The following table shows the number of employees and their median age in eight companies located in a district. CompanyNumber of employeesMedian age A 32 24 B 28 30 C 43 39 D 39 45 E 35 49 F 29 54…
Question and options
The following table shows the number of employees and their median age in eight companies located in a district.
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H.
In company F, the lowest possible sum of the ages of all employees is:
| Company | Number of employees | Median age |
|---|---|---|
| A | 32 | 24 |
| B | 28 | 30 |
| C | 43 | 39 |
| D | 39 | 45 |
| E | 35 | 49 |
| F | 29 | 54 |
| G | 23 | 59 |
| H | 16 | 63 |
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H.
In company F, the lowest possible sum of the ages of all employees is:
- 1506
- 1510
- 1566
- 1496
Answer and explanation
Correct answer: B - 1510
The minimum sum in company F is 1,510. Every F employee must be at least 50 because E has median 49 and F's ages are strictly higher than all of E's ages. F's median is its 15th age, so the smallest total is , attainable when every E employee is 49. Putting 15 employees at 50 gives 1,506 and moves F's median down to 50.
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IPMAT Indore
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