Difficulty: Hard

Average Score: 46%

Step 2: x - 10x - 20 = 38
Step 3: - 9x - 20 = 38
Step 4: - 9x = 58
Step 5: x = - 58/9

In which step does Paul's work include a mistake?

Rationale

Paul's work includes a mistake in Step 2.

In Step 2, Paul misapplies a crucial formula or concept that leads to an incorrect calculation or conclusion. This mistake affects the overall accuracy of his results, making it essential to identify and correct to ensure the integrity of the entire work.

A (Step 1) YOUR ANSWER

In Step 1, Paul correctly establishes the foundational information necessary for the subsequent steps. This initial setup is critical and does not contain any errors, thus ruling it out as the source of the mistake.

B (Step 2) CORRECT

This step contains the error where Paul incorrectly applies a formula or misinterprets a key concept. The mistake made in this step has ramifications on the calculations that follow, making it the pivotal point of failure in his work.

C (Step 3) YOUR ANSWER

Step 3 builds upon the results from Step 2, but since Step 2 is where the error occurs, Step 3 simply reflects the consequences of that mistake rather than introducing a new error. Therefore, it cannot be considered the point of mistake.

D (Step 4) YOUR ANSWER

In Step 4, Paul attempts to analyze the results from Step 3. While this step may have inaccuracies due to the earlier mistake, it does not contain an original error in the reasoning or calculations presented.

E (Step 5) YOUR ANSWER

Step 5 summarizes the findings and conclusions drawn from earlier steps. Although it may include misleading conclusions based on previous mistakes, the original error does not originate here but rather in Step 2.

Conclusion

Identifying the source of mistakes in a sequence of work is crucial for maintaining accuracy. In this case, Step 2 is where Paul makes a significant error, impacting all subsequent steps. Recognizing and correcting this mistake is essential for validating the overall work and ensuring that conclusions drawn are based on correct calculations and reasoning.