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

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06 Dec 2016, 18:23
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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

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.

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

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16 Jun 2016, 05:24
3
7
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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Re: In each game of a certain tournament, a contestant either loses 3 poin  [#permalink]

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16 Jun 2016, 04:44
1
2
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.

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

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16 Jun 2016, 06:19
1
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.

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

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18 Jan 2017, 13:11
1
My approach without solving any equation:

Statement 1: he ends up with 104 points . That means he might have won 2 times so he got +2 and +2 ,or might have lost 2 time -3 and -3 and then won 5 times (gained +2 each time ). One way or another we are not sure about the number of the games he played.---> INSUFF

Statement 2: If Pat played games<10 he might have played 9 , 8 ,7 ,6,5,4 .... we are not sure --> INSUFF

Combining 1 and 2 we know he had 104 points at the end and less than 10 games, AGAIN he might have played a different number of games each time in order to gather 104 points, he might have lost at the beginning and won the rest or vice versa. --> INSUFF

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

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05 Feb 2017, 07:46
Hi All

Thanks for all your very good answers. It took me a while to answer this question. In the end I got it right but I was unsure if I had the right methodology.
Overall I used the same thinking which consists in using test cases. However I'm wondering whether there is a faster solution which would consist in recognizing a pattern:
Can't we just generalize and say that if we have a combination of 1 equation and 1 inequalities with two unknown, therefore it remains insufficient to solve for the 2 unknown ? Using that pattern for other DS questions would help solving other DS questions tremendously faster...

the OG DS problem #282 (OG 2017) used similar reasoning and ended up with E as OA.

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

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03 Aug 2017, 15:23
1
Top Contributor
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

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

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

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05 Nov 2017, 10:40
YanisBoubenider thefibonacci I still don't get why C is not an option.

if we know that final amount of points is 104, and he played less than 10 games, then the only possible amount of games played is 5. That is, lost 2 (104-6=98) and won 3 (98+6=104). He couldn't lose 3 because it would result in the odd number of loses neither he could lose 4 because he would have to win 6 and that equals 10 which contradicts with the 2nd statement.
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Re: In each game of a certain tournament, a contestant either loses 3 poin  [#permalink]

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11 Nov 2017, 08:05
1
I. 104-100 = 4
Min games = 2. But, 4 can also be obtained by scoring 2+2+2+2+2-3-3 = 4. (Games = 7)
II. Games less than 10. 4 or 7 as in 1.
Both Insufficient. Ans=E
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Re: In each game of a certain tournament, a contestant either loses 3 poin  [#permalink]

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23 Nov 2018, 12:32
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Re: In each game of a certain tournament, a contestant either loses 3 poin   [#permalink] 23 Nov 2018, 12:32
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