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

The question is from CAT Ratio, Mixtures and Averages. Average and number of terms are given, no two terms are equal, how one number could be maximized? CCAT 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 50: Arun has 13 boxes of chocolates with him, with an average of 17 chocolates per box. If each box has at least 11 chocolates and no two boxes have equal number of chocolates, then what can be the maximum possible number of chocolates in any box?

1. 23
2. 25
3. 29
4. Can't be determined

Explanatory Answer

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

Total number of chocolates = 13 * 17 = 221
For one box to have maximum number of chocolates, the other boxes need to have minimum number of chocolates i.e. 11, 12, ………………….., 22
Total = 11 * 12 + (0+1+2+……………+11)
= 132 + 66 = 198
Therefore, maximum possible chocolates = 221 – 198 = 23

The question is "what can be the maximum possible number of chocolates in any box?"

Hence, the answer is "23".

Choice A is the correct answer.