# CAT Practice : Averages, Ratios, Mixtures

Averages

## Averages

Q.47: If the product of n distinct positive integers is n^n. What is the minimum value of their average if n=6?
1. 6
2. 10
3. $\frac{59}{6}$
4. 8

Choice D. 8

## Detailed Solution

Product = 66
=(2 * 3)6
=26 * 36
To find the minimum average, we have to find the smallest possible 6 positive numbers resulting in 2^6.3^6 =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 = $\frac{48}{6} = 8$

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