This Inference problem forces you to deal with the provided statistics, which guarantee that choice B must be true. To prove that, you could use a variable for the number of refrigerators that Fretter sold to residents of Oakland County (let's call it x) or you can borrow a tool from your Word Problems / Quantitative toolkit and pick a number (such as 50) .

You know that most (so > 1/2) of the refrigerators that Fretter sold were to residents of Oakland County. So the number of refrigerators that Fretter sold in total must be less than 2x, or less than 100.

You also know that more than 1/2 of the refrigerators sold to residents of Oakland County were NOT from Fretter. So Fretter's x (or 50) refrigerators are less than half of Oakland County's refrigerator sales. Oakland County's sales then are > 2x, or > 100. This allows you to directly compare the two totals: The number of total Fretter sales is less than the number of total Oakland County sales. Choice "In 2015, more refrigerators were purchased by residents of Oakland County than were sold by Fretter Appliances." is therefore proven.

Among the incorrect answer choices:

With choice "At least one store in Oakland County sold more refrigerators in 2015 than Fretter Appliances did.", recognize that no one store had to sell more in Oakland County than Fretter in order for Fretter's sales to be less than 50% of the county's. Several smaller stores could add up to that >50% amount.

With choice "Residents of Oakland County purchased more refrigerators in 2015 than in any previous year.", there is just no information to draw this conclusion: Fretter's 2015 was its greatest ever, but you don't have any information about Oakland County's historical sales.

Choice "Fretter Appliances sold more refrigerators to residents of Oakland County in 2015 than it did in any previous year." can be eliminated by considering extreme cases when picking numbers. If this year Fretter sold 100 refrigerators overall (its best year ever) and 51 in Oakland County (more than half its total sales), you could still have Fretter selling 90 last year (consistent with 2015 as its highest ever sales) with all 90 of them coming from Oakland County (just a much higher percentage of its sales coming from Oakland County in a previous year).

And choice "At least some residents of Oakland County purchased refrigerators from stores not located within Oakland County in 2015." is a choice that seems likely to be true, but that has no proof anywhere in the stimulus. On Inference questions, if you can't find direct proof, the answer choice is not necessarily true and must be eliminated.

This question stem is asking you to form a conclusion based on the information given, so you must pick the one answer that is guaranteed. As is true for all inference style questions, you should use process of elimination by evaluating each potential conclusion.

For "Most people eating vitamin-fortified foods are consuming dangerous amounts of vitamin C.", you do know that “most consumers overestimate the amount of one serving for these foods, ingesting two to four times what is considered one serving by the manufacturer” so it is safe to say that most people get more than their daily intake as recommended by the NAS. However, to be dangerous the recommended amounts must be “greatly exceeded” and we have no idea if “two to four times” meets that threshold. As a result this is not a proper inference.

For "Manufacturers need to change the amount listed as one serving on the packaging for vitamin-fortified foods.", there is no proof given in the stimulus that manufacturers need to do anything. While it is true that many consumers overestimate the amount of one serving, this does not allow you to conclude that manufacturers need to make a change (maybe the consumers just need to get better at estimating!). This type of prescription is virtually impossible to prove in an inference style question.

For "Any person eating vitamin-fortified foods will receive the daily intake for vitamin C that is recommended by the National Academy of Sciences.", the word “any” makes this easy to eliminate. We know that many, but not necessarily all, vitamin fortified foods contain 100% of the recommended vitamin C and that “most” consumers overestimate a serving. However, this still leaves open the possibility that some people are eating vitamin-fortified foods that do not contain vitamin C or that they are not getting a full serving’s worth.

For "Some people eating vitamin-fortified foods exceed the daily intake for vitamin C that is recommended by the National Academy of Sciences.", you know with certainty that most consumers are eating 2-4 servings of vitamin-fortified foods containing vitamin C, which provides more than 100% of the recommended amount. Since you only need to prove one person has consumed more than a serving of these foods to be sure of this conclusion, it must be true and "Some people eating vitamin-fortified foods exceed the daily intake for vitamin C that is recommended by the National Academy of Sciences." is correct.

For "People should avoid taking supplemental vitamin C if they are eating vitamin-fortified foods.", this is a similar prescription to what you saw in "Manufacturers need to change the amount listed as one serving on the packaging for vitamin-fortified foods.". There might be many reasons why someone wants or needs to take a vitamin C supplement even if they are eating the vitamin-fortified foods. Maybe their doctor wants them to have lots of extra vitamin C or maybe they are eating the vitamin-fortified foods that do not contain 100% of the recommended amount. This is not a proper inference.

This Boldface problem rewards those who can adeptly deconstruct arguments and find conclusions. Here the main conclusion of the argument is "the shareholders' optimism may be ill-founded" - you know that this is a conclusion because it is adjacent to the word "since" (which gives a reason for the conclusion - remember, conclusions must pass the "why test" in which some other portion of the argument tries to explain why it is true). And you know that it's the main conclusion because it follows "however," a signal that the author has introduced an idea and then transitioned to her main point.

With this knowledge you're ready to attack the answer choices and pick apart the subtle difference between popular choices. The first bolded portion is evidence that is used to support a conclusion (just not the main conclusion) - it's a reason that some shareholders believe that they do not have be be worried about the company's stock price.

The second bolded portion is evidence for the main conclusion - it's the reason that the shareholders' optimism may be unfounded.When you attack the answer choices, note that "The first is evidence that supports a conclusion; the second is that conclusion." and "The first is a premise that is accepted as true; the second is a conclusion that is contrary to the premise." each clearly mischaracterize the second bolded portion as a conclusion when in fact it is a premise.

Among the other choices, recognize that the goal of the argument - as evidenced by the conclusion - is to show that the shareholders' optimism is misplaced, NOT to clarify the initial fact. Again, this goes back to isolating and fixating on the conclusion. This is why choice "The first describes evidence that supports a conclusion; the second gives a reason for questioning that support." is correct: it properly notes the role of the second bolded portion, to support the conclusion that the optimism is unfounded (which, conceptually, is the same thing as questioning the shareholders' logic). Choices "The first describes the circumstance that the argument seeks to explain; the second provides evidence in support of the explanation that the argument seeks to establish." and "The first is a premise that is accepted as true; the second seeks to clarify the original premise." are each tempting, but each suggests that the purpose of the argument is to clarify the fact in the first sentence, when in fact the conclusion is clear in its intention to question the logic of the shareholders.

For any boldfaced question, it is essential that you first understand the complete argument. In this stimulus, it is stated that some economists believe that the enormous debt is the major impediment to job growth. As a result, these economists believe that spending should be cut immediately to reduce the debt. The evidence they give for their argument is that current debt levels are 96% of GDP and when total debt levels exceed 90% of domestic GDP, economic growth falls significantly causing job losses and overall economic malaise. The author of this argument agrees that reducing debt is essential but believes that an immediate reduction of spending would be problematic because the economy is too fragile. His recommendation and conclusion is that spending levels should be left constant in the short term and revenues increased with more taxes. Then, after the economy has recovered, spending should indeed be reduced. In summary, the author agrees with the economists that the major impediment to job growth is the high debt level but disagrees with their short term plan because the economists have not considered the fragile state of the economy. With that understanding of the argument, you must then attack each answer choice to see how the boldfaced sections are described:

"The first boldfaced portion is an opinion that the author of this argument believes is incorrect; the second boldfaced portion is support for that opinion." The author does not believe that first boldfaced portion is incorrect but rather believes it is correct. He disagrees with their assertion that “spending should be cut immediately” but agrees with this boldfaced portion. While the second boldface portion is described correctly, "The first boldfaced portion is an opinion that the author of this argument believes is incorrect; the second boldfaced portion is support for that opinion." is incorrect because of the description of the first boldfaced portion.

"The first boldfaced portion is an opinion that the author of this argument believes is incorrect; the second boldfaced portion is support for the author’s conclusion." This answer choice also incorrectly describes the first boldfaced portion. While the second does support the author’s conclusion, "The first boldfaced portion is an opinion that the author of this argument believes is incorrect; the second boldfaced portion is support for the author’s conclusion." contains the same error as "The first boldfaced portion is an opinion that the author of this argument believes is incorrect; the second boldfaced portion is support for that opinion." with the first boldfaced portion.

"The first boldfaced portion is an opinion that the author believes is correct; the second boldfaced portion is support for that opinion." The first boldfaced portion is an opinion that the author indeed believes is correct. The second boldfaced portion is the essential premise for that opinion so "The first boldfaced portion is an opinion that the author believes is correct; the second boldfaced portion is support for that opinion." is correct.

"The first boldfaced portion is an opinion upon which the author’s conclusion is based; the second boldfaced portion is evidence that contradicts that conclusion." In this choice, it is correct to say for the first boldfaced portion that the author’s conclusion is based on the opinion that the major impediment to job growth in the U.S. is the enormous national debt. However, the second boldfaced portion does not contradict the author’s conclusion but rather supports it so "The first boldfaced portion is an opinion upon which the author’s conclusion is based; the second boldfaced portion is evidence that contradicts that conclusion." is incorrect

"The first boldfaced portion is the author’s conclusion; the second boldfaced portion is support for that conclusion." The first boldfaced portion is not the author’s conclusion but rather the opinion of several other economists. The author’s conclusion is given in the last two sentences that are not boldfaced.

As you deconstruct the argument in this Boldface question, recognize first that the first bolded sentence is a premise, stated as a fact. Further, the beginning of the next sentence states "with that trend...," establishing that the argument will build from that fact. From here you can eliminate choices "The first states a position taken by the argument; the second introduces a conclusion that is refuted by additional evidence." and "The first is a conclusion that is later shown to be false; the second is the evidence by which that conclusion is proven false." (each of which says that the first portion is a conclusion). You can also be very skeptical of choice "The first is a premise that is later shown to be false; the second is a conclusion that is later shown to be false.": even though it correctly says that the first portion is a premise, note that it goes on to say that the argument proves that premise false. As you will see from the rest of the paragraph, the argument is concerned with attacking a conclusion drawn from that premise, but never tries to disprove the fact itself. For this reason, "The first is a premise that is later shown to be false; the second is a conclusion that is later shown to be false." is also incorrect.

As you look at the second bolded portion, note that the phrase "there has been debate as to whether we can conclude" is also direct cause for eliminating "The first is a premise that is later shown to be false; the second is a conclusion that is later shown to be false.": the second bolded portion is not the conclusion itself, but rather the introduction of the conclusion. You should see that this language matches choice "The first describes a premise that is accepted as true; the second introduces a conclusion that is opposed by the argument as a whole." perfectly, so choice "The first describes a premise that is accepted as true; the second introduces a conclusion that is opposed by the argument as a whole." is correct.

Similarly "The first is evidence that has been used to support a position that the argument as a whole opposes; the second provides information to undermine the force of that evidence." is incorrect, as the second bolded portion introduces a conclusion that could be drawn based on the first premise: it does not, as "The first is evidence that has been used to support a position that the argument as a whole opposes; the second provides information to undermine the force of that evidence." says "undermine that evidence." To the contrary, it builds upon it.

Note that the conclusion of this argument is the phrase "the answer is no," which comes right next to the explanation for that conclusion, "since motorists with more fuel-efficient vehicles..." This allows you to eliminate choice "The first is a conclusion that is later shown to be false; the second is the evidence by which that conclusion is proven false.", as the evidence for the argument's conclusion is everything beginning with "since," not the second bolded portion. Choice "The first describes a premise that is accepted as true; the second introduces a conclusion that is opposed by the argument as a whole." is correct.

As you assess the argument and scan the answer choices, it should become clear that you will need to determine the dean's conclusion. A few things are important in finding that: 1) note the word "but" to begin the second sentence. Transition language like that often signifies that the author is transitioning between contextual information and her main point, so you should pay even closer attention past "but" to find the conclusion there. 2) Remember the "why test" - in order to be a conclusion, a statement must be backed up with a reason "why" it's true somewhere else in the argument.

Note that the non-bolded initial clause of that sentence "cutting the marketing budget would be a terrible idea" does have a reason why: because if you did that, students wouldn't know about these great programs. The bolded portion does not have a reason why: "our unique programs cannot attract students if we do not properly market them" is given as a fact without the rest of the argument explaining why.

From that, you should see that the second bolded portion exists to support the author's conclusion. This will narrow you down to choices "The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion." and "The first is a conclusion that the dean supports; the second is evidence for that conclusion.".

From there, play the answers against each other. "The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion." says that the second portion is used to support the dean's conclusion, while "The first is a conclusion that the dean supports; the second is evidence for that conclusion." says that it's evidence for "that conclusion," meaning the first bolded portion. "our unique programs cannot attract students if we do not properly market them" does support the conclusion that cutting marketing would be a bad idea (choice "The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion.") but it doesn't support the idea that "we should cut unnecessary costs" (choice "The first is a conclusion that the dean supports; the second is evidence for that conclusion."). So the correct answer is "The first is a consideration that the dean agrees with; the second is support for the dean’s conclusion.".

In Method of Reasoning questions, the correct answer must be a completely-accurate description of the argument - your goal then should be to attack each answer choice to find a word or phrase that doesn't fit. Method of Reasoning makes for good process of elimination.

Choice "Claims that her decision is the only logical course of action." is incorrect in that the hiker does not single her decision out as the ONLY logical decision: she considers the merits of two other decisions and arrives at one she feels is best. Choice "Claims that her decision is the only logical course of action." is too strong.

Choice "Chooses a course of action based on experience in similar situations." is incorrect because the concept of experience never comes up in the argument. Similarly, choice "Makes a unilateral decision by dismissing the recommendations of others." mentions the recommendations of others but in the argument as given the only options discussed come straight from the hiker herself.

Choice "Recommends a choice based on the elimination of alternative options." is correct: she eliminates two options and arrives at the third, so it is true that she recommends a course of action based on the elimination of others.

And choice "Outlines the risks and benefits of all available courses of action." is incorrect in large part because of the word "all" - you do not know that the three options she discusses are the only available options, so "all" could include others. And she does not talk about the risks associated with the third plan, so she does not discuss the risks even of "all" plans that are included. 

The course of action that is advised against is planting genetically-altered trees to remove toxins. The similar, but limited, course of action is long-term research involving the planting of such trees in a closed environment. Positive results from the limited action – no serious damage to the environment – need to be seen; otherwise, we should “resist the temptation” to plant the trees in the open.

"After detailing concerns with two approaches to a problem, both are discarded in favor of an approach that does not raise the same concerns." This choice mentions two approaches, and then “another approach,” making for three approaches in total. However, only two approaches are ever mentioned: planting them in the general environment, or planting them in a closed environment.

"A possible future scenario is described as being unrealistic, while a different scenario is given more credence." No particular scenario is ever described as unrealistic.

"An experiment is recommended to determine the benefits of a new approach to a longstanding problem for which no other comparable solution is known." This choice starts out fine, but we cannot say that “no other comparable solution is known.” If anything, we are told that naturally occurring trees can be used to remove toxins, though slowly.

"The benefits and disadvantages of two remedial courses of action are weighed." It is not clear that the argument presents two distinct remedies. Even if we consider planting the trees in an open environment to be one remedy and planting the trees in a closed environment to be another remedy, no disadvantages to planting the trees in a closed environment are mentioned. If we consider planting naturally-occurring trees to be a second approach, then this answer choice does not even mention long-term research.

The correct answer is "A course of action is advised against unless a similar, but limited, course of action produces positive results."

The students have specifically expressed their concern that they can't borrow the materials from a public library, which is why they want the library open. The university administration counters with an alternative solution to the problem -- access the materials online. Accordingly, choice "The administration counters a concern with an alternative." is the correct answer. Answer choice "The administration incorrectly makes an assumption about students' preferences." is incorrect because it is not clear that the administration is assuming anything about the students' preferences; nor is it certain that, even if the administration assumes that the students will prefer online materials to hard copies, that assumption will be incorrect. Answer choice "The administration provides an explanation that it assumes will clarify its decision." is also incorrect; the administration does not explain its decision to close the library, but rather offers an alterative solution. Answer choice "The administration defends its actions by criticizing the logic of its opponents." is incorrect, as the administration does not criticize the students at all, but rather addresses their concerns. Similarly, answer choice "The administration makes an unwarranted assumption about the motives of some of the students." is also incorrect, as the administration does not address the motives of the students at all.