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

The question is from CAT Ratio, Mixtures and Averages. Another question on possible value. We need to find out the difference between maximum and minimum possible value. 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 7: In a class of 5 students, average weight of the 4 lightest students is 40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is the difference between the the maximum and minimum possible average weight overall?

1. 2.8 kgs
2. 3.2 kgs
3. 3 kgs
4. 4 kgs

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: Question to find the maximum and minimum possible values of the average of a few numbers given some other parts of the jigsaw.

Lets say that the students are named a, b, c, d and e, in increasing order of weights. The average of a, b, c and d is 40 kg, whereas the average of b, c, d and e is 45 kg.
The sum of a, b, c and d is 160 kg, and the sum of b, c, d and e is 180 kg.

What is the total weight of all the students?
There are two ways of looking at this.
a) 160 + e
b) 180 + a
Or, e is 20 more than a.

The total weight is 160 + e. So, the highest value of e will correspond to the highest possible average. The highest possible value of e occurs when it is 20 higher than the highest possible value for a, which is 40 (all the first 4 scores are equal to 40).
So, the highest possible average is \\frac{160 + 60}{5}\\) = 44
This will be the case when the weights are 40 kgs, 40kgs, 40 kgs, 40 kgs and 60 kgs.

Conversely, the least possible value for the average occurs when a is the least. This happens when e is the least too (since a is 20 less than e).
The least possible value for e is 45 = \\frac{180}{4}\\)
So, the least possible value for a would be 25.
The least possible average = \\frac{180 + 25}{5}\\) = 41

This will be the case when the weights are 25 kgs, 45kgs, 45 kgs, 45 kgs and 45 kgs. So, the difference between maximum possible and minimum possible average = 3 kgs.

The question is "What is the difference between the the maximum and minimum possible average weight overall?"

Hence, the answer is "3 kgs".

Choice C is the correct answer.