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In each game of a certain tournament, a contestant either loses 3 poin

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In each game of a certain tournament, a contestant either loses 3 poin [#permalink]

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New post 16 Jun 2016, 04:25
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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
[Reveal] Spoiler: OA

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Re: In each game of a certain tournament, a contestant either loses 3 poin [#permalink]

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New post 16 Jun 2016, 04:44
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


Both statements by themselves are clearly insufficient.

Taking both the statements together:

We have an addition of 4 points. So we need minimum of 2 games which add 2 points each.

Further any 3 point loss making games have to be cancelled out by the 2 point gain games. We need 3 games gaining 2 points each to cancel out 2 games losing 3 points each. 3+2=5 games. We need these 5 games to cancel out.

So we need 5x+2 games to get 104 points, where x>=0 and x represents the number of times the 3 gain making and the 2 loss making games (that cancel out each other) have to be played.

The only number of games satisfying the above equation which is less than 10 games is 2 (when x=0) and 7 (when x=1).

Since we have no single number of games we end up with E.

Answer: E
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Re: In each game of a certain tournament, a contestant either loses 3 poin [#permalink]

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New post 16 Jun 2016, 05:24
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


1) he gained 4 points
=> 2x - 3y = 4
multiple solutions -- (x,y) = (2,0) ; (5,2) ; ....
insufficient

2) he played fewer than 10 games
insufficient

(1)+(2): he gained 4 points in fewer than 10 games that he played
multiple solutions -- (x,y) = (2,0) ; (5,2) ; ....
insufficient

E.
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In each game of a certain tournament, a contestant either loses 3 poin [#permalink]

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New post 16 Jun 2016, 06:19
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



(1) No information about loosing or gaining of first 100 games,Insufficient

(2) No information about loosing or gaining any game,Insuffifient

(1)+(2) together didn't solve the issue raised above.

Correct Answer E
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In each game of a certain tournament, a contestant either loses 3 poin   [#permalink] 16 Jun 2016, 06:19
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