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

The question is from CAT Ratio, Mixtures and Averages. Another question on possible values. We need to find out the difference between the highest and lowest possible 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 19: Average of 6 distinct positive integers is 33. The median of the three largest numbers is 43. What is the difference between the highest and lowest possible median of the 6 numbers?

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: Given a set of numbers, mean of the overall set, and median of a subset, how does one find the possible range of the median of the overall set.

Let a, b, c, d, e, f be the six numbers in ascending order.
e = 43; a + b + c + d + e + f = 198
Median of 6 integers = \\frac{c + d}{2}\\)
\\frac{c + d}{2}\\) is maximum when c and d are maximum since e = 43, d_max = 42 and c_max = 41
\\frac{c + d}{2}\\) is minimum when c and d are minimum a_min = 1, b_min = 2, c_min = 3, d_min = 4
Therefore, = \\frac{c + d}{2}\\)min = 3.5
Max – min = 41.5 – 3.5 = 38

The question is "What is the difference between the highest and lowest possible median of the 6 numbers?"

Hence, the answer is "Highest and lowest possible median is 38".