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CAT 2017 Slot 1 — QA Question 3

Basics of AverageEasy

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

Answer & solution

Correct answer: 11

Answer: 11

Solution

Easy

To maximise the count of people under a fixed weight cap, make everyone as light as possible. But the constraints force at least one person at the heaviest weight (5757) and one at the lightest (5353); fill the remaining capacity with 5353 kg people.

1

Reserve the heaviest person. At least one person weighs 5757 kg, so set that aside first.

Remaining capacity=630−57=573 kg\begin{aligned} &\text{Remaining capacity} = 630 - 57 = 573 \text{ kg} \end{aligned}
2

Pack the rest at the lightest weight. Use 5353 kg people to maximise the number.

57353=10.81…(can’t exceed capacity)⇒ 10 people at 53 kg (=530 kg)\begin{aligned} &\frac{573}{53} = 10.81\ldots \quad\text{(can't exceed capacity)}\\ &\Rightarrow\ 10 \text{ people at } 53\text{ kg } (=530\text{ kg}) \end{aligned}
3

Total people. The 1010 light people plus the 11 heaviest. (The lightest-weight requirement is already met by these 5353 kg people.)

10+1=11(check: 530+57=587≤630)\begin{aligned} &10 + 1 = 11 \quad\text{(check: } 530+57=587\le 630) \end{aligned}
11 people11 \text{ people}

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CAT 2017 Slot 1 QA Q3: An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg a — Solution | TheCATExam