CAT 2021 Averages Question (Hard)

Question

The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is

Accepted Answer

Step 1 Total students 25 Average score 50 Total score 25 50 1250 Let each topper score . So, total score of 5 toppers 5x Remaining 20 students total score 1250 - 5x We want to maximize minimize score of the other 20 students Step 2 Other 20 scores are distinct integers with the lowest being 30. To m

CAT 2021

Quantitative

Averages

Hard

The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is

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