Question

Which of the following statements, if true, would prove the case that the vast majority of collectors find their collections worth less than they originally paid for them? A. The world’s most expensive stamps have doubled in value in the last 12 years. B. Over the years, high-quality stamps have risen in value at a rate equal to the growth rate of the rest of the economy. C. The collecting price for a stamp is determined more by rarity than original posting value. D. Commemorative stamps from the 1940s command the best prices. E. After decades, some new issues command higher prices for collecting than their original posting.

Short answer

None of the statements prove the majority of collections are worth less.

Step-by-step solution

- Understand the Problem Statement

The task here is to identify which statement would prove that most collectors find their collections worth less than they paid for them.

- Analyze Each Statement Individually

Go through each provided statement and evaluate whether it directly supports the conclusion that most collectors find their collections worth less over time.

- Evaluate Statement A

Statement A: 'The world’s most expensive stamps have doubled in value in the last 12 years.' This statement refers to very expensive stamps. It does not address the general population of collectors, so it doesn't support the conclusion.

- Evaluate Statement B

Statement B: 'Over the years, high-quality stamps have risen in value at a rate equal to the growth rate of the rest of the economy.' This suggests that some high-quality stamps maintain their value relative to the economy but does not suggest that the majority of collectors' stamps have devalued.

- Evaluate Statement C

Statement C: 'The collecting price for a stamp is determined more by rarity than original posting value.' This is about how prices are determined but doesn’t provide evidence on overall value trends for most collectors.

- Evaluate Statement D

Statement D: 'Commemorative stamps from the 1940s command the best prices.' This suggests certain stamps have high value, but doesn’t give information on the general trend affecting most collectors' collections.

- Evaluate Statement E

Statement E: 'After decades, some new issues command higher prices for collecting than their original posting.' This implies a rare scenario where stamps appreciate, not addressing the general case of most collectors.

- Conclude the Evaluation

None of the statements directly prove that the vast majority of collectors find their collections worth less. However, they do provide insight into specific scenarios influencing stamp value.

Key concepts

critical thinking

Critical thinking is essential in problem-solving, especially for GMAT questions.
This involves understanding the problem, breaking it down, and considering all provided information carefully.
To tackle the given exercise, we began by grasping the primary question - identifying evidence indicating that most collectors find their collections worth less.

To develop critical thinking:

• First, determine the main goal or question.
• Then, consider each piece of information provided.
• Next, evaluate how these pieces of information relate to the main goal.
• Finally, derive a reasoned conclusion based on your analysis.

This incremental approach is what we used in the step-by-step solution, allowing us to systematically rule out irrelevant statements.

evaluation of statements

Evaluation of statements is crucial in determining which information is relevant to the problem at hand.
This involves analyzing each statement and how it pertains to the initial assumption.

For the given exercise:

• We looked at each statement provided.
• We examined whether a statement provided evidence or contradicted the claim that most collectors find their collections worth less.
• This required understanding the context and details within each statement.

For instance, Statement A addresses very expensive stamps but not the general collector population.
Through precise evaluation, we could conclude it's not applicable to the general trend.

logical reasoning

Logical reasoning allows us to connect different pieces of information to form a cohesive argument.
It involves making inferences and reaching conclusions based on provided data.

The step-by-step solution used logical reasoning to:

• Determine whether the statements support the assumption.
• Identify gaps in information provided by each statement.
• Dismiss statements that do not directly support the assumption.
  For example, Statement C discusses how prices are determined, not overall value trends.

Logical reasoning requires recognizing which information is pertinent and forming a logical connection to the conclusion.

evidence assessment

Effective evidence assessment entails determining the strength and relevance of evidence in relation to the conclusion.

For this exercise, assessing the evidence involved:

• Considering whether each statement directly supports the conclusion.
• Recognizing statements offering only partial or contextual evidence, which may not directly prove the assumption.

By systematically assessing the evidence provided in each statement, we concluded none of the statements directly prove that the vast majority of collectors find their collections worth less.
However, they provide context for understanding factors affecting stamp value.
This evidence assessment approach ensures a thorough and accurate evaluation, essential for tackling GMAT problems effectively.