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Example
Whether the world is Euclidean or non-Euclidean is still an open question. However, if a star’s position is predicted based on non-Euclidean geometry, then when a telescope is pointed to where the star should be it will be there. Whereas, if the star’s position is predicted based on Euclidean geometry, then when a telescope is pointed to where the star should be it won’t be there. This strongly indicates that the world is non-Euclidean.
 
Which one of the following best expresses the main idea of the passage?
  1. The world may or may not be Euclidean.
  2. The world is probably non-Euclidean.
  3. The world is non-Euclidean.
  4. The world is Euclidean.
  5. The world is neither Euclidean nor non-Euclidean.
Solution
Choice (A) understates the main idea. Although the opening to the passage states that we don’t know whether the world is non-Euclidean, the author goes on to give evidence that it is non-Euclidean.
 
Choice (C) overstates the main idea. The author doesn’t say that the world is non-Euclidean, just that evidence strongly indicates that it is.
 
In choice (B), the word “probably” properly limits the scope of the main idea, namely, that the world is probably non-Euclidean, but we can’t yet state so definitively.
 
The answer is (B).

 
Example
An oligarchy is a government run by a small, conservative faction. Often, oligarchies consist of families such as the Royal Family in Saudi Arabia. Like the Royal Family in Saudi Arabia, no one person in an oligarchy has the power to make a particular investment. Therefore, risky investments are never made by oligarchies.
 
The conclusion of the argument is valid if which one of the following is assumed?
  1. Not all oligarchies are run by families.
  2. The Royal Family in Saudi Arabia has never made a risky investment.
  3. Conservative governments rarely make risky investments.
  4. Only liberal governments make risky investments.
  5. Only individuals make risky investments.
Solution
If risky investments are never made by oligarchies because no one person has the power to make a particu­lar investment, then it must be the case that only individuals make risky investments.
 
The answer is (E).
 




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