A soccer team played 25% more matches year-on-year in the second year

Question

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

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Thelionking1234 · Accepted Answer

Fastest and accurate way to tackle this question is to start with assuming some numbers.

First Year: 
Let's assume team played 100 year-on-year matches in first year.

Second Year: 
So in second year it played 125 matches. (25% more than played in first year) Team won 84% of the matches ~ 125 X 0.84 = 105 matches. & Lost =125-105 = 20 matches.

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.

First Year:

Team won 80% of the matches so = 80 Matches. Lost 20 Matches

Third Year:

Team played 4% fewer matches so 125 X 0.96 = 120 Matches. 
Lost 12.5% of the matches = 120 X 12.5/100 = 15 Matches so won = 120-15 =105 Matches.

Now from all results and given options we can conclude that if the given scenario is correct then Statement 1 and 2 must be true.

We do not have any option which says this. So None of the above (E) is the correct answer.

Hope this helps.

RiRa777 · Answer

Hi,

I can't believe that nobody here is a fan of the world's most popular game. A soccer game can have three results- win, lose or draw. We will analyse each statement in the question one by one and we will fill this table as we go.
Y MMM WWW LL D
1 
2 
3 
Y- Year, MMM- Matches Played, WWW- Won, LL- Lost, D- Draw

Statement 1: A soccer team played 25% more matches year-on-year in the second year of its formation. 
Lets say the number of matches played by the team in the first year is 100, then the table looks something like this-
Y MMM WWW LL D
1 100
2 125 
3

Statement 2: It won 84% of the matches it played in the second year.
So, 84% of 125= 105. The state of the table now is-
Y MMM WWW LL D
1 100 
2 125 105 
3

Statement 3: ....which was an improvement of 5% over the percentage of matches won in the first year. 
So, if 84% was an improvement of 5%(mind you, its percentage not percentage points and there is a difference between both) then if the team won x% of matches in the first year then, 105% of x= 84, which gives us x= 80. Now we know that team won 80% of matches in the first year. The table now looks like this:
Y MMM WWW LL D
1 100 80 
2 125 105 
3

Statement 3:In the third year, the team played 4% fewer matches year-on-year 
4% fewer matches is equivalent to saying 96% of 125= 120. The table:
Y MMM WWW LL D
1 100 80 
2 125 105 
3 120

Statement 4: ...but lost only 12.5% of the matches it played,
12.5% of 120= 15. We know how many they lost but that doesn't mean that they won all the remaining matches; we actually don't know how many matches they won. The table now:
Y MMM WWW LL D
1 100 80 
2 125 105 
3 120 NA 15

Statement 4: ....which was one less than the number of matches lost by the team in the second year.
So number of matches lost by the team in the second year is 15+1 i.e., 16. The table's situation now is as follows:
Y MMM WWW LL D
1 100 80 
2 125 105 16 
3 120 NA 15

We see that in the year 2, total matches= won+lost+draw, hence, draw= 125-(105+16)= 4. Finally, the table becomes:
Y MMM WWW LL D
1 100 80 
2 125 105 16 4
3 120 NA 15

Lets judge the validity of the conclusions provided in the question now, also, keep in mind that its a 'must be true' question.
I. The team lost the same number of matches in the first year and the second year---We do not have enough data to answer this so its not necessarily true. Hence, False.
II. The team won the same number of matches in the second year and the third year--- Again, we do not have enough data to answer this so its not necessarily true. Hence, False.
III. The team played five more matches in the third year than the first year--- We can see from the table that its not true. Hence, False.

Therefore, we cannot definitely conclude any of the statements to be true. So , the answer IMO is E.

Hope it makes things clear.

yashikaaggarwal · Answer

=>>> 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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HoneyLemon · Answer

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.

davidbeckham · Answer

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

Thelionking1234 · Answer

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.

Posted from my mobile device

Thelegend2631 · Answer

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

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Statement 1 and 2 are true. 
IMO E

100mitra · Answer

Correct Option E
1st Condition - True 
2nd Condtion - True 
3rd Condition - False 
Hence option - E

Sonia2023 · Answer

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

chetan2u · Answer

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.

Engineer1 · Answer

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.

KarishmaB · Answer

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.

Now, we are given: "In the third year, the team ... 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."

But as per our calculations, the team lost 16 matches in 2nd year and 12 in 3rd year, a difference of 4 matches. Hence the actual number of all matches is 1/4th the assumed values. Still the relation between them will not change.

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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Fish181 · Answer

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.

Gemmie · Answer

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

ss1203 · Answer

What does this line mean - "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."
I started with matches played in Year 1 = 100 and got matches in Y2 = 125 and Y2 = 120.

Y2: matches lost = 20; thought this meant that matches lost in Y2 = 19 but if we look at the given %, then matches lost in Y3 = 12/% * 120 = 15.

Please help to clarify this.

nisen20 · Answer

looks like this old stuff, tagged as OG 10, has provoked so many debates mainly concerning how to inteprete that horrible "improvment/percentage" prompt.

do we have an official explanation to illustrate what exactly was in test makers's mind when creating this monster?

i'm standing with guys who support (B) as the answer.
 
the team played  X  games in the first year,  1.25X  games in the second year, and  0.96 × 1.25X  games in the third year.
the team won  0.84 × 1.25X  games in the second year, and won another  0.875 × 0.96 × 1.25X = 0.84 × 1.25X  games in the third year.
it's crystal clear. the team won the same number of games in the seceond and third years respectively.

GMATinsight · Answer

Check the quick Simple and detailed explanation in the video here

https://www.youtube.com/watch?v=Il4lKf35rBw

Shrinathda · Answer

Good. The Example with 1st year as 20 instead of 100 will be apt so that it also takes care of ->  was one less than the number of matches lost by the team in the second year.

Adit_ · Answer

I was trying to solve and midway realised there is no mention of any draws and I was assuming win and loss are the only scenarios and then instantly went for none of the above.
The options were too specific and there is no range given that could make the options true if anything, not knowing anything about a draw rules them out completely according to my pre-thinking.

Is this a right way or did we have solve for each?  Bunuel   KarishmaB

A soccer team played 25% more matches year-on-year in the second year

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