Directions: Coach Johan sat with the scorecards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen go out. John summarised the batting performance through three figures, one for each game. In each figure, the three outer triangles communicate the number of runs scored by the three top scorers from India. K, R, S, V and Y represent Kaif, Rahul, Saurav, Virender and Yuvraj, respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournament; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number if his scores are arranged in a non-increasing order.

Batting performance of five Indian Batsmen in three Games of One-day International Cricket Tournament.

For how many Indian players is it possible to calculate the exact M-Index?

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More than 2

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Solution

The correct option is B 2
Runs scored by top three batsmen against Pakistan
$= 40 + 130 + 28 198 90 % = 198 100 % = 220 r u n s$
The rest of the players made only 22 runs.
Runs scored by top three batsmen against South Africa
$= 51 + 75 + 49 = 175 70 % = 175 100 % = 250$
The rest of the players made only 75 runs
Runs scored by top three batsmen against Australia
$- 55 + 87 + 50 - 192 80 % = 192 100 = 240$
The rest of the players made only 48 runs
$Y \to 40 + S o u t h A f r i c a + 87 = 127 + r u n s$
scored against South Africa.
$V \to 130 + S o u t h A f r i c a + A u s t r a l i a = 130 + r u n s$
scored against South Africa + Australia
$K \to 28 + 51 + A u s t r a l i a = 79 + R u n s$
scored aganist Australia.
$S \to P a k i s t a n + 75 + 50 = 125 + R u n s$ scored against Pakistan.
$R \to P a k i s t a n + 49 + 55 = 104 + R u n s$
scored splint Pakistan.
For Yuvraj. the middle number cannot be determined as we don't know the exact runs scored by him against South Africa.
Same is the ease with Virendra and Kaif.
For Saurav, the middle number will be 50 because what-ever runs he scores against Pakistan. they could be maximum 22 or minimum zero. This will not affect the middle number 50.
For Rahul middle index will be 49. (Same logic)

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Similar questions

Directions: Answer the questions based on the information given below.
During the recent India- Australia bilateral 7 one-day international matches series Dhawan, Rohit and Kohli were in tremendous form and combinedly scored 7 centuries in these 7 games. Further, it is also known about their scores in the series:
1. In each game exactly one batsman scored a century.
2. Each of these three players scored at least one century and no two batsmen scored an equal number of centuries.
3. Rohit did not score a century in the 2nd game and Kohli scored a century in the last game.
4. Dhawan did not score a century in the 1st and 4th game.
5 The player who scored a century in the 2nd game did not score a century in the 5th game.
6. The player who scored a century in the 4th game also scored a century in the 6th game.
7. The player who scored a century in the 3rd game did not score a century in the 1st game.
If Kohli scored a century in the 2nd game but failed to score a century in the 4th game and his highest score in the games was 125, then what could be the maximum possible runs scored by Kohli in the series?___.

Directions: Answer the questions based on the information given below.
During the recent India- Australia bilateral 7 one-day international matches series Dhawan, Rohit and Kohli were in tremendous form and combinedly scored 7 centuries in these 7 games. Further, it is also known about their scores in the series:
1. In each game exactly one batsman scored a century.
2. Each of these three players scored at least one century and no two batsmen scored equal number of centuries.
3. Rohit did not score a century in the 2nd game and Kohli scored a century in the last game.
4. Dhawan did not score a century in the 1st and 4th game.
5 The player who scored a century in the 2nd game did not score a century in the 5th game.
6. The player who scored a century in the 4th game also scored a century in the 6th game.
7. The player who scored a century in the 3rd game did not score a century in the 1st game.
How many centuries did Dhawan score?

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