CAT 2004 — DILR Question 22
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
Among the players mentioned, who can have the lowest R-index from the tournament?
Answer & solution
Only Kaif, Rahul or Yuvraj
- B
Only Kaif or Rahul
- C
Only Kaif or Yuvraj
- D
Only Kaif
If y2 < 40, then Y’s R-index = 87 − y2 > 47; i.e. 47 < Y’s R-index ≤ 87
If y2 > 40, then Y’s R-index = 87 – 40 = 47
∴ 47 ≤ Y’s R-index ≤ 87
Similarly,
23 ≤ K’s R-index ≤ 51
33 ≤ R’s R-index ≤ 55 (âµ r1, s1 < 28 and r1 + s1 ≤ 22)
53 ≤ S’s R-index ≤ 75 (âµ r1, s1 < 28 and r1 + s1 ≤ 22)
82 ≤ V’s R-index ≤ 130 (âµ v3, k3 < 50, v3 + k3 ≤ 48)
∴ Any one of Y, K or R could have the lowest R-index.
Hence, option (a).