Part 10 (2/2)

Back to problem Problem 3: Pattern There are two possible solutions to this problem. The first solution below could be accurate if the pattern alternates with one on top and three on the bottom. This solution is also accurate if we put vowels on the top and consonants on the bottom.

A second solution is possible if we put letters consisting only of straight lines on top and letters consisting of curves on the bottom.

Back to problem Problem 4: Nine Dots The aNine Dots Gamea serves as an example of a self-imposed barrier to creativity. As can be seen in the first solution below, the lines can be drawn outside of the perimeter formed by the nine dots. This usually cannot be seen because we are programmed to keep the lines within the boxed area. Another possibility, as depicted by the solution on the right, occurs by drawing lines that touch the corners of the various dots. Nothing states that the lines have to be drawn through the centers of the dots.

Back to problem Problem 5: Two Water Bucket Problem Back to problem

CHAPTER 3 a” DECISION MAKING.

Problem 6: Corporate Training Back to problem Problem 7: Singles Answer: 662a”3%. Two-thirds of the women are single (i.e., 20a”30 = 2a”3). An truly easy way to do this problem is to a.s.sume for simplicityas sake that there are 100 students in the course and fill in the given information, turning percentages into numbers. For example, if 70% of the students are male, then 30% must be female. If we a.s.sume there are 100 students then 70 are male and 30 are female. With this method, visualize the percentages in the matrixes below as being actual numbers and appearing without percent signs.

First, plug the given data from the problem into the matrix: Second, complete the matrix, totaling down and across: Back to problem Problem 8: Batteries Answer: 4%. To obtain the percentage of defective batteries sold by the factory, we fill in the information per the following matrix to obtain 3a”75 or 1a”25 or 4%. Picking the number a100a (which a.s.sumes 100 is the total number of batteries) greatly simplifies the task at hand.

First, plug the given data from the problem into the matrix: Second, complete the matrix, totaling down and across: Back to problem Problem 9: Interrogation Answer: 7%. Seven percent of all subjects will end up confessing to the crime and rightfully soaa”aaTheyare admitting they did it and they really did do it!a Step 1: Fill in the given information.

Step 2: Complete the matrix, totaling down and across: Back to problem Problem 10: Set Menu Answer: 24. The diagram that follows serves both as a decision-event tree and a probability tree. First, there are twenty-four ways by which a diner can choose his or her meal. Second, if we a.s.sume that every dish has an equal probability of being chosen, then the probability of any meal being chosen is 1a”24. For example, one person could choose soup, pasta, pie, and coffee (1a”2 - 1a”3 - 1a”2 - 1a”2 = 1a”24a). Another person might choose salad, fish, cake, and tea (1a”2 - 1a”3 - 1a”2 - 1a”2 = 1a”24a).

Back to problem Problem 11: Investor Answer: $55,000.

First Investment: Second Investment: Third Investment: First Investment: WA = $90,000(1a”6) + $50,000(1a”2) + a'$60,000(1a”3) = $20,000 Second Investment: WA = $100,000(1a”2) + a'$50,000(1a”2) = $25,000) Third Investment: WA = $100,000(1a”4) + $60,000(1a”4) + (a'$40,000)(1a”4) + (a'$80,000)(1a”4) = $10,000 So, the aggregate value of all three investments is: Expected Return = $20,000 + $25,000 + $10,000 = $55,000 Note: Expected Return is calculated using the weighted average formula.

Back to problem

CHAPTER 4 a” a.n.a.lYZING ARGUMENTS.

Comparison and a.n.a.logy a.s.sumptions Problem 12: Crime Choice E. The key to understanding this problem is to see the scope s.h.i.+ft that occurs as a result of switching terms from acrimea to areported crime.a Obviously, reported crime is not the same thing as actual crime. As answer choice E states: aIt is possible for reported crime to have gone down while actual crime has remained the same or actually gone up.a In order to make comparisons we need to stick to terms that are of equivalent meaning.

Choice A is incorrect. This answer choice slightly strengthens, not weakens, the original argument. In choice B, it does not matter whether police officers, as citizens themselves, voted for a bill on initiatives to reduce crime in the city. It also does not matter, as in choice C, whether most arrests were repeat offenders. Whether first-time offenders or repeat offenders, crime is crime.

The fact that crime has come to include white-collar crime (choice D) actually strengthens the argument. It suggests that there could be more incidences of crime (or cases of reported crime), which makes a decrease in crime (or cases of reported crime) potentially that much more significant.

Back to problem Problem 13: Hyperactivity Choice D. The idea that more types of behavior are deemed hyperactive indeed weakens the claim that children today are more hyperactive than they were ten years ago. In short, there are more ways to acheck offa and confirm hyperactive behavior. In order to compare the hyperactivity of children today versus ten years ago, we need an even playing field in terms of the comparability of terms: the definition of hyperactivity or the criteria for hyperactive behavior must remain consistent over time. Choices A and B are effectively out of the argumentas scope. We are not talking about creativity and spontaneity, nor are we primarily concerned about other potentially more serious issues beyond hyperactivity. The impact of having more or fewer pictures in childrenas books remains unclear (choice C) as does an increase in ailments such as Attention Deficit Hyperactivity Disorder (ADHD) per choice E.

Back to problem Representativeness a.s.sumptions Problem 14: Movie Buffs Choice B. This is a cla.s.sic representative sample a.s.sumption question. The argument a.s.sumes that a sample based on people attending Sunday matinees (afternoon showings) is representative of the whole country of moviegoers. The question is, aHow representative is the opinion of those attending Sunday matinees?a For example, Sunday matinee moviegoers might consist of a disproportionate number of family viewers (i.e., people with children) who prefer not to watch bizarre or violent movies during their Sunday afternoons. For this sample to be representative, we need to survey at least some Sat.u.r.day night moviegoers, Sat.u.r.day matinee moviegoers, and weekday moviegoers.

Choice A does weaken the argument somewhat by suggesting that people will see a movie regardless of its genre just so long as their star actor (or actress) appears. Choice C is incorrect because we are concerned about the current tastes of moviegoers and not the movie hits of yesteryear.

Choice D is incorrect. We cannot a.s.sume that increased book sales and college enrollment in criminology courses is necessarily linked to trends among moviegoers. As far as we know, the moderate increase in course enrollments is the result of many other factors.

Choice E is incorrect because it notionally strengthens the idea that movie producers should stop producing these types of movies because they are financially unsound. If actorsa salaries are high, then movie production costs will be higher, putting pressure on the bottom line.

Back to problem Problem 15: Bull Market Choice A. This argument a.s.sumes that the whole of the Indian economy can be judged from the strength of the stock market, here the National Stock Exchange (NSE) index. In choice B, the fact that the Bombay Stock Exchange (BSE) index (another major stock exchange in India) has gone up does lend support for the comments made but it does not lend as much support as does choice A. Choice A provides direct support for the key a.s.sumption in the argument.

The fact that the National Stock Exchange (NSE) index was down this time last year, choice C, neither lends support for nor weakens the argument at hand. The fact that the Asian and European economies are also considered strong (choice D) lends some tangential support to a strong Indian economy, but it is hard to draw any firm conclusions from this fact. The fact that the National Stock Exchange (NSE) index is subject to great fluctuations (choice E) serves to weaken the comments made.

This is essentially the same argument used in the example t.i.tled aFinlanda in chapter 2, which may also be viewed under the guise of a representativeness a.s.sumption. The argument concludes (in the agenerala) that Finland is the most technologically advanced country on earth; the argument uses as evidence (in the aparticulara) the fact that more people per capita own mobile phones in Finland than anywhere else on earth.

Back to problem Problem 16: Putting Choice C. The argument a.s.sumes that the ability to putt is the pivotal factor in determining whether a person can achieve a low golf score. A good golf game has many ingredients, including putting, driving, iron shots, chipping, sand trap shots, judging weather, pacing, strategy, temperament, experience, physical fitness, and compet.i.tiveness. This pa.s.sage a.s.sumes that it all happens on the putting green. Although it would be impossible to argue that putting is not an important component to achieving a low score in golf, it is certainly not the only factor.

Choice A is incorrect. We cannot a.s.sume that there is no way to improve a golf game other than with quality equipment. Practice itself might be enough to simply improve a golf game. The argument does suggest that if a person wants to make great improvements in his or her golf game then he or she needs to make improvements in putting and, ideally, purchase a new Sweet Spot Putter.

Choice B is incorrect because it forms an unwarranted comparison that is not a.s.sumed in the argument. We do not know whether a new Sweet Spot Putter will improve an amateuras game more than it will improve a professionalas game or vice-versa. Likewise, choice D is incorrect because we do not know whether the new Sweet Spot Putter is superior to any other putter currently on the market. For all we know, the Sweet Spot Putter is just one of three new miracle putters.

Per choice E, we also have no way of knowing whether lessons are, or are not, as effective at improving the accuracy of a playeras putting as is the use of quality equipment.

Authoras note: Broadly speaking, representative sample a.s.sumptions are applicable any time that we argue from the particular to the general. Surveys or questionnaires are so often used as the basis for representative sample a.s.sumptions, as seen in problem 14, t.i.tled Movie Buffs. In the previous problem, t.i.tled Bull Market, the strength of the Indian economy (the agenerala) is based on the strength of the National Stock Exchange (NSE) index (the aparticulara). In the problem at hand, success in the game of golf is a.s.sumed to rest primarily on the ability to make putts. Here again, we argue primarily from the particular (aputtinga) to the general (agolfa).

Back to problem aGood Evidencea a.s.sumptions Problem 17: Criticas Choice Choice C. Since there are certainly far more than 100 contemporary and 100 non-contemporary novels to choose from, a question arises as to whether those novels chosen are representative of the entire population of contemporary and non-contemporary novels. It is possible that the author of Decline of the Novelist chose novels which best supported his/her thesis a” that todayas novelists are not as skillful as the novelists of yesteryear. Choice A might weaken the argument slightly but certainly wouldnat weaken it seriously. Choice B, while highly plausible, is irrelevant to the argument because the author focuses his/her argument on technical skill. Choice D is simply out of scope since we donat know anything about the literary skill required to do screenplays. Choice E is irrelevant; it doesnat matter whether the average reader is familiar with the terms of literary criticism; it only matters that the bookas author is familiar with these terms.

Back to problem Problem 18: Temperament Choice E. This is an example of proof by selected instances. Each person a” Steve and John a” will simply choose examples which support his intended claim. Steve picks red-haired people who have bad tempers to support his claim that red-haired people are bad tempered. John picks red-haired people who have good tempers to support his claim that red-haired people are not bad-tempered. The fact that the number of red-haired people (choice A) that one person knows is more or less than the number of red-haired people that the other person knows has no clear effect on reconciling the two statements. In fact, it is quite possible that the percentage of red-haired people that each knows is quite close, say five percent. After all thatas the magic of percentages as opposed to numbers a” percentages express things in relative terms. In choice B, it is only plausible that the number of red-haired people both Steve and John know would be, in aggregate, less than the total of non-red-haired people both know. Confirmation of this likely reality will not reconcile the two seemingly contradictory statements.

It is also unclear whether choice C has any effect. Any mis-a.s.sessments may prove net positive or net negative or may have a counterbalancing effect. It is almost axiomatic that both Steve and John know of friends who are not red-haired and have bad tempers, but this will do nothing to reconcile the contradictory statements, so choice D is out. Note that the procedure for actually proving whether or not red hair is correlated with bad temper falls within the context of experimental design. Refer to Hypothesis Testing in chapter 3.

Authoras note: Here is a follow-up problem which mimics a true-to-life scenario. Surveys or questionnaires completed and returned may not be representative of respondentsa viewpoints in general if surveys or questionnaires not returned would have yielded conflicting information.

President: aIam worried about the recent turnover in MegaCorp. If employees leave our company disgruntled, such negative feelings can hurt our reputation in the marketplace.a Human Resources Manager: aYour concerns are unfounded. As part of our post-employment follow-up process, we send questionnaires to each employee within thirty days of his or her leaving the company. These questionnaires seek honest answers and remind employees that all responses will be kept confidential. Of the last 100 employees who left our company, 25 have responded, and only 5 people have mentioned having had any negative employment experience.a The Human Resource Manageras argument is most vulnerable to criticism on the grounds that it fails to acknowledge the possibility that A) Opinions expressed in such questionnaires are not always indicative of how employees actually felt.

B) Many of those who harbored truly negative feelings about their employment experience at MegaCorp did not respond to the questionnaire.

C) The Public Relations firm Quantum, recently hired by MegaCorp has successfully designed several programs specially aimed at boosting the companyas public image.

D) Questions asking about negative employment experiences have been placed at the end, not at the beginning, of the questionnaire.

E) The response rate in general for questionnaires is 10 percent, meaning that only 1 in 10 questionnaires can be expected to be completed and returned.

The correct answer is choice B. If those former employees of MegaCorp who harbor very negative feeling about the company remain silent (i.e., they donat respond to the questionnaire), then such views have been omitted from inclusion. Choice A may also be a concern, but it is impossible to tell whether it refers to employees who felt much better about their employment experience or much worse (we canat a.s.sume employees necessarily felt worse!). In choice C, we canat a.s.sume that the public relations efforts of Quantum have any affect on the employees who have left the company; besides, designing and implementing programs are two different things. The placement of questions within the questionnaire (choice D) is likely irrelevant or its impact inconclusive. Choice E strengthens the Human Resource Manageras claim because the response rate achieved by MegaCorp (i.e., 25a”100 = 25%) is greater than the general response rate of 10 percent; of course, the higher the response rate the better.

Back to problem Cause-and-Effect a.s.sumptions Problem 19: Cyclist Choice C. This argument turns correlation into causation. There is likely a high correlation between low body fat and being a world-cla.s.s cyclist. But there may well be a high correlation among other variables as well. For example, a high correlation also likely exists among muscular strength and world-cla.s.s cycling, technical skills (maneuvering a bike) and world-cla.s.s cycling, and being a world-cla.s.s cyclist.

This problem can also be solved as an, aif a thena type problem. The original reads, aIf one is a world-cla.s.s cyclist, then one has 4 to 11 percent body fat.a When the aif a thena statement is erroneously reversed and the argument becomes, aIf one has 4 to 11 percent body fat, then one can be a world-cla.s.s cyclist.a Having low body fat is a necessary but not a sufficient condition for being a world-cla.s.s cyclist. aIf a thena type statements are discussed in chapter 5.

Back to problem Problem 20: SAT Scores Choice B. The argument basically says that SAT scores have gone up because students are better test takers, not because students possess better academic skills. Are students smarter or just better test takers?

Choices A and E may appear tricky. Actually the author doesnat deny his opponentsa figures or suggest his evidence is flawed. In fact, the author agrees with his opponentsa facts (test scores are getting higher). What the author is saying is that his opponentsa evidence is incomplete, not flawed. Choice D is not correct. The argument is not flawed due to circular reasoning. In circular reasoning, a conclusion is based on evidence, and that same piece of evidence is based on the conclusion. Choice D in this problem is incorrect for the same reason that choice E is incorrect in the previous problem, Cyclist. An argument that a.s.sumes what it seeks to establish is a circular argument.

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