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
E , 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 –
Correct Hence E .
.