be political leaders such as Barrack Obama or Hilary Clinton generating commercials that speak positively on topics in their own personal agendas but speak negatively on another’s. Once again, propaganda is generally used as a medium in which politicians attempt to instil novel ideologies into the minds of others who view them.

Finally, some may argue that advertisements generated by commercial firms are in themselves already contributing to a change in consumer ideology since they directly promote consumerism. Others may cite that propaganda is not attempting to manipulate the minds of individuals as a result of political agendas; but rather, propaganda is a relevant part to promoting a country’s values and culture. However, these arguments are weakened since consumers are known to independently go shopping at stores; and propaganda is generally used as a tool by political parties to confront each other indirectly.

In sum, I agree that a nation’s advertisements demonstrate the ideas of nation to a certain degree. However, the term advertisements must be separated into the categories of commercial advertisements and propaganda; therefore, on balance, since commercial advertisements are much more prevalent, advertisements do not accurately reflect the ideas of a nation.

30 Minutes.

Essay #7:

Note: This one is also a bit shaky.

Analysis of an issue:

Since science and technology are becoming more and more essential to modern society, schools should devote more time to teaching science and technology and less to teaching the arts and humanities”

Discuss the extent to which you agree or disagree with the opinion stated above. Support your view with reasons and/or examples from your own experience, observations, or reading.

Whether schools should devote more time to teaching science and technology courses and less to teaching the arts and humanities is dependent on many factors. In my view, the teaching of science and technology courses is only relevant if the country has the infrastructure to support the education provided – this is true for developed nations. Therefore, for most countries, I would agree that the devotion of more time towards training students in science and technology should place priority over arts and humanities.

The main reason for my view is that there is an obvious discrepancy between the computing abilities of emerging students from post-secondary education and those of the baby-boomer generation. From personal experience, students have demonstrated a greater ability to type and navigate through computer systems as compared to their baby-boomer counterparts. This is not limited to simply school work, but increased understanding of computer systems and applications increases an individual’s ability and efficiency in the workforce. Finally, it almost seems that there will always be a discrepancy since technology is constantly changing; therefore, it would be advisable for students to constantly learn of such novel forms of technology as well.

The second reason for my view is that science is also changing constantly. Although filled with an endless amount of jargon, science is just as fluid, if not more, than technology. Thousands of novel research methods are constantly being suggested through research papers churned out by master’s students, post-doctoral students, and professors alike each year. It would be highly beneficial for students to be well-informed, if not professionally educated, in these areas to garner a better understanding of how the world is changing each day. Admittedly, students need not be informed of such topics to perform other occupations; however, it would definitely be beneficial if the ignorance in the discussion of such topics was rectified.

In sum, I agree that schools should devote more time to teaching courses in technology and sciences than the arts and humanities. However, this does not mean that arts and humanities are not important – they are; on balance, however, it would be more relevant for students if teachers in developed countries placed emphasis on teaching courses in science and technology.

30 Minutes.

GMAT Questions #2

Posted: August 5, 2010 by kdawgz in GMAT

The GMAT also consists of a verbal section which includes two timed essays, 30-minutes each, one on the analysis of an argument, and one on the analysis of an issue. Since I was slacking a bit at work today, I was able to compose two essays on the latter topic. This is only the second time I’ve attempted writing these, so they are most likely far from being anything but poor essays. I managed to finish them both under the time constraints. I also cheated a bit and applied the template suggested by Peterson’s GMAT Answers to the Real Essay Questions, 3rd Edition in terms of their transition words and style. Feel free to rip them apart…especially if the arguments are not sound (hopefully my writing skills, or lack thereof, will make up for my previous embarrassment in math). Thanks in advance.

Essay #1:

Topic: “In any large business organization, teamwork is the ultimate key to the organization’s success.”

Directive: In your view, how accurate is the foregoing statement? Use reasons and/or examples from your experience, observation, and/or reading to explain your viewpoint.

Whether teamwork is the ultimate key to an organization’s success is entirely dependent on what is defined as success. If success equates to streamlined decision making, completing tasks initiated by a bureaucratic organizational culture, and simply obeying orders, then teamwork can possibly be deemed as unnecessary towards an organization’s success. In my view, however, success equates to both the human and material aspect of an organization which entails satisfied employees in an encouraging organizational culture, and being successful in generating profits at the same time.

The main reason for my view is that many of the current organizations deem success based on what is recorded on a business’s or corporation’s financial statements – the bottom line. Although the end result is that companies have been able to generate profits, the end should not justify the means. To achieve the end result, employees may have been laid-off, restructuring may have occurred, there may only be one authoritative dictator dictating actions required by disgruntled employees, and other maltreatment of employees may have been evident. As per my view stated above, success is a combination of material gains and intangible gains from employee satisfaction; as such, teamwork is paramount.

Another reason for my view is that teamwork is more efficient in generating creative ideas and simply completing job tasks. This is greater exemplified in organizations that adopt a flat structure. For example, if employees regularly require assistance from managers, and due to the facilitation of teamwork in a flat structure, fellow employees will be more able to interact with their colleagues on a regular basis on not only how to complete tasks, but working together to generate new ideas and innovations to further the organization’s growth. Admittedly, some employees may prefer receiving tasks from an authority figure, a flat structure, however, as alluded to earlier, will also foster increasing morale and rapport between employees for even further success for the organization.

In sum, I agree that teamwork is the ultimate key to an organization’s success. It must be noted, however, that in some organizations, teamwork is not required based on the goals of the organization. For such organizations, however, this may lead to disgruntled employees and high employee turnover. Therefore, on balance, the facilitation of teamwork between employees is vital to an organization’s success.

Essay #2

Topic: “Financial gain should be the most important factor in choosing a career.”

Directive: Discuss the extent to which you agree or disagree with the opinion stated above. Support your views with reasons and/or examples from your own experience, observations, or reading.

Whether financial gain is the most important factor in choosing a career is questionable. In my view, career choice is completely dependent on the individual and the circumstances that the individual faces while that decision process is taking place.

The main reason for my view is due to the very idea of career choice in most developed nations. It must also be noted that these developed nations tend to be democratic in nature; and in general, each individual in these countries including, but are not limited to, Canada, the United States, India, China, Australia, and Japan, have ample access to the education required for an infinite number of careers and professions. In this case, financial gain may not be the most important factor because it is generally accepted that one should choose a career path in which they enjoy. Finally, the reasons for career choices in such cases may include the enjoyment of art, music, counselling others, and the endless number of different personality preferences that individuals possess.

Another reason for my view is that if an individual chooses a career simply due to financial gain, studies have shown that such careers have become unfulfilling for the individual. Individuals become depressed, unsociable, and may succumb to the vicious cycle that most individuals face: Eat, sleep, work; eat, sleep work. Admittedly, this is simply a trend and does not occur in all cases; however, it occurs often enough that it must be mentioned.

Some may argue financial gain is the first, and foremost, factor in developing a career choice. Such arguments may further cite that those individuals who do not have the opportunities to a proper education, and therefore, professional careers, search – relentlessly at that – for any means in which they can obtain money. Such individuals are those who require the money simply to survive – not for luxuries. In the end, however, it is not financial gain that is the most important factor for the career choice; it is the necessity to meet basic needs that drives an individual to select a career – any career – legal or illegal.

In sum, I agree that financial gain may be the most important factor in career choice for those individuals who do not have many career choices. However, for the well educated and those with access to endless job opportunities, on balance, place enjoyment over financial gain when determining their future career paths.

GMAT Questions #1

Posted: August 3, 2010 by kdawgz in GMAT

I’m one of those ambitious students that is trying to get into a good grad school, namely, the ones below. As GMAT studies continue and exam day is coming up in a couple of weeks, there is still lots of room for improvement.

Here are the few questions that I got wrong and cannot answer myself on the last sample test I did, granted most of the ones I was able to correct myself were silly mistakes anyway:

A. The function of f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number, then f(p) =

  1. p-1
  2. p-2
  3. p+1/2
  4. p-1/2
  5. 2

Having not done math for awhile, I don’t know where to begin to solve this problem. The correct answer is p-1. An explanation would be appreciated!

B. If the two regions below have the same area, what is the ratio of t:s?

I generally understand the rules of geometry and special triangles but an explanation for this answer would be great too. The answer is 2:4root3

C. For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75=3x5x5. How many two digit positive integers have length 6?

This question is confusing because, technically, from what I understand, it is possible for: 1x1x1x1x7x7x2 =98, 1x1x2x2x2x2 = 16, and 1x1x1x1x1x7x7 = 49 etc. But the answer is only TWO. Help.

D. Set S consists of 20 different positive integers. How many integers in S are odd? (Data sufficiency problem)

  1. 10 of the integers in S are even
  2. 10 of the integers in S are multiples of 4

So immediately looking at the data given in (1) and (2), statement (1) is definitely sufficient to answer the question. As for statement (2), I thought it was sufficient because all multiples of 4 are multiples of 2 and are therefore even – EXCEPT 1. Maybe that’s where I went wrong. Anyway the answer was: Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question. I originally put each statement alone is sufficient.

Data sufficiency questions have five answer choices:

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH Statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.

E. In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?

The answer is 13 but the method escapes me :(.

I know when I find out what the answer to some of these, I deserve a knock on the head. But no pain no gain. Gotta learn from mistakes!