# In each game of a certain tournament, a contestant either loses 3 points or…

## Solution:

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**