CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

The question is from CAT Ratio, Mixtures and Averages. Average of 5 numbers and the average of the largest 3 numbers are given and we need to determine the minimum and maximum possible value of the median. CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023.

Question 17: The average of 5 distinct positive integers if 33. What are the maximum and minimum possible values of the median of the 5 numbers if the average of the three largest numbers within this set is 39?

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: Finding the maximum and minimum possible values of the median given the average of a set of numbers.

Let the numbers be a, b, c, d, e in ascending order. a + b + c + d + e = 165. Average of the three largest numbers is 39, so c + d + e = 117, or a + b = 48.

We need to find the maximum and minimum possible values of c.

For minimum value, a and b have to be minimum. a + b = 48. Let us assume a = 23, b = 25, ca can be as low as 26.
23, 25, 26, 45, 46 is a possible sequence that satisfies the conditions.

For maximum value, we need d + e to be minimum as c + d + e = 117. we can have c = 38, d = 39 and e = 40. Or, the maximum value c can take = 38.

23, 25, 38, 39, 40 is a possible sequence that satisfies the conditions specified.

Hence, the minimum value of the median is 26 and maximum value of the median is 38

The question is "What are the maximum and minimum possible values of the median of the 5 numbers if the average of the three largest numbers within this set is 39?"

Hence, the answer is "Min is 26 and Max is 38".