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

**Problem**

**Problem**

What is the annual rate of growth of population of bacteria which has increased by 25% in the first hour 30% in the second hour and 10% in the third hour?

- 25
- 21
- 20
- 23
- None of these

**The Usual Method**

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Annual rate of growth = Geometric Mean (GM) as shown below:

= = 1.21

i.e. 21 %

**(Ans: 2)**

*Estimated Time to arrive at the answer = 120 seconds as this method requires finding a cube root which can best be done in an iterative manner without the use of a calculator*

**Using Technique**

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Simply find the Arithmetic Mean (AM) of the three percentage values

i.e. = = 21

or 21.67%

We already know that AM > GM and that the difference is small when the individual values are ‘near’ each other. Thus the actual answer has to be less than 21.67% but close to it. Hence, the answer must be 21% or option ‘2’.

**(Ans: 2)**

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