Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Certain instruments used in veterinary surgery can be made either of stainless steel or of nylon. In a study of such instruments, 50 complete sterilizations of a set of nylon instruments required \(3.4\) times the amount of energy used to manufacture that set of instruments, whereas 50 complete sterilizations of a set of stainless steel instruments required \(2.1\) times the amount of energy required to manufacture that set of instruments. If the statements above are true, each of the following could be true EXCEPT: (A) The 50 complete sterilizations of the nylon instruments used more energy than did the 50 complete sterilizations of the stainless steel instruments. (B) More energy was required for each complete sterilization of the nylon instruments than was required to manufacture the nylon instruments. (C) More nylon instruments than stainless steel instruments were sterilized in the study. (D) More energy was used to produce the stainless steel instruments than was used to produce the nylon instruments. (E) The total cost of 50 complete sterilizations of the stainless steel instruments was greater than the cost of manufacturing the stainless steel instruments.

Short Answer

Expert verified
Option (B) cannot be true.

Step by step solution

01

Understanding the Proportions

We are given that sterilizing nylon instruments takes 3.4 times the manufacturing energy, while sterilizing stainless steel instruments takes 2.1 times the manufacturing energy. Essentially, if the energy required to manufacture nylon is \( E_n \) and for stainless steel is \( E_s \), then the energy for 50 sterilizations of nylon is \( 3.4E_n \), and for stainless steel is \( 2.1E_s \).
02

Analyze Option (A)

Option (A) suggests that sterilizing nylon uses more energy than sterilizing stainless steel, i.e., \( 3.4E_n > 2.1E_s \). There is a possibility this is true if the manufacturing energy of nylon \( E_n \) is reasonably higher than \( E_s \) or if their ratio fits certain values.
03

Analyze Option (B)

Option (B) states that each complete sterilization of nylon uses more energy than manufacturing nylon itself. If true, \( \frac{3.4E_n}{50} > E_n \) simplifies to \( 3.4 > 50 \), which is false. Thus, sterilization does not use more energy per instance than manufacturing does.
04

Analyze Option (C)

Option (C) states more nylon instruments than stainless steel instruments were sterilized. Nothing in the problem provides a direct measure to count instruments, so this is possible depending on relative choices in amounts sterilized.
05

Analyze Option (D)

Option (D) suggests producing stainless steel uses more energy than nylon, i.e., \( E_s > E_n \). This may or may not be true since we lack direct energy cost values but is plausible depending on efficiencies.
06

Analyze Option (E)

Option (E) assesses that the cost of sterilizing stainless is higher than production cost \( 2.1E_s > E_s \). Therefore, \( 2.1 > 1 \) is trivially true, showing sterilization uses more total energy than manufacturing independently these instruments.
07

Identify the False Statement

After reviewing each statement, option (B) is the only one that arrives at a mathematical contradiction, as the energy per sterilization cannot exceed the manufacturing one by their ratio.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Energy Consumption
Energy consumption plays a crucial role in decision-making, both for economic and environmental reasons. In the context of this exercise, evaluating the energy used in the sterilization and manufacturing process for veterinary surgery instruments is important.

When comparing energies, you'll often see terms like "times the energy," meaning how much more energy one process uses compared to another. For instance, if sterilization uses "3.4 times" the energy it takes to manufacture the instruments, this signals that the sterilization process is much more energy-intensive than production. It's essential to grasp this multiplier effect as it directly impacts costs and resource management.

By understanding energy consumption in devices, such as the veterinary tools in this exercise, we gain insights into optimizing both manufacturing and operating costs. This encourages advancements in techniques and materials, potentially lowering energy needs in the future.
Veterinary Surgery
Veterinary surgery involves various procedures necessary for the health and well-being of animals. Instruments used in these surgeries are critical, and their preparation, including sterilization, must comply with stringent sanitary standards.

Instruments made from different materials can behave differently. For instance, stainless steel is durable and generally more resistant to damage during sterilization. Nylon, while lighter and sometimes cheaper, may not endure as many sterilization cycles, leading to higher energy costs as reflected in the exercise data.

Different surgeries require specific instruments, and veterinary surgeons choose materials based on the intended purpose and the animals being treated. A deeper understanding of these instruments' properties can aid in better choice, ensuring effective surgeries while considering the environmental and energy costs.
Instrument Sterilization
Sterilization of instruments is essential in any surgical practice to prevent infections. This process requires the application of heat, chemicals, or radiation, all of which demand significant energy.

In the exercise, it's shown that nylon instruments require more energy for sterilization compared to their stainless steel counterparts. This could be due to the lower thermal tolerance of nylon, necessitating more careful, and energy-intensive cycles to ensure complete sterilization without damage.

Efficiency in sterilization processes is critical to minimize not only energy consumption but also to prolong the lifespan of the instruments. Through careful selection of materials and process optimization, veterinary practices can effectively manage their environmental impact and reduce operational costs over time.
Mathematical Contradiction
A mathematical contradiction occurs when an assumption or statement negates itself or leads to an impossible conclusion. In logical reasoning exercises, identifying contradictions is key to solving problems.

In the given exercise, option (B) presents a contradiction by claiming each sterilization requires more energy than the manufacturing of the instrument itself. Simplifying gives an incorrect inequality \(3.4/50 > 1\), suggesting sterilization per instance uses more energy than producing one instrument, which is false as sterilization percentage exceeds that of production.

Identifying such contradictions helps in refining arguments and developing better problem-solving skills. Recognizing that a statement leads to an impossible outcome is a powerful tool to understand the underlying logical framework of any problem, assisting students and professionals alike in making reasoned decisions.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Infants younger than six months who have normal hearing can readily distinguish between acoustically similar sounds that are used as part of any language not only those used in the language spoken by the people who raise them. Young adults can readily distinguish between such sounds only in languages that they regularly use. It is known that the physiological capacity to hear begins to deteriorate after infancy. So the observed difference in the abilities of infants and young adults to distinguish between acoustically similar speech sounds must be the result of the physiological deterioration of hearing. The reasoning in the argument is flawed because the argument (A) sets an arbitrary cutoff point of six months for the age below which infants are able to distinguish acoustically similar speech sounds (B) does not explain the procedures used to measure the abilities of two very different populations (C) ignores the fact that certain types of speech sounds occur in almost all languages (D) assumes that what is true of a group of people taken collectively is also true of any individual within that group (E) takes a factor that might contribute to an explanation of the observed difference as a sufficient explanation for that difference

Recently discovered fossil evidence casts doubt on the evolutionary theory that dinosaurs are more closely related to reptiles than to other classes of animals. Fossils show that some dinosaurs had hollow bones a feature found today only in warm-blooded creatures, such as birds, that have a high metabolic rate. Dinosaurs had well-developed senses of sight and hearing, which is not true of present-day cold-blooded creatures like reptiles. The highly arched mouth roof of some dinosaurs would have permitted them to breathe while eating, as fast-breathing animals, such as birds, need to do. Today, all fast-breathing animals are warm-blooded. Finally, fossils reveal that many dinosaurs had a pattern of growth typical of warmblooded animals. The argument in the passage proceeds by (A) attempting to justify one position by demonstrating that an opposing position is based on erroneous information (B) establishing a general principle that it then uses to draw a conclusion about a particular case (C) dismissing a claim made about the present on the basis of historical evidence (D) assuming that if all members of a category have a certain property then all things with that property belong to the category (E) presenting evidence that a past phenomenon is more similar to one rather than the other of two present-day phenomena

Lucien's argument against the public-housing advocates' position is most vulnerable to which one of the following criticisms? (A) It offers no justification for dismissing as absurd the housing advocates' claim that there are many homeless people in the city. (B) It treats information acquired through informal conversations as though it provided evidence as strong as information acquired on the basis of controlled scientific studies. (C) It responds to a claim in which "available" is used in the sense of "affordable" by using "available" in the sense of "not occupied." (D) It overlooks the possibility that not all apartment buildings have vacant apartments for rent. (E) It fails to address the issue, raised by the public-housing advocates' argument, of who would pay for the construction of more low-income housing.

It might seem that an airline could increase profits by reducing airfares on all its flights in order to encourage discretionary travel and thus fill planes. Offers of across-the-board discount fares have, indeed, resulted in the sale of large numbers of reduced-price tickets. Nevertheless such offers have, in the past, actually cut the airline's profits. Which one of the following, if true, most helps to resolve the apparent discrepancy described above? (A) Fewer than 10 percent of all air travelers make no attempt to seek out discount fares. (B) Fares for trips between a large city and a small city are higher than those for trips between two large cities even when the distances involved are the same. (C) Across-the-board discounts in fares tend to decrease revenues on flights that are normally filled, but they fail to attract passengers to unpopular flights. (D) Only a small number of people who have never before traveled by air are persuaded to do so on the basis of across-the-board discount fares. (E) It is difficult to devise an advertising campaign that makes the public aware of across-the-board discount fares while fully explaining the restrictions applied to those discount fares.

The incidence in Japan of most types of cancer is remarkably low compared to that in North America, especially considering that Japan has a modern life- style, industrial pollution included. The cancer rates, however, for Japanese people who immigrate to North America and adopt the diet of North Americans approximate the higher cancer rates prevalent in North America. If the statements above are true, they provide the most support for which one of the following? (A) The greater the level of industrial pollution in a country, the higher that country's cancer rate will tend to be. (B) The stress of life in North America is greater than that of life in Japan and predisposes to cancer. (C) The staple foods of the Japanese diet contain elements that cure cancer. (D) The relatively low rate of cancer among people in Japan does not result from a high frequency of a protective genetic trait among Japanese people. (E) The higher cancer rates of Japanese immigrants to North America are caused by fats in the North American diet.

See all solutions

Recommended explanations on English Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free