1) Explanation

Let's break down the sentence to understand the context and the meaning required for the blank:
- "Although her friends dreaded the onset of tax season, Jane's $\qquad$ nature forced her to keep carefully organized records throughout the year, and she was able to quickly and easily fill out the complex forms."
- The word "Although" sets up a contrast. Jane's friends dreaded tax season, implying it was difficult or messy for them.
- Jane, however, was able to handle it "quickly and easily" because she kept "carefully organized records throughout the year."
- Therefore, the blank needs a word that describes a nature characterized by meticulousness, diligence, precision, or extreme attention to detail, especially regarding organization and accuracy.

Let's evaluate the given options:
- A. assiduous: Showing great care and perseverance. This fits the idea of someone who diligently keeps records.
- B. mathematical: Relating to mathematics. While tax forms involve numbers, her nature is described by her organizational habits, not necessarily her mathematical ability.
- C. fastidious: Very attentive to and concerned about accuracy and detail. This perfectly describes someone who would keep "carefully organized records" and handle "complex forms."
- D. chary: Cautiously or suspiciously reluctant to do something. This is the opposite of the proactive and efficient behavior described.
- E. punctilious: Showing great attention to detail or correct behavior. This is a strong synonym for meticulous and fastidious, directly fitting the description of someone who is precise and careful with records and forms.
- F. calculating: Acting in a scheming or manipulative way. This has a negative connotation and does not fit the context of being organized for tax purposes.

Conclusion:

The context of "carefully organized records" and easily handling "complex forms" points to a nature that is highly detail-oriented, precise, and diligent. Both "fastidious" and "punctilious" are strong synonyms that convey this exact meaning. "Assiduous" also fits, but "fastidious" and "punctilious" are more precise in describing the attention to detail aspect, which is key to "carefully organized records."

The final answer is $\(\mathrm{C}, \mathrm{E}\)$.