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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
4
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=>>> Let matches played in first year = x
=>>> matches won in first year= x*80/100 = 0.8
=>> matches lost in first year = 0.2x

=>>> Matches played in Second year = 25% more than first year = 1.25X
=>>> Matches won in second year(5% increase in second year) = 1.25x*84/100 = 1.05x
Matches lose in second year = =>> 1.25x-1.05x = 0.2x

=>>> Matches played in third year = 4% less than 2nd year = 1.25x*96/100 = 1.2x
=>> Matches won in third year = 1.2x*87.5/100 = 1.05x
=>>> matches lose in third year = 1.2x*12.5/100 = 0.15x

Also, matches lost in third year= 1 less than matches lost in 2nd year
0.15x = 0.20-1
1 = 0.05x
X= 20
Total matches played in first year = 20

Statement 1: Players lost same no. Of matches in year 1&2
Matches lost in year 1 = 0.2x = 0.2*20 = 4
Matches lost in year 2 = 0.2x = 0.2*20 = 4 (True)

Statement 2: The team won the same number of matches in the second year and the third year
Matches won in 2nd year = 1.05x
Matches won in 3rd year = 1.05x
(True)

Statement 3: The team played five more matches in the third year than the first year
Matches played in first year = 20
Matches played in third year= 1.2x = 1.2*20 = 24
Players played only 4 more matches in third year. (False)

Only statement 1 & 2 are correct. But we don't have that option so,

IMO E

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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
1
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Bunuel wrote:
A soccer team played 25% more matches year-on-year in the second year of its formation. It won 84% of the matches it played in the second year, which was an improvement of 5% over the percentage of matches won in the first year. In the third year, the team played 4% fewer matches year-on-year but lost only 12.5% of the matches it played, which was one less than the number of matches lost by the team in the second year. Which of the following statements must be correct?

I. The team lost the same number of matches in the first yea and the second year
II. The team won the same number of matches in the second year and the third year
III. The team played five more matches in the third year than the first year

A. I only
B. II only
C. III only
D. I, II and III
E. None of the above


B , IMO

Question
------------------------1st Year-----------------------------------------2nd year------------------------------------------- 3rd year

Played-------------------x---------------------------------------------1.25x-------------------------------------------0.96 *1.25 x

Won----------------0.84 *1.25 x / 1.05 ---------------------------0.84 *1.25 x--------------------------------------NA-----------

Loss----------------- NA-------------------------------------------0.16 *1.25 x------------------0.125 * 0.96 * 1.25 x = 0.16 *1.25 x -1

0.125 * 0.96 * 1.25 x = 0.16 *1.25 x -1
1 = 1.25 x (0.16 – 0.125 *0.96 ) => x = 1 / 1.25 * 0.04 = 20

Now lets fill the table with X = 20


------------------------1st Year-----------------------------------------2nd year--------------------------------------- 3rd year

Played-------------------x=20-----------------------------------------1.25x=25-------------------------------0.96 *1.25 x = 24

Won----------------0.84 *1.25 x / 1.05 = 20----------------0.84 *1.25 x = 21-------------------------------24-3= 21

Loss----------------- 0 ----------------------------------0.16 *1.25 x = 4------------0.125 * 0.96 * 1.25 x = 0.16 *1.25 x -1 = 3


I. The team lost the same number of matches in the first year and the second year – No
II. The team won the same number of matches in the second year and the third year – Correct
III. The team played five more matches in the third year than the first year – No

Hence B.

Originally posted by HoneyLemon on 07 Jun 2020, 04:53.
Last edited by HoneyLemon on 07 Jun 2020, 05:22, edited 1 time in total.
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
2
Kudos
Quote:
Now it is given that there was an improvement of 5% over the percentage of matches won in the first year. So 84% is with 5% of improvement from first year. So we can deduce that team won 80% of the matches in first year.


Can someone please explain this? Why is this 80% and not 79%?
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
2
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davidbeckham wrote:
Quote:
Now it is given that there was an improvement of 5% over the percentage of matches won in the first year. So 84% is with 5% of improvement from first year. So we can deduce that team won 80% of the matches in first year.


Can someone please explain this? Why is this 80% and not 79%?


Here GMAT is playing with the words. Read this carefully.

there was an "improvement of 5% over the percentage" of matches won in the first year.

It does not mean increase of 5%, rather it means 5% improvement. Let say first year team won X% of matches. It is given that in second year it won 84% so equation becomes 1.05X = 84. Which gives us X = 80%.

I hope now it is clear.

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Originally posted by Thelionking1234 on 17 Jul 2020, 17:24.
Last edited by Thelionking1234 on 26 Jul 2020, 09:51, edited 1 time in total.
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
1
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There are so many seemingly Bulky Equations and solutions making things even more complex.

Since we know in second year, They played 25% more which is 5/4 times what they played in first year.

You can assume
First year = 80
=> Second year = 100 or \(( 80*5/4)\)

Second
won 84: lost 16


Second year winning percentage is 5 percent better.


Hence in 1st year
1.05x = 84.
X = 80 ( or else you know 4 is 5% of 80 anyway)
80% won
First : Won = 64
Lost = 16

Third :
Played 96.
Lost = \(96*12.5\)
\(=> 96*1/8= 12\)
Lost = 12
Won = 84



Posted from my mobile device

Statement 1 and 2 are true.
IMO E
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
Correct Option E
1st Condition - True
2nd Condtion - True
3rd Condition - False
Hence option - E
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
chetan2u - Can you please clarify the below doubt?
The question mentions "which was an improvement of 5% over the percentage of matches won in the first year" and I think everybody has used 80%. How should we infer that they are talking about 5% increase in the % (80%*1.05) or flat increase in the % itself (79%+5%)? How do we write the latter?

Thank you :)
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
1
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Expert Reply
Sonia2023 wrote:
chetan2u - Can you please clarify the below doubt?
The question mentions "which was an improvement of 5% over the percentage of matches won in the first year" and I think everybody has used 80%. How should we infer that they are talking about 5% increase in the % (80%*1.05) or flat increase in the % itself (79%+5%)? How do we write the latter?

Thank you :)


It is given that improvement of 5% OVER the previous year.
OVER clearly means you are taking base as previous year %. Invariably, most of the question would mean but in case it has to mention the latter, I believe words could be: It was 84% in the second year, a % that was 5% more as compared to % of last year.
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
 
Bunuel wrote:
A soccer team played 25% more matches year-on-year in the second year of its formation. It won 84% of the matches it played in the second year, which was an improvement of 5% over the percentage of matches won in the first year. In the third year, the team played 4% fewer matches year-on-year but lost only 12.5% of the matches it played, which was one less than the number of matches lost by the team in the second year. Which of the following statements must be correct?

I. The team lost the same number of matches in the first yea and the second year
II. The team won the same number of matches in the second year and the third year
III. The team played five more matches in the third year than the first year

A. I only
B. II only
C. III only
D. I, II and III
E. None of the above



Are You Up For the Challenge: 700 Level Question

 

­I read through the thread and I am confused. Why do some people say A and B both are correct? I got only B correct. I am thrown off by "It won 84% of the matches it played in the second year, which was an improvement of 5% over the percentage of matches won in the first year." What does this mean?
Moreover, I believe we should simply calculate for Win and Loss, no Tie etc. This is a question that I'll probably guess and forget in the exam, but here it is for the practice and concept.

MartyMurray KarishmaB chetan2u, please help explain the OA. Thank you.

 ­
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
Expert Reply
Bunuel wrote:
A soccer team played 25% more matches year-on-year in the second year of its formation. It won 84% of the matches it played in the second year, which was an improvement of 5% over the percentage of matches won in the first year. In the third year, the team played 4% fewer matches year-on-year but lost only 12.5% of the matches it played, which was one less than the number of matches lost by the team in the second year. Which of the following statements must be correct?

I. The team lost the same number of matches in the first yea and the second year
II. The team won the same number of matches in the second year and the third year
III. The team played five more matches in the third year than the first year

A. I only
B. II only
C. III only
D. I, II and III
E. None of the above



Are You Up For the Challenge: 700 Level Questions


Since everything is in percentages, assume values. Instinctively, I took 100 for first year but a 25% increase and then 84% is too much of calculation. So instead I will take second year matches played as 100.


First year matches played is 80 (so that when increased by 25%, it becomes 100).
Say they won x% matches.


Second year matches played is 100
Matches won = 84% = 84
Matches lost = 16

A 5% increase on x% gave 84%. x% is likely to be 80%. Why? Since base is smaller, the amount of increase will be a bit lower than 5 to give 5%.
Check - 4/80 is 5%. Correct.
So they won 80% matches in first year.
Matches won in first year is 64
Matches lost is 16


In third year, they played 4% fewer matches so they played 96 matches.
They lost 12.5% ie 1/8 of these. So they lost 12 and won 84 in third year.


I. The team lost the same number of matches in the first year and the second year

Correct. 16 each.


II. The team won the same number of matches in the second year and the third year

Correct. 84 each


III. The team played five more matches in the third year than the first year

Incorrect. It played 16 more.

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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
why is it E? B should be the correct answer right??? When you do the math with test number of 100 games, it equals out to 105 wins each for year 2 and year 3.
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
Win rate of Y2 is 84%, which is 5% more than the percentage of Y1
Win rate of Y1 is x%
=> 84% = \(\frac{105}{100}\) * x%
=> 84% = \(\frac{21}{20}\) * x%
=> x = ­ 84% * \(\frac{20}{21}\) = 80%      


       Total played                      Won                          Lost                           Draw

Y1   200 (supposedly)               160 (80% win rate)     [_]                             [_]
 
Y2   250 (25% more than Y1)    210 (84% win rate)     31 (1 more than Y3)    9 = (250-210-31)

Y3   240 (4% fewer than Y2)     [_]                                30 (lost 12.5%)        [_]

I. The team lost the same number of matches in the first year and the second year
We don't know the number of matches lost in Y1
=> No

II. The team won the same number of matches in the second year and the third year
We don't know the number of matches won in year 
=> No

III. The team played five more matches in the third year than the first year
Team played 250 matches in Year 2 and 240 matches in Y3
=> No
 ­
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Re: A soccer team played 25% more matches year-on-year in the second year [#permalink]
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