What is the value of G. M. for 4 and 16?

Question

Accepted Answer

The correct option is 4:

The question asks for the Geometric Mean (G.M.) of two numbers, 4 and 16. The Geometric Mean is a type of average that is defined as the nth root of the product of n numbers. For two numbers, 'a' and 'b', the Geometric Mean is calculated as the square root of their product $(\sqrt{a 	imes b})$. In this case, the product of 4 and 16 is $4 	imes 16 = 64$. Taking the square root of 64 gives $\sqrt{64} = 8$. The Geometric Mean is particularly relevant in economics and finance for calculating average growth rates, and it is always less than or equal to the Arithmetic Mean.

The incorrect option is 1:
This option suggests the answer is 12. This value (12) is the **Arithmetic Mean (A.M.)** of 4 and 16, which is calculated as $(4 + 16) / 2 = 20 / 2 = 10$. Therefore, 12 is incorrect for both the Geometric Mean and the Arithmetic Mean, and the difference is likely an error in calculation or an intended distractor.

The incorrect option is 2:
The value 2 is the result of dividing 4 by 2, or the square root of 4, or it could be a simple miscalculation. It is not derived from the formula for the Geometric Mean, which requires multiplying the two values first before taking the square root.

The incorrect option is 3:
This option is 64. This value represents the **product** of the two numbers ($4 \times 16 = 64$). The Geometric Mean formula requires the square root of the product, not the product itself. Since the Geometric Mean is a type of average, it must fall between the lowest and highest values in the set (4 and 16), which 64 clearly does not.