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. Range of the average and all the numbers but one is given, we need to determine the number of possible values for that one number. 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 48: If M is a positive integer such that average of 31, 33, M, 36. 37 lies b/w 40 and 43 (both inclusive). What is the number of possible values of M?

1. 16
2. 20
3. 24
4. No such M exists

Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: How the individual data points affect the average?

31 + 33 + 36 + 37 = 137
If Avg (inc M) = 40 => Total 40 x 5 = 200 => M = 200 – 137 = 63
If Avg (inc M) = 43 => Total 43 x 5 = 215 => M = 215 – 137 = 78
Therefore, Number of possible values M can take = 78 – 63 + 1 (Don’t forget to add the 1) = 16

The question is "What is the number of possible values of M?"

Hence, the answer is "16".

Choice A is the correct answer.