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# [Smart Math] Averages Problem 1

Here’s and example of a SMART MATH problem for AVERAGES.

### Problem

What is the Geometric mean of 24, 27 and 72?

1. 29
2. 30
3. 36
4. 42
5. 54

### The Usual Method

First get the factors of each of the numbers

24 = $2^{3}\times 3^{1}$
27 = $3^{3}$
72 = $2^{3}\times 3^{2}$

Geometric mean for them is given by:
$\sqrt[3]{24\times 27\times 72}$=
$\sqrt[3]{2^{6}\times 3^{6}}$
= $2^{2}\times 3^{2}$= 4 x 9 = 36

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds

### Using Technique

i.e. $\frac{24+27+72}{3}$ = 41