First, four practice CR questions asking for the assumptions of arguments.
1) In anticipation of the coming year, Tecumseh Autos, a national auto manufacturer, is anticipating sales of its vehicles. Tecumseh manufactures compact cars, sedans, minivans, trucks, SUVs, and sports cars. In all categories of vehicles, Tecumseh sets prices so that the profit per vehicle is, on average, about the same. Since the best indicator for sales in each category are the sales last year, Tecumseh’s marketing analysts’ prediction of the three most profitable categories of vehicles in the coming year will be compact cars, minivans, and SUVs respectively.
Tecumseh’s marketing analysts’ prediction relies on which one of the following assumptions?
(A) Across all manufacturers, the most popular cars on the road in America are compact cars, minivans, and SUVs.
(B) The models of Tecumseh’s compact cars to be sold in the upcoming year are identical to or similar to those of last year.
(C) Last year, no other category of Tecumseh’s vehicles generated more profits than SUVs and less than minivans.
(D) The prediction will be refined after an analysis of the sales in the first quarter of this year.
(E) The number of models of compacts cars that Tecumseh produces is greater than the number of models of either minivans or SUVs.
2) Most people can gain vitamin C from fruits such as oranges and cantaloupes. People with Laestrygonian Disease have weakened digestive systems that cannot digest fruit or vitamin supplements. The easiest foods for these people to digest are grains such as rice and barley. Regular intake of vitamin C would be extremely beneficial to those who suffer from Laestrygonian Disease, so scientists have figured out a way to create “fortified rice” by infusing rice with high doses of vitamin C. This fortified rice will provide great benefit to those with Laestrygonian Disease.
Which one of the following is an assumption on which the conclusion depends?
(A) Eventually, this fortified rice will be the optimal way for most people to have a regular intake of vitamin C.
(B) The problems that folks with Laestrygonian Disease have digesting fruit are different from their problems digesting vitamin supplements.
(C) People with Laestrygonian Disease will not be unable to assimilate the form of vitamin C that is present in the fortified rice.
(D) Only people whose diets consist largely of grains would be able to derive benefit from the vitamin C in the fortified rice.
(E) Vitamin C is the only nutrient which can be infused into rice in such high quantities without compromising the nutritional integrity of the vitamin.
3) Sale Analyst: When polled, all consumers consistently say that, for household staples, they would buy the lowest cost items. Even when other factors, such as inherent product quality, are introduce, all consumers still argue that low cost should be the highest priority in buying household staples. Therefore, these responses demonstrate how little most people are aware of the actual priorities that drive their purchasing decisions.
The conclusion above is properly drawn if which of the following is assumed?
(A) Many people on restricted incomes are not able to afford any brands of household staples more expensive than the lowest cost items.
(B) Consumers do not always have the motivation to be truthful about their real motivations when responding to a stranger giving a poll.
(C) Often, higher priced brands of household staples, especially organic versions, are more nutritious and are rated better-tasting in double-blind tests.
(D) People often give unreliable and self-contradictory explanations after the impulse purchase of a snack or dessert.
(E) For many household staples, famous name brands with recognizable ads consistently outsell less expensive brands of the same products.
4) Urban planner: The mayor of Dismaston supports a new tax code that would assess local businesses on the property value of their site rather than on their income or profits; the mayor argues that this change will not contribute to any loss in tax revenue for the city. Several city council members disagree, citing similar changes to tax code that were unsuccessful in cities similar to Dismaston. The council members’ argument is without merit, though, because property values rise steadily each year, while business incomes fluctuate wildly with the national economy.
Which of the following is an assumption on which the argument depends?
(A) The new tax code would not apply to the significant number of online business associated with the city that have no physical presence on a piece of property in the city.
(B) In previous years, the successes and failures of many previous Dismaston tax codes to generate income have been mirrored by similar tax codes in the the same cities similar to Dismaston in other respects.
(C) A small number of store fronts in the downtown neighborhood are vacant: under the new code, these businesses are likely to owe higher taxes than they have paid, unless some loophole is written into the law.
(D) The annual percentage rise in real estate values in Dismaston has been consistently more than the average annual growth rate percentages across all businesses with properties in Dismaston.
(E) In any year, some unsuccessful businesses will close and other businesses, some quite promising, will open, but total amount of property in the city is fixed and unchanging, providing greater stability.
Detailed explanations will come at the end of this article.
Assumptions are the linchpins of arguments, the glue that binds together the evidence and the conclusion. Ideally, assumptions are what make the conclusion follow logically from the evidence. I have already written about assumptions in CR arguments in two blogs:
If you are not familiar with the Negation Test, then I would definitely recommend studying this powerful technique for isolating assumptions of arguments.
If you had any insights reading this blog or the linked blogs, you may want to revisit the questions at the top before jumping into the explanations below. If you have discovered your own strategies for analyzing the assumptions of arguments, please feel free to let us know in the comments section!
Practice problem explanations
1) The credited answer is (C). Tecumseh predicts the best-selling vehicle categories this year will be, in order, (1) compact cars, (2) minivans, and (3) SUVs. Since they used last year’s sale to make these prediction, those three categories must have been first, second, and third in last year’s sale. Sales are probably based on total revenue, but because every model of car generates approximately the same amount of profit, the order in sales would be the same as the order in profit. Thus, last year, compact cars generated the most profit, minivans the second most, and SUVs the third most. Thus, no other car had profits between minivans and SUVs.
The scope of (A) is too wide. The most popular cars on the road would include many makes, not just cars from Tecumseh. What is true for other manufacturers may or may not be true for Tecumseh. This choice is incorrect.
Choice (B) is not necessarily true. It could be true that some models were radically enhanced or changed. We don’t know how this year’s sales actually will proceed. All we know is Tecumseh’s prediction, and for Tecumseh to have made this particular prediction, we need not know anything about continuity or change in any model. This choice is incorrect.
Choice (D) might be a good idea, but this would be well after the fact, well after the prediction. In this argument, we are not as interested in whether the prediction will be true: we are simply interested in how the marketing analysts arrived at this particular prediction. What they do afterwards might be great, but it doesn’t play into the logic of how they made the prediction. This choice is incorrect.
Choice (E) is not precise. The total number of compact cars that Tecumseh sold last year must be greater than the total number of minivans, but we have no information about how many models Tecumseh has in each category. Suppose they had one one model of compact car, and sold a thousand of them, and suppose they had twelve models of minivans and sold ten of each. They would have sold many more compact cars, and have generated much more in profits in that category, despite the fact that they have only one model. This choice is incorrect.
2) The credited answer is (C). If folks with Laestrygonian Disease cannot assimilate the Vitamin C in the rice, then it won’t help them, and eating the fortified rice will not provide them any particular benefit. If we negate this option, it shatters the argument. This is a true assumption.
(A) This may be true, although I am skeptical that any human-made improved food would be better than the fruits designed by Nature! Regardless, whether this is true or not does not have any bearing on how helpful the fortified rice will be for the folks with Laestrygonian Disease. This option is incorrect.
(B) This is intriguing. Let’s negate this. Suppose it were the exact same problem, say, the exact same missing enzyme, that made it impossible to digest both fruit and vitamin supplements. Then what? Would that mean they also couldn’t digest the fortified rice, or get the vitamin C they need from it? We cannot say. It’s conceivable that the argument could still work, so negating this does not destroy the argument. This is not an assumption.
(D) Let’s negate this. Suppose the fortified rice benefits everyone—even the no-carbs fanatic who hasn’t touched carbs in a decade: even when this person breaks his carb-fast and has the fortified rice, he has benefit from it. What then? Whether these other people benefit or not from the fortified rice has no bearing on whether it helps the folks with Laestrygonian Disease. This choice is incorrect.
(E) Let’s negate this. Suppose we can infused dozens of other vitamins and minerals into the rice, all with high nutritional yield. That would only be good for the folks with Laestrygonian Disease—the more vitamins, the better! It certainly would not impact whether these folks derived any benefit from the vitamin C in the rice. This choice is incorrect.
3) This argument contains an interesting leap. Folks say they will buy the cheapest items, therefore, they aren’t aware of their actual purchasing patterns. This means, the sales analyst must be assuming that many consumers buy brands of household staples that are not the cheapest.
The credited answer is (E). If famous brand of household staples are more expensive yet outselling the cheaper no-name brand, then it must mean that the vast majority of consumers are buying them. This behavior belies their stated priorities. This would justify the Sale Analyst’s conclusion about the divergence of their stated priorities and their actual purchases.
(A) This is a relatively small segment of the population, and it would not explain the macro-patterns that the author is addressing. Also, keep in mind, the difference in price between the cheapest brand of a household staple and a more expensive name-brand might be under 50¢. Even for people on Food Stamps, if these folks really wanted the more expensive brand on that single item, they probably could afford it. For a few reasons, this answer does not work.
(B) Let’s negate this. Suppose consumers are 100% swear-on-the-Bible truthful in what they tell pollsters. If anything, this would strengthen the Sales Analyst’s argument: if consumers entirely candid in saying they will buy one thing, and then they go and buy something else, they really aren’t aware of their shopping priorities! Negating this could strengthen the argument, so this is not an assumption.
(C) This is tempting. Certainly if these more expensive brands are organic and nutritious and yummy, there would be a number of reasons that people might buy them. BUT, do we know that people will actually shell out the extra money to buy them? Maybe, maybe not. If we had evidence that consumers actually were purchasing these more expensive brands, that would be a compelling assumption: unfortunately, as is, this is only suggestive. This choice is incorrect.
(D) This is suggestive. Suppose explanations after an impulse purchase are unreliable. Does this mean that explanations before the purchase of a household staple would also be unreliable? Maybe, maybe not. This might suggest some kind of pattern, but we don’t have the evidence to conclude anything. This option is incorrect.
4) This is a very tricky argument. The mayor has a new tax code: tax business on property value, not on business income. (In real world terms, these seems a most dubious plan!) Some city council members disagree for various reasons. The actual argument that concerns us is the speaker’s argument, the argument of the Urban Planner. The Urban planner disagrees with these city council members, so in essence, he agrees with the mayor and thinks the mayor’s plan is a good one. The urban planner’s stated reason is that business income fluctuates wildly, and therefore it must not be as dependable a source of income via taxes as are the steadily rising levels of property values. In other words, taxes on property will go steadily up, and therefore will make more money than the up-and-down yields from business income taxes.
The credited answer is (D): Let’s negate this. Suppose the annual percentage rise in real estate values, in property values, has been consistent less than the average annual growth rate percentages across all businesses with properties in Dismaston. Thus, even though individual business may be fluctuating, when we average over all businesses, the growth rate is higher for that average than is for property values. Thus, revenue from taxes on business income would grow faster than revenue from taxes on property. If this negation is true, it devastates the mayor’s position, and therefore devastates the position that the Urban Planner is taking. Because the negation is so destructive, the un-negated version that appears in choice (D) must be an assumption.
(A) Presumably, business that have no physical presence would not fall under this new tax code; if all these business with no physical property went from their current tax to zero, that would be a major income loss, and such a loss presumably would be obvious to the mayor who claims that there will be no loss. What tax code applies to these online businesses is unclear, but this is out of scope. This choice is incorrect.
(B) This is suggestive of the conclusion of the council member’s argument. If other Dismaston tax codes have fared about as well as similar codes in similar cities, we might expect the same for the current code. This is suggestive, but not conclusive, and it supports the wrong argument, the council member’s argument, not the urban planner’s argument. This choice is incorrect.
(C) If there’s no loophole, this would support the mayor’s plan, which would support the urban planners argument. This is a support, but not an assumption. Even if the loophole is written and the small number of vacant storefront pay nothing, this does not necessarily mean anything about the success or failure of the mayor’s plan. This choice is incorrect.
(E) Well, if we totally negate this, then it would mean that there’s total business stability in Dismaston: the same businesses now have all been in business for 50 years, and all will continue in business for at least another fifty years. It’s not particularly clear if this makes any difference at all to the mayor’s plan. Since negating it doesn’t destroy the mayor’s plan, this is not an assumption. This choice is incorrect.