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PERCENTAGES

by ROHIT11111 » Thu Nov 05, 2015 4:15 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

ANS-B
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by moron » Thu Nov 05, 2015 9:00 am
Key information in the question
First half of the season a football team participating in the local league won --> x
First half of the season a football team participating in the local league won 40% --> 0.4x
Win all its matches except two in the second half of the season. --> 2x-2
Entire season the percentage of matches won by the team was 66.67%
Team played double the number of matches in the second half of the season as compared
to the first half --> 2x

So total games played: x+2x=3x
Games won: 2x-2+0.4x=2.4x-2
(100)*2.4x-2/3x=66.67
Finding the value of x is difficult calculation. I used answer choice and see what choice (100)*2.4x-2/3x gives answer 66.67- Answer-B
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by GMATinsight » Sat Nov 07, 2015 4:22 am
ROHIT11111 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
ANS-B
Writing equation is the best method to solve this question.
Le's number of matches in first half is x
Then number of matches in second half = 2x

Win in first half = 40% of x = 0.4x
Win in second half = 2x-2

total win = 0.4x + 2x-2 = 2.4x - 2
% win = 66.67% = 2/3

2.4x-2/3x = 2/3

7.2x-6 = 6x
1.2x = 6
x = 5
Answer: Option B
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