IKMC 2015 - Grades 11-12 - Self-study Question 15

Question 15

The geometric mean of n positive numbers is $\sqrt[n]{x_1x_2\cdots x_n}$. Six numbers are split into two groups of three with geometric means 3 and 12. What is the geometric mean of all six?

$4$
$6$
$15/2$
$15/6$
$36$