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Averages Smart Math

[Smart Math] Averages Problem 1

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

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

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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

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Simply find the Arithmetic Mean of the numbers:
i.e. \frac{24+27+72}{3} = 41
Now you already know that Arithmetic Mean > Geometric Mean > Harmonic Mean, hence, the answer should be less then 41 but close to it. From amongst the options, the only one satisfying this condition is option ‘3’.

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds
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