Question:
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?
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?
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
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
This is the second match, against Team D, whose top 5 batsmen average 180 runs, the lowest of the three opponents. Even so, Team A should send in whichever 5 of its 10 batsmen gives it the best chance of winning.
Step 2: Key Formula or Approach:
Use the same two checks as the earlier two questions in this caselet: add up each option's 5 batsmen's career averages for expected runs, then check the average percentage dismissed below 20 for risk.
Step 3: Detailed Explanation:
Averages: RD 40, ST 44, SG 41, VS 31, RU 28, YS 35, VV 35, MK 30, MT 36, MD 45. Add up the average of each option's 5 batsmen:
Option A, RD + RU + MK + VS + YS: \(40+28+30+31+35=164\)
Option B, ST + RD + VV + SG + MD: \(44+40+35+41+45=205\)
Option C, RD + ST + SG + VS + MD: \(40+44+41+31+45=201\)
Option D, SG + RU + YS + MK + MD: \(41+28+35+30+45=179\)
Option E, ST + RD + MK + MD + SG: \(44+40+30+45+41=200\)
Option B has the highest combined average, 205 runs, ahead of C at 201 and E at 200, and well clear of D at 179 and A at 164, both of which include the weaker RU or MK without enough compensation elsewhere.
Check the failure rate for the top three. For B: ST 20, RD 20, VV 35, SG 25, MD 30, which averages to \(\frac{20+20+35+25+30}{5}=26\%\). For C: RD 20, ST 20, SG 25, VS 50, MD 30, which averages to \(\frac{20+20+25+50+30}{5}=29\%\). For E: ST 20, RD 20, MK 30, MD 30, SG 25, which averages to \(\frac{20+20+30+30+25}{5}=25\%\). E is very slightly safer than B, but B's combined average is 5 runs higher and B also carries a better century rate overall, since VV scores a century in 5 percent of innings versus MK also at 5 percent, while B's other four names match E's other four almost run for run. Given B's clear lead on total average and a failure rate only 1 point above E's, B is the stronger overall choice, and it is comfortably ahead of C, which is dragged down by the fragile VS.
Step 4: Final Answer:
Option B, ST, RD, VV, SG, MD, has the highest total career average (205) among the five choices and a failure rate close to the best of the group, so it gives Team A the best chance of winning the second match against Team D. As with the earlier two questions in this caselet, the official XAT key marks the data here as ambiguous with no fixed correct option; the working above identifies the strongest supported choice.
\[ \boxed{\text{Option 2: ST, RD, VV, SG, MD}} \]
This is the second match, against Team D, whose top 5 batsmen average 180 runs, the lowest of the three opponents. Even so, Team A should send in whichever 5 of its 10 batsmen gives it the best chance of winning.
Step 2: Key Formula or Approach:
Use the same two checks as the earlier two questions in this caselet: add up each option's 5 batsmen's career averages for expected runs, then check the average percentage dismissed below 20 for risk.
Step 3: Detailed Explanation:
Averages: RD 40, ST 44, SG 41, VS 31, RU 28, YS 35, VV 35, MK 30, MT 36, MD 45. Add up the average of each option's 5 batsmen:
Option A, RD + RU + MK + VS + YS: \(40+28+30+31+35=164\)
Option B, ST + RD + VV + SG + MD: \(44+40+35+41+45=205\)
Option C, RD + ST + SG + VS + MD: \(40+44+41+31+45=201\)
Option D, SG + RU + YS + MK + MD: \(41+28+35+30+45=179\)
Option E, ST + RD + MK + MD + SG: \(44+40+30+45+41=200\)
Option B has the highest combined average, 205 runs, ahead of C at 201 and E at 200, and well clear of D at 179 and A at 164, both of which include the weaker RU or MK without enough compensation elsewhere.
Check the failure rate for the top three. For B: ST 20, RD 20, VV 35, SG 25, MD 30, which averages to \(\frac{20+20+35+25+30}{5}=26\%\). For C: RD 20, ST 20, SG 25, VS 50, MD 30, which averages to \(\frac{20+20+25+50+30}{5}=29\%\). For E: ST 20, RD 20, MK 30, MD 30, SG 25, which averages to \(\frac{20+20+30+30+25}{5}=25\%\). E is very slightly safer than B, but B's combined average is 5 runs higher and B also carries a better century rate overall, since VV scores a century in 5 percent of innings versus MK also at 5 percent, while B's other four names match E's other four almost run for run. Given B's clear lead on total average and a failure rate only 1 point above E's, B is the stronger overall choice, and it is comfortably ahead of C, which is dragged down by the fragile VS.
Step 4: Final Answer:
Option B, ST, RD, VV, SG, MD, has the highest total career average (205) among the five choices and a failure rate close to the best of the group, so it gives Team A the best chance of winning the second match against Team D. As with the earlier two questions in this caselet, the official XAT key marks the data here as ambiguous with no fixed correct option; the working above identifies the strongest supported choice.
\[ \boxed{\text{Option 2: ST, RD, VV, SG, MD}} \]
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