This question tests your understanding of gerunds and prepositions in English grammar. The structure of the sentence requires specific verb forms after the preposition "of".

The sentence is: "One way of _____ the wealth or poverty of a country is by _____ out how much it produces in one year."

The key to solving this is to identify that the words "of" and "by" are both prepositions. A fundamental rule in English is that a preposition must be followed by a noun, pronoun, or a gerund (a verb form ending in '-ing' that functions as a noun).

Step 1: Analyze the first blank
The first blank comes after the preposition "of". Therefore, it must be filled with a gerund (an '-ing' form of the verb). Looking at the options, both "determining" and "finding" are gerunds. "Determine" and "to determine" are incorrect here because they are an infinitive and a base form, which cannot follow a preposition directly.

Step 2: Analyze the second blank
The second blank comes after the preposition "by". The same rule applies; it must be followed by a gerund. Therefore, "finding" is the correct choice. "To find" is an infinitive and is grammatically incorrect in this position.

Step 3: Evaluate the options
Let's examine each pair:

• determining / finding: Both "determining" and "finding" are gerunds, making them the correct choices to follow the prepositions "of" and "by".
• determining / to find: "to find" is an infinitive and cannot follow the preposition "by".
• determine / finding: "determine" is a base verb form and cannot follow the preposition "of".
• to determine / finding: "to determine" is an infinitive and cannot follow the preposition "of".

Final Answer: The correct words to fill in the blanks are determining and finding.

Related Topics & Formulae

Gerunds: A gerund is a verb form that ends in '-ing' and acts as a noun in a sentence (e.g., Swimming is fun. I am good at drawing).

Prepositions: Words that show the relationship between a noun (or pronoun) and other words in a sentence (e.g., of, by, for, with, about). A simple "formula" to remember is: Preposition + Noun/Pronoun/Gerund.

Infinitive: The base form of a verb preceded by "to" (e.g., to find, to determine). It is used as a noun, adjective, or adverb, but not directly after a preposition.