Bunuel wrote:
In each game of a certain tournament, a contestant either loses 3 points or gains 2 points. If Pat had 100 points at the beginning of the tournament, how many games did Pat play in the tournament?
(1) At the end of the tournament, Pat had 104 points
(2) Pat played fewer than 10 games
We are given that in each game of a certain tournament, a contestant either loses 3 points or gains 2 points.
We can let the number of 2-point gains = x and the number of 3-point losses = y. We are also given that Pat started with 100 points at the beginning of the tournament. Thus, we can express his final score as F = 100 + 2x - 3y. We need to determine how many games Pat played in the tournament, or x + y.
Statement One Alone:At the end of the tournament, Pat had 104 points.
Using the information from statement one, we can substitute 104 for F:
104 = 100 + 2x - 3y
4 = 2x - 3y
We do not know the value of either x or y. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:Pat played fewer than 10 games.
Using the information in statement two, we know that x + y < 10; however, that is not enough information to determine a value of x + y. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:From statements one and two, we know that 2x - 3y = 4 and that x + y < 10; however, that is not enough information to determine a value of x + y. For instance, x = 2 and y = 0, or x = 5 and y = 2, both of which satisfy 2x - 3y = 4 and x + y < 10.
Answer: E
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