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# M10 Q35

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Re: M10 Q35 [#permalink]

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13 Sep 2012, 06:33
40-9= need 31 more points at least
20-5= in 15 games

let x= # wins
let (15-x)= # ties
we want to see min amount of wins with max ties

3x+(15-x)>=31
3x+15-x>=31
2x>=16
x>=8

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Re: M10 Q35 [#permalink]

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13 Sep 2012, 09:27
If the answer is 8... then is it necessary rest all the matches will be drawn... not a single match will be defeated and score 0....
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Re: M10 Q35 [#permalink]

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14 Sep 2012, 08:18
The Answer is C.
In order to have the least % of victory, the defeat must be 0.
Let x = # of victory after 5 games
y = # of draw after 5 games.

We have:
3x+y=40-9=31 (points)
x+y=15 (games)

Then 2x=16=> x=8
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Re: M10 Q35 [#permalink]

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16 Sep 2012, 13:54
I think you have to consider the defeated matches for the second equation, even though it does not affect the final result.

magnetictempest wrote:
I set this up in two equations:

1) 3W + D = 31
To minimize the number of wins, then we need to maximize the number of points via draw. Total points add up to the remaining 31 points to make it to 40 incremental to the 9 obtained after 5 games.

2) W + D = 15
Total number of wins + draws should add up to the 15 games to make 20 games on top of the 5 games already played

W = 8
D = 7

Minimum wins is 8 => c)
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Re: M10 Q35 [#permalink]

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16 Sep 2012, 13:59
hit and trial is very efficient for this type of problem, save lots of time..

debaranjansahoo wrote:
I know answer is 8. By guessing i started with 7 and ended up with 8. Does any one know any direct method to get the answer for these types of questions rather than hit and trial method.
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Re: M10 Q35 [#permalink]

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12 Sep 2013, 12:01
If the team wins 6 times, to get the maximum points, they should get 20-5-6 draws = 9 draws and it gets 9 + 6*3 + (20-5-6)*1 = 36 points <40 pts -> A is wrong
If it wins 7 times, if the gets 10 draws and loses 3 times the team will reach the 40 points at the end --> Answer is B = 7
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Re: M10 Q35 [#permalink]

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15 Sep 2013, 17:58
The Team has currently scored 9 points in 5 matches , so in the remaining 15 matches it is needs to score 31 points with the condition ( Least number of matches to win ) .
For example
If it has 14 Draws + 1 Win = 14 + 3 = 17 score (REJECTED)
If it has 13 Draws + 2 Wins = 13 + 3*2 = 19 score (REJECTED)

We can formulate D + 3 * W = 31 ( where D = draws , W = wins )
This equation is only satisfied when D = 7 , W = 8

7 ( Draws )* 1 + 3 * 8 ( wins ) = 31 .

Hence least number of wins to obtain a score of 40 in 20 matches is : 8

Hope this helps !!
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The scoring system in a certain football competition goes as [#permalink]

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24 Jul 2014, 03:10
The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 9 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?

A) 6
B) 7
C) 8
D) 9
E) 10

[Reveal] Spoiler: My Doubt
Can someone please explain.

Last edited by Gnpth on 24 Jul 2014, 03:22, edited 3 times in total.
formatted the topic
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The scoring system in a certain football competition goes as [#permalink]

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24 Jul 2014, 03:21
The team has 9 Points now.

And they need 31 points from remaining 15 matches.

The questions ask for minimum wins, by plugging in(Normally start plugging in with option C)

So, 8 Wins will give us 8*3= 24.

and 7 draws will give us 7*1= 7. Total 31 Points.

Hence the answer is 8.
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Re: M10 Q35 [#permalink]

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24 Jul 2014, 03:30
Vijayeta wrote:
The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 9 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?

A) 6
B) 7
C) 8
D) 9
E) 10

[Reveal] Spoiler: My Doubt
Can someone please explain.

Merging similar topics. Please refer to the discussion o pages 1 and 2.

Also, please search before posting. Thank you.
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Re: M10 Q35   [#permalink] 24 Jul 2014, 03:30

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# M10 Q35

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