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 playerandrsquo;s individual runs were the same as anyone elseandrsquo;s or as the average. Nobody had scored more than 45 runs.Q.What was the average of their runs scored?a)17b)19c)23d)29Correct answer is option 'C'. Can you explain this answer?

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CLAT Exam > CLAT Questions > At the end of the T20 cricket match, every pl...

Q. What was the average of their runs scored?

a)
17
b)
19
c)
23
d)
29

Correct answer is option 'C'. Can you explain this answer?

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At the end of the T20 cricket match, every player had scored a prime n...

There 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

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Directions:Answer the question on the basis of the information given below.There is an intense competition for getting into Indian team for two slots of openers. BCCI Selection Committee decides to closely monitor Dileep Trophy matches for the purpose. To keep the performance in proper perspective, it is, however, decided to award the players grades instead of recording the runs scored directly. Formula for grades is as under:Performance of three of the openers P, Q and R (under consideration for selection) in the four matches in which they participated is as under:(i) Every player scored at least one century, and at least one century was scored in every match (match I, match II, etc.).(ii) In two of the matches, Q scored 0 and 30 runs. No other scores of Q or any other players were less than 40.(iii) In each of the four matches, the grades obtained by the three openers were all different. However, it was only in match I and match III that grades not awarded to any of the three openers were identical.(iv) R secured the same grade in both match II and match IV.(v) P in match IV received the same grade as Q in his first match and R in his third match. None of them secured that grade in match II.(vi) In one of the matches, P obtained the same grade as in match III. However, the grades of Q and R in these two matches were different. Only in this particular match (other than match III), was a half century scored and a player got F grade simultaneously.Points for grades A, B, C and F are 4, 3, 1 and 0, respectively, and top 2 batsmen out of 3 are to be selected on the basis of points in the four matches (those selected should have more points than the third player for selection based on points).Consider following statements:Statement I: The average of runs scored by P in a match is at least 58.Statement II: R and P are the top performing batsmen.Statement III: The cumulative score of the three batsmen is the least in match IV.Q. Which of the above statements is/are not definitely true?

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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 average of their runs scored?a)17b)19c)23d)29Correct answer is option 'C'. Can you explain this answer?

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