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In each game of a certain tournament, a contestant either

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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In each game of a certain tournament, a contestant either

Post Thu Aug 03, 2017 12:13 pm
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

Official Guide question
Answer: E

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Post Fri Dec 08, 2017 7:21 am
jjjinapinch 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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Post Thu Aug 03, 2017 8:28 pm
Hi jjjinapinch,

We're told that - in each game of a certain tournament - a contestant either loses 3 points or gains 2 points. We're told that Pat STARTED the tournament with 100 points. We're asked for the number of games that Pat played in the tournament. This question can be solved with a bit of 'brute force' arithmetic.

1) At the end of the tournament, Pat had 104 points

There are a number of different ways for Pat to get to a total of 104 points, starting with the simplest...
IF... Pat WON two games, then that would be 2(2) = 4 points on top of the 100 that Pat already had... and the answer to the question is 2.
IF... Pat WON five games and lost two games, then that would be 5(2) - 2(3) = 10 - 6 = 4 points on top of the 100 that Pat already had... and the answer to the question is 7.
Fact 1 is INSUFFICIENT

2) Pat played fewer than 10 games

With this Fact, we know that Pat played from 0 - 9 games in the tournament.
Fact 2 is INSUFFICIENT

Combined, we already have two examples that 'fit' both facts:
-Won 2 games and the answer to the question is 2
-Won 5 games and lost 2 games and the answer to the question is 7
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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Post Fri Dec 08, 2017 7:21 am
jjjinapinch 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

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

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