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Admissions Success Stories In each game of a certain tournament, a contestant either

This topic has 2 expert replies and 0 member replies

In each game of a certain tournament, a contestant either

Post Fri Aug 10, 2018 5:44 am

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Source: Official Guide

In each game of a certain tournament, a contestant either loses 3 points or gain 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.

The OA is E.

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GMAT/MBA Expert

Post Fri Aug 10, 2018 11:19 am
AAPL wrote:
Source: Official Guide

In each game of a certain tournament, a contestant either loses 3 points or gain 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.

The OA is 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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Brent

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GMAT/MBA Expert

Post Fri Aug 10, 2018 1:08 pm
AAPL wrote:
Source: Official Guide

In each game of a certain tournament, a contestant either loses 3 points or gain 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.
Here is an algebraic way to combine the two statements:

Let G = a game that results in a 2-point gain and L = a game that results in a 3-point loss.

Statement 1:
Since the played games yield a total of 4 points beyond the intital 100 points, we get:
2G - 3L = 4
2G = 4 + 3L
Note:
Since the expression in blue is equal to an even integer -- 2G -- L must be EVEN.

Statement 2:
Since fewer than 10 games are played, we get:
G+L < 10
G < 10 - L
2G < 20 - 2L

Substituting 2G = 4+3L into 2G < 20-2L, we get:
4 + 3L < 20 - 2L
5L < 16
L < 3.2
Implication:
L must an even nonnegative integer less than 3, with the result that L=0 or L=2.

If we substitute L=0 into 2G = 4+3L, we get:
2G = 4
G = 2.
In this case, L+G = 0+2 = 2, implying that the number of games = 2.

If we substitute L=2 into 2G = 4+3L, we get:
2G = 4 + (3*2)
2G = 10
G=5.
In this case, L+G = 2+5 = 7, implying that the number of games = 7.

Since the number of games can be different values, the two statements combined are INSUFFICIENT.

The correct answer is E.

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