Here we have a strengthen with necessary premise question. Remember that a premise is necessary for a conclusion if the falsity of the premise guarantees or brings about the falsity of the conclusion. First we check to see if the answer choice strengthens the passage, and then, if it does strengthen, we negate the answer choice to see if its negation makes the argument fall apart. If the answer choice does both those things then it is our correct answer.
Conclusion: "we can be sure that the game must have originated sometime between approximately A.D. 1000 and Cortez's arrival."
Why: We are told that when Cortez arrived in Mexico in A.D. 1519, he observed the inhabitants playing a ceremonial game with a rubber ball. We also know that the pre-Columbian inhabitants of Mexico began to use rubber around A.D. 1000.
So, we must connect the concept of "first using rubber" and "playing the ceremonial game with a rubber ball."
Answer choice (D): "The game had been played since its inception with a rubber ball."
Does this strengthen? Yes. If the game had been played since its inception with a rubber ball, then it couldn't have been played before the use of rubber. Therefore, the conclusion that the game must have originated sometime between approximately A.D. 1000 and Cortez' arrival is strengthened.
Does the negation of the answer choice make the premise fall apart? Yes.
Negation: The game had not necessarily been played since its inception with a rubber ball.
This leaves the possibility that before rubber was used, the ball was made out of some other material--making it possible that the game could have originated long before the use of rubber, since it didn't originally use a rubber ball. Thus, the negation of this answer choice makes the argument fall apart
Therefore, answer choice (D) is our answer.
Hope that clears things up! Please let us know if you have any other questions.
