CAT 2004 — DILR Question 23
Answer the following question based on the information given below.
Coach John sat with the score cards 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 got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scorers from India, where 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
For how many Indian players is it possible to calculate the exact M-index?
Answer & solution
- A
0
- B
1
2
- D
More than 2
Consider the game against Pakistan (G1).
Runs scored by Y, V and K = 40 + 130 + 28 = 198
Total runs scored = 198/0.9 = 220
∴ Runs scored by R (r1) and S (s1), r1, s1 < 28 and r1 + s1 ≤ 22
Consider the game against South Africa (G2).
Runs scored by K, R and S = 51 + 49 + 75 = 175
Total runs scored = 175/0.7 = 250
∴ Runs scored by Y (y2) and V (v2), y2, v2 < 49 and y2 + v2 ≤ 75
Consider the game against Australia (G3).
Runs scored by R, Y and S = 87 + 55 + 50 = 192
Total runs scored = 192/0.8 = 240
∴ Runs scored by V (v3) and K (k3), v3, k3 < 50, v3 + k3 ≤ 48
R’s M-index = 49
S’s M-index = 50
V’s M-index ≤ 49
Y’s M-index is either 40 or between 41 and 49.
The M-index of only R and S can be exactly calculated.
Hence, option (c).