ThinkMBA

A class has \(40\) students whose average weight is \(40\) kg. Now, \(m\) new students join the class, and their average weight is \(n\) kg. If \(m+n=50\), what is the maximum possible average weight of the class now?

The average score of \(10\) students in a class is \(60\). If the scores of the top five students are not considered, the average score of the remaining students falls by \(5\). The pass mark is \(40\) and the maximum mark is \(100\). It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, what is the maximum possible score of the topper?

The scores of a class are divided into \(5\) ranges: \(51\) to \(60\), \(61\) to \(70\), \(71\) to \(80\), \(81\) to \(90\), and \(91\) to \(100\). The number of students in these ranges are respectively \(3, 8, 7, 4\), and \(3\). It is also known that the number of students who scored \(76\) or more is at least one more than the number of students who scored below \(75\). What is the minimum possible overall average score of the class?

In a class of \(5\) students, the average weight of the \(4\) lightest students is \(40\) kg, and the average weight of the \(4\) heaviest students is \(45\) kg. What is the difference between the maximum and minimum possible overall average weight of the class?

In a dataset of \(25\) observations, consider the following two questions.

I. Can \(20\) observations be below the average? II. Can \(20\) observations lie strictly between the median and the average?

School X has \(3\) classes: A, B, and C. The average score of Class B is \(16\) more than the average score of Class C. The strengths of Classes A, B, and C are in the ratio \(2:3:5\), respectively. If the average score of the school is \(2\) less than the average score of Class A, find the difference between the average score of Class A and Class C.

Natural numbers from \(1\) to \(25\), both inclusive, are split into \(5\) groups of \(5\) numbers each. The medians of these \(5\) groups are \(A, B, C, D\), and \(E\). If the average of these medians is \(m\), what are the smallest and largest possible values of \(m\)?

Four numbers \(p,q,r\), and \(s\) are chosen, and they need not be distinct. The smallest average of any three of these four numbers is \(30\), and the largest average of any three of these four numbers is \(40\). What range of values can the average of all four numbers take?

The average of \(5\) distinct positive integers is \(33\). If the average of the three largest integers in this set is \(39\), what are the minimum and maximum possible values of the median of the \(5\) integers?

Consider \(5\) distinct positive numbers \(a,b,c,d,e\). Their average is \(k\). If \(b\) is removed from the set, the average drops to \(m\), where \(m

During a school event, a certain number of merit badges were distributed among a class. One student received \(\frac{1}{6}\) of the total number of badges. This number of badges was \(5\) times the average number of badges received by each of the remaining students. How many students were there in the class?

Four numbers \(a,b,c\), and \(d\) are chosen, and the numbers may be equal. The smallest average of any three of these four numbers is \(30\), and the largest average of any three of these four numbers is \(40\). What range of values can the average of all four numbers take?

The average age of a couple was \(24\) years. After their first and second children, who were twins, were born, the average age of the family became \(13.5\) years. The average age of the family just after the third child was born was \(13.2\) years. The average age of the family after the fourth child was born was \(16\) years. The current average age of the family is \(19\) years. What is the current age of each twin child?

In a group of \(20\) people, the oldest person is \(90\) years old. If this oldest person is replaced by a new person and the average age of the group decreases by \(4\) years, find the age of the new person.

Samarth takes up a \(12\)-month project and wants to earn at least Rs. \(6000\) per month on average to make the project worthwhile. For the first \(11\) months, his average earning is Rs. \(5500\) per month. What should be his earning in the last month so that his overall average becomes Rs. \(6000\) per month?

In a sports event, Group A has \(20\) teams with an average score of \(20\), and Group B has \(25\) teams with an average score of \(25\). In Group A, the highest score is \(25\) and the lowest score is \(15\). In Group B, the highest score is \(32\) and the lowest score is \(24\). What can be the minimum and maximum values of Group B's average score if \(5\) teams are transferred from Group A to Group B?

The average of \(9\) consecutive numbers is \(T\). If the next \(3\) consecutive numbers are also added to the set, by how much will the average increase?

A shopkeeper has \(13\) boxes of chocolates, with an average of \(17\) chocolates per box. If each box has at least \(11\) chocolates and no two boxes have the same number of chocolates, what is the maximum possible number of chocolates in any one box?