CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

The question is about different Medians of 5 different groups. A set is divided into 5 parts, we need to find out the average of the medians of each part and maximize it. Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 7: Positive numbers 1 to 55, inclusive are placed in 5 groups of 11 numbers each. What is the maximum possible average of the medians of the 5 groups?

1. 34
2. 28
3. 35
4. 38

Explanatory Answer

Method of solving this CAT Question from Number Theory - Digits: Questions based on medians are more logic puzzles than math questions. Try this one to know that.

We need to maximise each median in order to have the overall maximum median possible.

The highest possible median is 50 as they should be 5 numbers higher than the median in the group of 11. So, if we have a set that has a, b, c, d, e, 50, 51, 52, 53, 54, 55, the median will be 50. In this set, it is best not to waste any high values on a, b, c, d or e as these do not affect the median. So, a set that reads as 1, 2, 3, 4, 5, 50, 51, 52, 53, 54, 55 will also have median 50.

The next set can be 6, 7, 8, 9, 10, 44, 45, 46, 47, 48, 49. The median will be 44.

The medians of the 5 groups can be 50, 44, 38, 32, 26. The highest possible average of the medians will be 38.

The question is "What is the maximum possible average of the medians of the 5 groups?"

Hence the answer is "38"

Choice D is the correct answer.