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by sgr21 » Mon Nov 04, 2013 12:58 am
In the first half of the season a football team participating in the local league won 40% of its matches. It then went on to win all its matches except two in the second half of the season. If it is known that for the entire season the percentage of matches won by the team was 66.67% and that the team played double the number of matches in the second half of the season as compared to the first half of the season then how many matches did the team play in the first half of the season?
(A) 2
(B) 5
(C) 10
(D) 15
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by pareekbharat86 » Mon Nov 04, 2013 2:18 am
Let x be the no. of games played in the 1st half of the season,
Therefore, 2x shall be the no. of games played in the 2nd half (given)
Therefore, total games played= 3x
% of games won in 2nd half= (2x-2)/2x

Now use the weights formula-

(no.of games in 1st half)*(% of wins in 1st half)+ (no.of games in 2nd half)*(% of wins in 2nd half)= (total games)*(total % of wins)

Now plug the values:

x*0.40 + 2x*[(2x-2)/2x]= 3x * 0.6667

Simplifying this will give you,

x= 5.

Is this the OA?
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by GMATGuruNY » Mon Nov 04, 2013 4:21 am
sgr21 wrote:In the first half of the season a football team participating in the local league won 40% of its matches. It then went on to win all its matches except two in the second half of the season. If it is known that for the entire season the percentage of matches won by the team was 66.67% and that the team played double the number of matches in the second half of the season as compared to the first half of the season then how many matches did the team play in the first half of the season?
(A) 2
(B) 5
(C) 10
(D) 15
(E) 20
We PLUG IN THE ANSWERS, which represent the number of games played in the first half of the season.

Answer choice C: first half = 10 games
Since twice as many games are played in the 2nd half, 2nd half = 20 games.

Whole season:
Total games = 10+20 = 30.
Since 2/3 are won, total won = (2/3) * 30 = 20.

1st half:
Since 2/5 are won, number won = (2/5) * 10 = 4.

2nd half:
Number won = total won - number won in the 1st half = 20-4 = 16.
Number lost = total games in the 2nd half - number won in the 2nd half = 20-16 = 4.

Doesn't work: only 2 games should be lost in the second half.
Since the result is TWICE what is required, all of the values in the problem -- including the value in the correct answer choice -- must decrease by 1/2.

The correct answer is B.
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by sgr21 » Mon Nov 04, 2013 6:14 am
yes dear c is d OA thnk u guys!!
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by theCodeToGMAT » Mon Nov 04, 2013 6:32 am
Another Approach: Using Weighted Average

First half, M1 = 40%

Second Half, M2 = (x-2)/x * 100 = (100X - 200)/X

M = 66.67% = 200/3

N2 = 2N1

Using Weighted Average Formula

N1/N2 = [(100X - 200)/X - 200/3]/(200/3 - 40]

1/2 = (300X - 600 - 200X)/3X / (80/3)

80X = 2(100X - 600)
80X = 200X - 1200
1200 = 120X

X = 10

So, "5"

Answer [spoiler]{B}[/spoiler]
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by theCodeToGMAT » Mon Nov 04, 2013 6:33 am
sgr21 wrote:yes dear c is d OA thnk u guys!!
I guess you meant [spoiler]{B}[/spoiler]
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by Brent@GMATPrepNow » Mon Nov 04, 2013 6:49 am
sgr21 wrote:In the first half of the season a football team participating in the local league won 40% of its matches. It then went on to win all its matches except two in the second half of the season. If it is known that for the entire season the percentage of matches won by the team was 66.67% and that the team played double the number of matches in the second half of the season as compared to the first half of the season then how many matches did the team play in the first half of the season?
(A) 2
(B) 5
(C) 10
(D) 15
This approach is almost identical to sgr21's approach, except there's a slight difference in the way the final equation is solved.

Let x = the number of games played in the 1st half of season
This means that 2x = the number of games played in the 2nd half of season (since we're told that the team played double the number of matches in the second half of the season as compared to the first half)
So, in the entire year, there were 3x games played altogether.

In the first half of the season, the team won 40% of its matches.
So, the number of wins in the 1st half = 0.4x

It then won all its matches except two in the second half of the season.
So, the number of wins in the 2nd half = 2x - 2

In total, the team won 0.4x + 2x - 2 games.
Simplify: the team won 2.4x - 2 games


For the entire season the percentage of matches won by the team was 66.67%
I'm assuming that this is meant to mean that the team won 2/3 of it's matches.
From this, we can write: (2.4x - 2)/3x = 2/3
To solve for x, cross multiply to get: (3)(2.4x - 2) = (2)(3x)
Simplify: 7.2x - 6 = 6x
Rearrange: 1.2x = 6
Solve: x = 5
Answer = B

Cheers,
Brent
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by mainbhidhruv » Mon Nov 04, 2013 7:08 am
Option A : 40% of 2 = not an integer - neglect
Option B : 40% of 5 = 2 , => 10 - 2 = 8 wins in Second half
2+8 = 10, 10/15 = 2/3 = 66.67 % Correct

So OA is B
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