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This chapter is from the book

Logical Reasoning Question Types

A careful analysis of past, released LSAT exams reveal that there is a limited number of types of questions that appear on the Logical Reasoning sections. We’ve listed them below, along with specific strategies for each one. If you haven’t done so yet, review Chapter 3 before going any further in this chapter. In our following discussion, we assume that you are familiar with the terminology and concepts found in Chapter 3.

The Logical Reasoning question types found on the LSAT are

  • Assumption
  • Weaken/Strengthen
  • Conclusion
  • Method of Argument
  • Principle
  • Point of Contention
  • Role of Fact
  • Flaw
  • Paradox
  • Parallel Structure

Question Type: Assumption

Assumption questions ask you to identify the missing link in the logic of the stimulus argument.

Some example question stems are

  1. Which one of the following, if assumed, allows the argument’s conclusion to be properly drawn?
  2. Which one of the following is an assumption on which the argument depends?
  3. The final conclusion above follows logically if which one of the following is assumed?
  4. The claim made by the official in the argument above depends on the presupposition that
  5. Which one of the following is an assumption on which the argument relies?

Strategies

The most time-efficient way to answer assumption questions is to recognize the missing link in the argument as you read the stimulus. Sometimes, the wording of the argument and the answer choices can be confusing. So, you might want to employ the technique of negating the answer choices that you want to test. Negation is fully explained in Chapter 3, “Introduction to LSAT Logic.”

Because an assumption is an unstated piece of evidence, this technique “knocks out” each answer choice that you test, one by one. When you test the correct answer, you are knocking out a piece of evidence, and the argument should suffer accordingly.

In tutoring sessions, we often use the analogy of testing to see if a wall within a house or an office is important to the structure by knocking the wall down to see if the roof falls in. If the roof falls in, we have shown that the wall was important. If there is no effect on the structure, the wall was not a load-bearing wall. In other words, the wall was irrelevant to the strength of the structure.

Sample Assumption Question

Consider the following example:

  1. The birth rate in Country X is down this year by 12% compared to last year. The death rate in Country X has remained stable for several years. Therefore, the population of Country X is decreasing measurably.

    Which of the following is assumed by the author of the argument above?

    1. The causes of the declining birthrate in Country X can be discovered through physician surveys.
    2. Statisticians are able to predict future changes in the size of the population of Country X.
    3. Country Y, which has a nearly identical population to Country X, is experiencing the same population shift as Country X.
    4. There was no significant migration into Country X during the time under discussion.
    5. The causes of the declining birthrate in Country X are primarily economic in nature.

The best answer is D. You might be able to answer the question directly by simply recognizing the missing piece of evidence and selecting it. However, if you aren’t able to do so, you can still determine the correct answer by negating whichever answer choices you view as potentially correct. It is not likely that you will have time to carefully negate each choice presented. So, you will need to “filter out” choices that you find clearly irrelevant.

Let’s say that you could easily recognize that answer choice C is irrelevant since it discusses Country Y and, therefore, it can’t possibly be the missing link between the stated evidence and the stated conclusion, which both involve Country X. Likewise, let’s say that you could eliminate answer choice B, which is about predicting the future, whereas the stimulus argument is about the recent past.

That leaves answer choices A, D, and E still in contention. Try to negate answer choice A. You should come up with something like: “The causes of the declining birthrate in Country X cannot be discovered through physician surveys.” Since physicians play no part in the stimulus argument, you should recognize that neither the original phrasing of answer choice A, nor its negation, has any bearing on the relationship between the evidence and the conclusion stated in the argument. Similarly, negating E with “The causes of the declining birthrate in Country X are not primarily economic in nature,” has no impact on the likelihood that the conclusion is valid. However, if you negate answer choice D, you get “There was significant migration into Country X during the time under discussion.” This would dramatically call into question the stated conclusion that the population of Country X is declining measurably. Therefore, answer choice D must be correct.

Question Type: Weaken/Strengthen

You will have to attack a significant number of weaken and strengthen questions in order to end up with a respectable LSAT score. This question type also sometimes appears in the Reading Comprehension section of the exam. Since the LSAT is set up to test your understanding of the structure of arguments, the correct answer choices for weakening and strengthening questions will more often undermine or support their respective conclusions structurally rather than by directly attacking stated evidence, or by providing new evidence. You can undermine conclusions by finding a key assumption in the argument and then finding the answer choice that will make that assumption more likely to be true or less likely to be true, as the case may be.

Some example question stems are

Weaken

  1. Which one of the following, if true, would most weaken the above argument?
  2. The prediction that ends the paragraph would be most seriously called into question if it were true that
  3. Which one of the following, if true, most weakens the researcher’s argument?
  4. Which one of the following, if true, most calls into question the argument that…?
  5. Which one of the following, if true, most undermines the conclusion?
  6. Which one of the following, if true, would be the strongest challenge to the author’s conclusion?

Strengthen

  1. Which one of the following, if established, does most to justify the position advanced by the passage?
  2. Which one of the following, if true, provides the best reason in favor of the proposal?
  3. Which one of the following, if true, most strengthens the argument?
  4. Which of the following principles, if valid, most helps to justify the scientist’s reasoning?
  5. Which one of the following, if true, most helps to support the claim that…?
  6. Which one of the following, if true, most supports the proposal?

Strategies

To answer either a weaken or strengthen question, you must first identify the key assumptions in the argument. This should become second nature to you as you practice for test day. Once you become proficient at identifying assumptions, you can more easily choose answers that either support or undermine them. In some cases of weaken questions, the correct answer actually contradicts a statement made in the stimulus argument.

Sample Weaken/Strengthen Questions

Consider the following example:

  1. More and more computer software that is capable of correcting not just spelling, but also grammar and punctuation is being developed. Therefore, it is increasingly unnecessary for working reporters and writers to have a complete knowledge of the principles of English grammar and punctuation. Consequently, in training journalists, less emphasis should be placed on the principles of grammar so that students and professors can concentrate on other important subjects.

    Which one of the following, if true, most seriously weakens the argument given for the recommendation above?

    1. The effective use of software that corrects grammar and punctuation requires an understanding of grammatical principles.
    2. Much of the software that corrects grammar and punctuation is already in use.
    3. Development of more complex ethical guidelines for reporters and writers has meant that professors and students in journalism schools must allow time for teaching such issues.
    4. Most of the software that is capable of correcting grammar and punctuation can be run on the types of computers available to most media outlets.
    5. The journalism curriculum already requires that journalism students be familiar with, and able to use, a variety of software packages.

The best answer is A. If journalists must be able to understand the principles of grammar in order to effectively use the software described, the conclusion of the argument—that less emphasis should be placed on such principles in journalism school—is less likely to be true. Answer choices B, D, and E are irrelevant to the argument. Answer choice C actually strengthens the argument by making the conclusion just slightly more likely to be true.

Question Type: Conclusion

These questions ask you to draw a conclusion from evidence presented within the stimulus. In some cases, the conclusion that you are asked to draw is based on only part of the stimulus and will not necessarily be the main idea of the stimulus paragraph. Some conclusion questions use the terms “infer” and “imply.”

Some example question stems are

  1. If the statements above are true, which one of the following must also be true on the basis of them?
  2. If the environmentalist’s statements are true, they provide the most support for which one of the following?
  3. Which one of the following statements is most strongly supported by the information above?
  4. Amy’s reply is structured to lead to which one of the following conclusions?
  5. Which one of the following inferences is most strongly supported by the information above?
  6. Which one of the following can be properly inferred from the argument above?

Strategies

To correctly answer these questions you must consider the validity of the argument. Look for the logical end of the chain of reasoning started in the stimulus argument.

Sample Conclusion Question

Consider the following example:

  1. Physician: The continued use of this drug to treat patients with a certain disease cannot be adequately supported by the proposition that any drug that treats the disease is more effective than no treatment at all. What must also be taken into account is that this drug is very expensive and has notable side effects.

    Which one of the following most accurately expresses the main point of the physician’s argument?

    1. The drug is more effective than no treatment at all.
    2. The drug is more effective than other forms of treatment for the disease.
    3. The drug is more expensive than other forms of treatment for the disease.
    4. The drug should not be used to treat the disease unless it is either effective or inexpensive.
    5. The drug’s possible effectiveness in treating the disease is not sufficient justification for using it.

The best answer is E. According to the physician, the fact that the drug might be somewhat effective is not enough reason to continue to use it. The physician suggests that other factors beyond mere effectiveness, such as cost and side effects, be considered when deciding whether to use the drug. Answer choice A is incorrect because, although it might be inferred from evidence presented in the stimulus, the question stem calls for the main point of the argument. Answer choices B and C are incorrect because no comparison is made between the drug and any other form of treatment for the disease. Answer choice D is incorrect because the physician also contends that the side effects of the drug should be considered when deciding whether to use the drug.

Question Type: Method of Argument

Method of argument questions ask you to recognize the way that the argument is put together. You must choose the answer that properly describes the structure of the stimulus argument. Some, but certainly not all, method of argument questions are based on dialogues.

Some examples of question stems are

  1. The scientist’s argument proceeds by
  2. Trillian’s response to Douglas proceeds by
  3. Karen uses which one of the following argumentative techniques in countering Rob’s argument?
  4. The argument criticizing the essay employs which one of the following strategies?
  5. The relationship of Svetlana’s statement to Katalya’s argument is that Svetlana’s statement

Strategies

To answer these questions correctly, you must pay attention to the structure of the argument rather than to the content or subject matter. Describe the argument in your own words (paraphrase) and try to match up the analogous parts of your paraphrased argument to the answer choices.

Sample Method of Argument Question

Consider the following example:

  1. It is widely accepted that eating sugar can cause weight gain. Indeed, many people who are susceptible to weight gain report that, in their own experience, eating large amounts of sugar is invariably followed by a measurable weight gain within a few days. However, it is likely that common wisdom has confused cause and effect.

    Recent studies suggest that hormonal changes associated with stress can cause weight gain, and there is ample evidence that people who are fond of sugar tend to eat more of it when they are under stress.

    The argument employs which one of the following argumentative strategies?

    1. It cites evidence that questions the accuracy of the evidence advanced in support of the position that is being called into question.
    2. It gives additional evidence that suggests an alternative interpretation of the evidence offered in support of the position being challenged.
    3. It relies upon the superiority of science versus common opinion as a means of dismissing the relevance of evidence based upon common experience.
    4. It shows that the position being challenged is not consistent with cited, proven factual evidence.
    5. It calls into question the intelligence of those who subscribe to a certain popularly held belief.

The best answer is B. The additional evidence provided is regarding hormonal changes causing weight gain; the alternative interpretation of the correlation between sugar consumption and weight gain is the possibility that both the weight gain and sugar consumption are, in fact, caused by stress.

Question Type: Principle

These questions ask you to identify a rule, or principle, that supports the stimulus argument presented. In some cases, you are required to choose an argument that conforms to the stimulus principle.

Some example question stems are

  1. The reasoning above most closely conforms to which one of the following principles?
  2. Which one of the following conforms most closely to the principle illustrated above?
  3. Which one of the following employee behaviors most clearly violates the company policy outlined above?
  4. Which one of the following illustrates a principle most similar to that illustrated by the passage?

Strategies

The first step in answering these questions is to identify the rule or principle in the stimulus argument. Then, select the answer choice that relies on the same rule or principle. You should generally avoid any answer choices that include the same subject matter as that of the stimulus argument; focus on the rule or principle, not on the content.

Sample Principle Question

Consider the following example:

  1. The best way to create a successful party is to visualize the guests discussing it with friends the next day. The hostess should first decide what aspects of the party will lead to favorable comments from guests during those conversations and then come up with refreshments and activities that will actually cause such post-party talk to occur.

    Which one of the following illustrates a principle most similar to that illustrated by the passage?

    1. When planning a vacation, some travelers decide first where they want to go, and then plan their route. But, for most people, financial issues must also be taken into account.
    2. When landscaping the grounds of a new home, you should start with the topsoil and then choose your shrubbery and other foliage.
    3. Good moviemakers do not extemporaneously film their movies in one or two days with no script; a movie cannot be separated from the story upon which it is based.
    4. In negotiating an employment contract, the best method is to make as many outlandish demands as possible and then agree to forgo the most outrageous of them.
    5. To make a great golf shot, you should picture the ball landing where you want it to land, and then you will be able to line up your body and your club accordingly.

The best answer is E. The underlying principle in the stimulus argument is that it is best to work backward from a desired result in order to achieve that result. In the stimulus, the desired result is a successful party. In the correct answer, the desired result is a great golf shot. Answer choices B, C, and D are incorrect because they work forward rather than backward.

Question Type: Point of Contention

These questions always involve a dialogue between two people who disagree about something. You are expected to choose the answer that best describes the crux of the disagreement.

Some sample question stems are

  1. Todd’s and Andy’s positions indicate that they disagree about the truth of which one of the following?
  2. A point on which Randy and Salvatore’s views differ is whether
  3. William and Max disagree over whether
  4. The dialogue most supports the claim that Heather and Mike disagree about whether

Strategies

Your first step is to understand, then succinctly summarize the first party’s argument. Next, determine where the first and second parties differ in their statements. Paraphrasing will help you get to the root of the argument and quickly locate the correct answer.

Sample Point of Contention Question

Consider the following example:

  1. Jason: The Internet is making more information available to more people than ever before in history. So, people can simply learn all they need to know without seeking the advice of experts.

    Mark: In the past, the need for experts actually increased as the volume of knowledge increased. Therefore, the Internet will surely increase our dependence on experts.

    The dialogue most strongly supports the claim that Jason and Mark disagree with each other about whether

    1. the Internet will contribute significantly to the increase in the spread of information throughout society
    2. the Internet will increase the likelihood that people will seek the advice of experts when searching for knowledge
    3. the Internet makes more information available to more people
    4. experts will increase their reliance on the Internet in the future
    5. explaining knowledge to specialists can only be accomplished by Internet experts

The best answer is B. Jason thinks that experts will become irrelevant because of direct public access to information. Mark thinks that the opposite will occur.

Question Type: Role of Fact

Some of the questions ask about the role, or function, of a specific fact that is included in the stimulus argument.

Some sample question stems are

  1. The claim that taxes should increase in proportion to a person’s income plays which one of the following roles in the argument?
  2. The claim in the first sentence of the passage plays which one of the following roles in the argument?
  3. Joshua’s statement that “this claim simply cannot be proved” plays which one of the following roles in his argument?
  4. Which one of the following most accurately describes the role played in the passage by the claim that fish have gills?

Strategies

To answer these questions correctly, you must determine the reason why the author included this particular fact or detail. Most of the incorrect answer choices will either be too narrow or too broad, or beyond the scope of the stimulus argument.

Sample Role of Fact Question

Consider the following example:

  1. Some environmentalists have argued that there are two independently sufficient justifications for recycling waste materials: one based on economics and the other based on the aversion to the continued consumption of pristine global resources. But suppose that recycling were not economically efficient. Then it would be less clear that an aversion to consuming pristine global resources is enough of a reason to recycle.

    Which one of the following most accurately describes the role played in the argument by the supposition that recycling is not economically efficient?

    1. It is used to disprove the environmentalist position that we should recycle.
    2. It is used to show that the two reasons given by environmentalists are each individually sufficient.
    3. It is used to disprove the claim that recycling is beneficial.
    4. It is used to weaken the claim that consumption of pristine resources is sufficient reason to recycle.
    5. It is used to show that there is no sufficient reason for recycling.

The best answer is D. The author of the argument asks the reader to go along with the supposition that recycling is not economically efficient in order to show that a mere aversion to consuming pristine resources might not be a sufficient, independent justification for recycling after all. Answer choices A, C, and E are incorrect because the argument does not actually show that there is no support for recycling. Answer choice B is incorrect because the argument is meant to question the reasons given for recycling, not to shore up the reasons given by environmentalists.

Question Type: Flaw

These questions ask you to identify an error of reasoning in the stimulus argument.

Some sample question stems are

  1. Which one of the following, if true, identifies a flaw in the plan for the program?
  2. The argument is vulnerable to criticism on the grounds that the argument
  3. The reasoning above is questionable because it fails to exclude the possibility that
  4. The reasoning in the politician’s argument is flawed because this argument
  5. Ralph’s reasoning in his response to Jessica is most vulnerable to criticism on the grounds that it
  6. Which one of the following is a questionable argumentative strategy employed in the above argument?

Strategies

The question stem tells you that a problem exists with the logic of the argument. You just have to choose the answer that describes the flaw. Most flawed arguments include an unwarranted assumption; in other words, the argument is weakened by a missing link between the stated evidence and the stated conclusion. The author of the argument is taking something for granted that is not necessarily true.

Sample Flaw Question

Consider the following example:

  1. Giant Motors is attempting to dominate the automobile market by promoting its products with an expensive television advertising campaign. But, the results of recent surveys reveal that, in the opinion of 85 percent of all consumers, Giant Motors already dominates the market. Since any product with more than half of all sales in any given market is already dominant, Giant Motors dominates the market now and must only preserve its market share in order to continue to dominate its market.

    The argument commits which one of the following errors in reasoning?

    1. Failing to eliminate the possibility that what seems to be the outcome of a specific market condition might actually be the cause of the condition
    2. Confusing a condition necessary for certain outcome to obtain for a condition that, alone, is sufficient to assure that result
    3. Treating the failure to establish the falsity of a specific claim as tantamount to showing that such a claim is certainly accurate
    4. Accepting evidence that a claim is believed to be true as evidence that the claim, itself, is actually true
    5. Describing the results of a survey that was done in the past as acceptably predicting future conditions

The best answer is D. The survey results only show the opinions of consumers. The stimulus argument relies upon those beliefs as fact in concluding that Giant Motors dominates the automobile market. There is no reason to accept the opinion of consumers as an accurate measure of Giant Motors’s actual share of the automobile market. Each of the other answer choices describes an error in reasoning that is irrelevant to the stimulus argument.

Question Type: Paradox

A paradox arises when you are presented with two statements that are both true, yet they appear to be mutually contradictory. The key words to help you spot paradox question stems are “explain” and “reconcile.”

Some sample questions stems are

  1. Which one of the following, if true, most helps to explain why the people mentioned continued to grow beans?
  2. Which one of the following, if true, most helps to explain the finding of the caffeine study?
  3. Which one of the following, if true, helps to reconcile the statements above?
  4. Which one of the following, if true, does the most to reconcile the apparent conflict in the system described above?

Strategies

The stimulus argument in paradox questions usually includes a term that either must be redefined in order to resolve the paradox, or contains a misinterpretation of a term upon which the author relies. You must recognize the contradiction that exists and look for an answer choice that more clearly defines a critical term.

We often refer to the “bumblebee paradox” with our tutoring students. Current research suggests that a bumblebee’s wings are aerodynamically unsound; as a result, a bumblebee should not be able to fly. However, bumblebees do fly, so clearly the term “aerodynamically unsound” is poorly defined.

Sample Paradox Question

Consider the following example:

  1. Researchers concur with one another on the issue of the harm that can result when children are exposed to microscopic asbestos fibers. The resulting disease, asbestosis, is almost always debilitating and even sometimes fatal. Many older school buildings contain asbestos insulation around hot water pipes and heating ducts because, until recently, the dangers of asbestos were unknown. Yet, these same researchers also agree that laws requiring the removal of asbestos from schools could actually lead to an increased likelihood of exposure to asbestos fibers to the students who attend those schools.

    Which one of the following, if true, most helps to resolve the apparent discrepancy in the researchers’ positions?

    1. New insulation materials used instead of asbestos are as potentially harmful to children as asbestos is.
    2. The money that would be spent on the removal of asbestos from schools could be spent in other ways that would be more likely to increase the overall health of school children.
    3. Other sources of asbestos, such as automobile and household uses, are responsible for more cases of asbestosis than school-based sources are.
    4. Removing the asbestos from older schools disperses a large quantity of asbestos fibers into the air, where they are more easily inhaled than when they are left in place around the pipes and ducts.
    5. Lead-based paint poses more of a health hazard to children than asbestos does.

The best answer is D. Answer choice D provides an explanation for the suggestion not to remove the asbestos. Essentially, this answer boils down to pointing out that the act of removal itself is more dangerous than simply leaving the hazard in place. Answer choices A, C, and E are all incorrect because they focus on other potential sources of harm rather than the apparent conflict between the two positions that the researchers hold simultaneously: 1) that asbestos can cause serious harm, and 2) that it should not be removed from schools. Answer choice B is incorrect because it focuses on financial issues rather than the seemingly logical inconsistency inherent in the researchers’ positions.

Question Type: Parallel Structure

These questions ask you to match up two arguments that share structural characteristics. There are usually two parallel structure questions in each Logical Reasoning section. They are usually in the second half of the section, and they can usually be recognized by their length since each answer choice is a complete argument. Sometimes the stimulus argument is flawed. In such a case, you must identify the answer choice argument that shares the same flaw.

Some sample question stems are

  1. Which one of the following arguments is most similar in its reasoning to the argument above?
  2. The flawed reasoning in which one of the following arguments most closely resembles the flawed reasoning in the professor’s argument?
  3. The reasoning in the argument above most closely parallels that in which one of the following?
  4. The flawed pattern of reasoning in the argument above is most similar to that in which one of the following?
  5. Which one of the following contains questionable reasoning most similar to that in the argument above?
  6. The pattern of reasoning in which of the following is most similar to that in the mayor’s argument?

Strategies

One way to approach the parallel structure questions is to reason by analogy. In other words, if you match up the analogous parts, the structure becomes clearer. The structure of the argument is more important than the content or subject matter of the argument.

Do not be fooled by answer choices that refer to the same subject matter as that presented in the stimulus argument. You are expected to see past the facts presented and look at the relationship between the evidence and conclusion in the argument.

Sample Parallel Structure Question

Consider the following example:

  1. Murcheson’s drawing of the Lincoln Monument contains several inaccuracies. Therefore, your attempt to reproduce the drawing of the monument will not be a very accurate reproduction of the drawing.

    Which one of the following is most similar in its flawed reasoning to the flawed reasoning in the argument above?

    1. Katrina’s presentation was made up primarily of fabrications and distortions. So the video recording made of it cannot be of good quality.
    2. An architect who creates a model of an ugly building must necessarily create an ugly model, unless the sculpture is a distorted representation of the building.
    3. If a puppy’s coloring resembles its mother’s, then if the mother’s fur is curly, the puppy’s fur must also be curly.
    4. Kelly imitated Rory. But, Kelly is different from Rory, so Kelly could not have imitated Rory very well.
    5. Quentin’s second movie is similar to his first. Therefore, his second movie must be entertaining since his first movie won many awards.

The best answer is A. The flaw in the stimulus argument is that it concludes that a reproduction of a flawed reproduction cannot, itself, be an accurate reproduction. Answer choice A makes the same mistake. In this instance, Murcheson’s drawing and Katrina’s presentation fill the same role as one another in their respective arguments. And, video recording of Katrina’s presentation is analogous to the attempted reproduction in the stimulus argument. Some of the other answer choices are also flawed arguments; however, they do not share the same structure.

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Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020