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The question is from CAT Ratio, Mixtures and Averages. Given the product of n digits, our task is to minimize the average of those numbers which is related to the sum of those numbers. 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 2019.

Question 47: If the product of n distinct positive integers is nn. What is the minimum value of their average if n = 6?

  1. 6
  2. 10
  3. \\frac{59}{6}\\)
  4. 8

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Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: How you would relate the product with its average?

Product = 66
=(2 * 3)6
=26 * 36
To find the minimum average, we have to find the smallest possible 6 positive numbers resulting in
26.36 = 2 * 22 * 23 * 3 * 32 * 33
Therefore, 2,4,8,3,12,18 are the numbers since any other combination will result in either a larger number or a number being repeated.
Therefore, Minimum Average = \\frac{48}{6}\\) = 8

The question is "What is the minimum value of their average if n = 6?"

Hence, the answer is "8".

Choice D is the correct answer.

 


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