Question:hard

Team A is a cricket team picking its playing eleven from its regular pool of batsmen for a league where it faces Teams B, C and D. The table below lists the past performance record of Team A's top 10 batsmen: their career batting average, and three tendencies expressed as a percentage of their innings, namely how often they get out for under 20 runs, how often they get out for a score close to their own average, and how often they go on to score more than a century.

For reference, the average score of the top 5 batsmen of each opposing team is: Team C, 270 runs; Team B, 215 runs; Team D, 180 runs; Team A (itself), 215 runs.

Team A would play the second match with D. Based on the statistics above, whom should the manager choose so that A has maximum chances of winning?

Show Hint

Total the career averages of each five-man group, then use the dismissed-below-20 rate only to break close ties.
Updated On: Jul 10, 2026
  • RD, RU, MK, VS, YS
  • ST, RD, VV, SG, MD
  • RD, ST, SG, VS, MD
  • SG, RU, YS, MK, MD
Show Solution

The Correct Option is B

Solution and Explanation

Apply the same composite reliability score used for the first two questions in this caselet, score = average minus half the percentage dismissed below 20, plus the century percentage, to see which group is strongest against Team D:

  • RD: $40 - 0.5(20) + 3 = 33$
  • ST: $44 - 0.5(20) + 10 = 44$
  • SG: $41 - 0.5(25) + 10 = 38.5$
  • VS: $31 - 0.5(50) + 15 = 21$
  • RU: $28 - 0.5(55) + 12 = 12.5$
  • YS: $35 - 0.5(40) + 10 = 25$
  • VV: $35 - 0.5(35) + 5 = 22.5$
  • MK: $30 - 0.5(30) + 5 = 20$
  • MT: $36 - 0.5(45) + 10 = 23.5$
  • MD: $45 - 0.5(30) + 10 = 40$

Add up the score of each option's five named batsmen:

  1. RD, RU, MK, VS, YS (option A): $33+12.5+20+21+25=111.5$, by far the weakest group, since it carries RU, the lowest scorer on the whole table.
  2. ST, RD, VV, SG, MD (option B): $44+33+22.5+38.5+40=178$, the highest total, built around the four strongest all-round scorers, ST, MD, SG and RD, with VV as a safe fifth choice.
  3. RD, ST, SG, VS, MD (option C): $33+44+38.5+21+40=176.5$, just behind B, since VS's score of 21 is lower than VV's 22.5.
  4. SG, RU, YS, MK, MD (option D): $38.5+12.5+25+20+40=136$, well behind, dragged down by RU and MK together.
  5. ST, RD, MK, MD, SG (option E): $44+33+20+40+38.5=175.5$, close to B and C but a shade lower, since MK's score of 20 is the weakest link among the top three groups.

Option B tops the list at 178, narrowly ahead of C at 176.5 and E at 175.5, and far ahead of D at 136 and A at 111.5. The margin between B, C and E is small, but B wins because VV's balance of a reasonable average with a lower failure rate edges out both VS, who is dismissed below 20 half the time, and MK, whose average is the lowest of the three candidates for the fifth slot.

Let's summarize:

  • ST, RD, MD and SG form the strongest and most consistent core across all three matches in this caselet.
  • Against Team D, the safest fifth choice is VV rather than VS or MK, since VV combines a decent average with a lower chance of a cheap dismissal.

So for the second match against Team D, Team A should field ST, RD, VV, SG, MD, option B, while noting again that the official key records this caselet's data as ambiguous, with no single fixed answer stated.

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