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In each game of a certain tournament, a contestant either

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In each game of a certain tournament, a contestant either

by jjjinapinch » Thu Aug 03, 2017 12:13 pm

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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

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Answer: E
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Aug 03, 2017 2:22 pm

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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

Official Guide question
Answer: E
Target question: How many games did Pat play in the tournament?

Jump straight to...

Statements 1 and 2 combined
There are several CONFLICTING situations that that satisfy BOTH statement 2. Here are two:
Case a: Pat plays 2 games and wins both of them to add 4 points to the 100 points she started with. In this case, Pat plays 2 games
Case b: Pat plays 7 games and wins 5 of them and loses 2 to add 4 points to the 100 points she started with. In this case, Pat plays 7 games
Since we cannot answer the target question with certainty, the combined statements are NOT

Answer: E

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by [email protected] » Thu Aug 03, 2017 8:28 pm

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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

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