Mean, Median & Mode - Past Year Questions

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Q1:

Suppose a,ba, b and cc are three real numbers such that Max(a,b,c)+Min(a,b,c)=15\text{Max} (a, b, c) + \text{Min} (a, b, c) = 15, and Median(a,b,c)−Mean(a,b,c)=2\text{Median} (a, b, c) - \text{Mean} (a, b, c) = 2. Then the median of a,ba, b and cc is
Answer options
Option 2
Correct Answer
Explanation →

Q2:

The following table shows the number of employees and their median age in eight companies located in a district.
CompanyNumber of employeesMedian age
A3224
B2830
C4339
D3945
E3549
F2954
G2359
H1663
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.
The highest possible age of an employee of company A is:
29
Correct Answer
Explanation →

Q3:

The following table shows the number of employees and their median age in eight companies located in a district.
CompanyNumber of employeesMedian age
A3224
B2830
C4339
D3945
E3549
F2954
G2359
H1663
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.
The median age of employees across the eight companies is:
45
Correct Answer
Explanation →

Q4:

The following table shows the number of employees and their median age in eight companies located in a district.
CompanyNumber of employeesMedian age
A3224
B2830
C4339
D3945
E3549
F2954
G2359
H1663
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:
1510
Correct Answer
Explanation →

Q5:

Let 50 distinct positive integers be chosen such that the highest among them is 100, and the average of the largest 25 integers among them exceeds the average of the remaining integers by 50. Then the maximum possible value of the sum of all the 50 integers is _________.
3150
Correct Answer
Explanation →

Q6:

A class consists of 30 students. Each of them has registered for 5 courses. Each course instructor conducts an exam out of 200 marks. The average percentage marks of all 30 students across all courses they have registered for, is 80%. Two of them apply for revaluation in a course. If none of their marks reduce, and the average of all 30 students across all courses becomes 80.02%, the maximum possible increase in marks for either of the 2 students is
6
Correct Answer
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Q7:

The average marks of 6 students in a test is 64. All the students got different marks, one of the students obtained 70 marks and all other students scored 40 or above. The maximum possible difference between the second highest and the second lowest marks is
Answer options
Option 2
Correct Answer
Explanation →

Q8:

The average of five distinct integers is 110 and the smallest number among them is 100. The maximum possible value of the largest integer is
144
Correct Answer
Explanation →

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