The Little Blue Reasoning Book - Brandon Royal [60]
First, plug the given data from the problem into the matrix:
Second, complete the matrix, totaling down and across:
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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 3⁄75 or 1⁄25 or 4%. Picking the number “100” (which assumes 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:
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Problem 9: Interrogation
Answer: 7%. Seven percent of all subjects will end up confessing to the crime and rightfully so — “They’re admitting they did it and they really did do it!”
Step 1: Fill in the given information.
Step 2: Complete the matrix, totaling down and across:
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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 assume that every dish has an equal probability of being chosen, then the probability of any meal being chosen is 1⁄24. For example, one person could choose soup, pasta, pie, and coffee (1⁄2 × 1⁄3 × 1⁄2 × 1⁄2 = 1⁄24 ). Another person might choose salad, fish, cake, and tea (1⁄2 × 1⁄3 × 1⁄2 × 1⁄2 = 1⁄24 ).
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Problem 11: Investor
Answer: $55,000.
First Investment:
Second Investment:
Third Investment:
First Investment:
WA = $90,000(1⁄6) + $50,000(1⁄2) + −$60,000(1⁄3) = $20,000
Second Investment:
WA = $100,000(1⁄2) + −$50,000(1⁄2) = $25,000)
Third Investment:
WA = $100,000(1⁄4) + $60,000(1⁄4) + (−$40,000)(1⁄4) + (−$80,000)(1⁄4) = $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.
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CHAPTER 4 – ANALYZING ARGUMENTS
Comparison and Analogy Assumptions
Problem 12: Crime
Choice E. The key to understanding this problem is to see the scope shift that occurs as a result of switching terms from “crime” to “reported crime.” Obviously, reported crime is not the same thing as actual crime. As answer choice E states: “It is possible for reported crime to have gone down while actual crime has remained the same or actually gone up.” 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.
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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 “check off” 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