Question

An advertisement for Royal Rat Rations states: "7 out of 8 veterinarians recommend Royal Rat Rations for your fancy rat." No other information about the data is provided by the company. Based on this data, which of the following inferences is most valid? A) Royal Rat Rations provides the best nutrition for fancy rats. B) If you do not feed your rat Royal Rat Rations, your rat will be unhealthy. C) Only one veterinarian does not recommend Royal Rat Rations for your fancy rat. D) Of the veterinarians surveyed by Royal Rat Rations, the majority recommend Royal Rat Rations for your fancy rat. $$ \frac{1}{2} t+4=\frac{3}{4} t-5 $$

Short answer

The most valid inference based on the given data is Option D: Of the veterinarians surveyed by Royal Rat Rations, the majority recommend Royal Rat Rations for your fancy rat.

Step-by-step solution

Examine Option A

Option A claims that Royal Rat Rations provides the best nutrition for fancy rats. However, the given data only states that 7 out of 8 veterinarians recommend it. We don't have any information about the actual nutritional content of the rat rations. This inference may be too strong based on the provided information.

Examine Option B

Option B states that if you do not feed your rat Royal Rat Rations, your rat will be unhealthy. Again, the given data only communicates that the majority of veterinarians recommend this particular brand. It does not state that a rat fed a different brand will be unhealthy. This inference is unsupported by the data.

Examine Option C

Option C states that only one veterinarian does not recommend Royal Rat Rations for your fancy rat. According to the given data, this is true since 7 out of 8 veterinarians recommend the product, leaving only one veterinarian who does not recommend it. This inference accurately reflects the provided information.

Examine Option D

Option D says that of the veterinarians surveyed by Royal Rat Rations, the majority recommend Royal Rat Rations for your fancy rat. This inference is also accurate, as 7 out of 8 veterinarians recommending the product is indeed a majority.

Choose the Most Valid Inference

Based on the given information and analysis, option C and option D are accurate. However, option D provides a slightly more comprehensive view of the situation, stating that the majority of the surveyed veterinarians recommend Royal Rat Rations. Therefore, the most valid inference among the given options is Option D.

Key concepts

Logical Reasoning

Logical reasoning is the process of using structured thinking to evaluate arguments and make decisions. It's important to identify what the information truly tells us and distinguish it from what it might suggest. The Royal Rat Rations advertisement claims that 7 out of 8 veterinarians recommend their product. This statement suggests reliability but does not provide detailed evidence.
Consider the exercise. Each option presents a potential inference based on the data. Recognizing that the data only provides the number of veterinarians who recommend, allows for critical assessments.
A logical reasoning approach involves:

• Evaluating the information presented: What exactly does "recommend" mean in this context?
• Questioning assumptions: Is "recommend" synonymous with "best" or "necessary"?
• Analyzing language: The term "majority" in Option D relies on a numerical understanding of 7 out of 8.

Logical reasoning also involves distinguishing between what is explicitly stated and what might be implied. This skill is vital for making valid conclusions that are supported by evidence.

Data Interpretation

Data interpretation is the ability to read and extract meaning from data points and statistics. In the context of this exercise, the data indicates how many veterinarians recommend a particular product. Interpreting this involves not just reading the numbers but understanding broader implications.
The number "7 out of 8" readily translates to:

• A majority recommendation, which is foundational to Option D's validity.
• One veterinarian not recommending the product, accurately reflecting Option C.

However, interpretation should be cautious. The data lacks details about sample size, selection methods, and criteria for "recommendation." Semantics matter. Data without context can lead to misinformed decisions. Understanding how to interpret data critically is key in avoiding assumptions or overgeneralized conclusions.

Problem Solving

Problem solving involves applying different strategies systematically to find solutions. Here, the task is to identify the most valid inference based on the given data. The approach is step-by-step evaluation: examining each option against the provided facts.
Strategies for effective problem solving include:

• Carefully analyzing each statement: Is it logical given the full information?
• Cross-referencing the data: Does it confirm or refute each potential inference?
• Prioritizing clarity: Which inference best reflects all known facts?

In this case, Option D emerges as the most valid inference because it aligns directly with the definition of a majority. Critical thinking plays a fundamental role in assessing possible solutions to ensure they fit accurately with available data.

SAT Preparation

SAT preparation requires familiarity with critical thinking and problem-solving skills, as these are core elements of the test. Questions often simulate real-world scenarios, requiring logical deduction based on limited data.
This exercise mimics these conditions by asking for valid conclusions from an advertisement claim. Successfully navigating such questions involves:

• Analyzing provided statements to see how they align with given data.
• Understanding statistics and probability to evaluate what terms like "majority" denote.
• Practicing concise reasoning and avoidance of assumptions in real-world scenarios.

Inferences, predictions, and conclusions formed from raw data must be backed by evidence, just as the exercise illustrates with the veterinarian recommendation problem. Mastery over these skills prepares students not only for the SAT but for various real-life problem-solving situations.