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At the end of the T20 cricket match, every player had scored a prime number of runs and the average of the 11 players was also a prime number. No player’s individual runs were the same as anyone else’s or as the average. Nobody had scored more than 45 runs.
Q. What was the maximum number of runs scored by a single player?
  • a)
    43
  • b)
    41
  • c)
    37
  • d)
    29
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
At the end of the T20 cricket match, every player had scored a prime n...
here are 14 prime numbers less than 45 which are as follows:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43
Sum of all these 14 prime numbers = 281
Let’s validate answer options
a) Let the average = 17 ⇒ sum of scores of 11 players = 17 × 11 = 187
187 + the average value (17) = 204
Sum of remaining 2 values to be eliminated = 281 – 204 = 77 (odd number)
= odd value + even value, 2 is the only even prime number value
⇒ odd value must be = 75, not possible
b) Let the average = 19 ⇒ sum of scores of 11 players = 19 × 11 = 209
209 + the average value (19) = 228
Sum of remaining 2 values to be eliminated = 281 – 228 = 53 (odd number)
= odd value + even value, 2 is the only even value among available prime numbers
⇒ odd value must be = 51, not possible
c) Let the average = 23 ⇒ sum of scores of 11 players = 23 × 11 = 253
253 + the average value (23) = 276
Sum of remaining 2 values to be eliminated = 281 – 276 = 5 (odd number)
= odd value + even value = 2 + 3
⇒ Scores of 11 players are 5, 7, 11, 13, 17, 19, 29, 31, 37, 41 and 43 and their average score = 23
d) Let the average = 29 ⇒ sum of scores of 11 players = 29 × 11 = 319 which is more than the sum of all 14 available prime numbers, so not possible
Maximum number of runs scored by single player = 43
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Most Upvoted Answer
At the end of the T20 cricket match, every player had scored a prime n...
Scored a century (100 runs).
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