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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 the team scored 9 points after 5 games, what is the least number of the remaining matches it has to win to reach a 40-point mark by the end of the tournament?

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 the team scored 9 points after 5 games, what is the least number of the remaining matches it has to win to reach a 40-point mark by the end of the tournament?

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

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.

3 points for win (w); 1 point for draw (d) 20 total - 5 played = 15 games left = # wins + # draws --> w + d = 15 points to make = 40 total - 9 so far = 31 points --> 3w + 1d = 31 subtract: -(w+d)-15

-w - d = -15 3w + d = 31 ___________ + 2w = 16 w = 8

Make a note of what we have to find out. We need to find how many winning matches are needed to get 40 points?

Since 9 points are achieved in 5 matches we are left with 31 points that should be filled with less winning matches. If you try with 8; you will have 8*3(win)+7*1(draw)=31.

Apply-"hit and trial" , start with the middle number(when you see the ACs in order such as 6,7,8,9,10 ,because it will tell you whether you have to go up or down . in this question one might get lucky because C=8 is the right answer.GMAT loves to ask such questions, because in the middle of the test GMAT wants you to boggle with simple yet silly manual calculation.
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