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In cricket, the term batting average gives an indication of how many runs a batsman has scored per innings in which he was dismissed. So, the batting average is given by the formula: (Total runs scored/Number of times the player was out)
For a particular player, the data for the last 25 matches that he batted in has to be considered. The following facts are known:
i. He was dismissed in each of the matches that he batted in
ii. The runs scored by him in any two matches is not same
iii. The sum of his five highest scores is 337
1. If the sum of his lowest five scores was 121, what would be the highest average possible?
2. If the sum of his lowest five scores was 121 and his average was more than 40, what is the maximum number of matches in which he scored less than 40?
3. If the sum of his lowest five scores was 121, what is the minimum possible value of his sixth highest score?
4. If he scored 2 centuries in these 25 matches, what is the maximum possible value of his lowest score?
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