Elevator Weight Limit

CAT 2017 Slot 1 · QA · Medium · Averages

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An elevator has a weight limit of 630 kg630\text{ kg}. It is carrying a group of people of whom the heaviest weighs 57 kg57\text{ kg} and the lightest weighs 53 kg53\text{ kg}. What is the maximum possible number of people in the group?

Answer

11

Explanation

To maximize the number of people nn, we should minimize their weights. There is at least 1 person of weight 57 kg57\text{ kg} and 1 person of weight 53 kg53\text{ kg}. All other (n−2)(n - 2) people can weigh at least 53 kg53\text{ kg}. Total weight = 57+53+(n−2)×53≤63057 + 53 + (n - 2) \times 53 \le 630 110+53(n−2)≤630110 + 53(n - 2) \le 630 53(n−2)≤520  ⟹  n−2≤9.81  ⟹  n−2=9  ⟹  n=1153(n - 2) \le 520 \implies n - 2 \le 9.81 \implies n - 2 = 9 \implies n = 11.

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