Question

Geometric Mean (G.M.) Of Six Numbers Is 16. If G.M. Of First Four Of Them Is 8 Then G.M. Of Other Two Is :​

Answer 1

The mean of the Other Two is 32.

Given:

Geometric Mean (G.M.) Of Six Numbers Is 16. G.M and Of the First Four Of Them Are 8.

To Find:

The mean of Other Two.

Solution:

To find the mean of the other two numbers we will follow the following steps:

As we know,

Mean is the average of all the numbers or equal to the ratio of the sum of all the numbers to the total numbers.

So,

Let the first six numbers be:

a, b, c, d, e, f

Their mean is 16 so,

$\frac{a + b + c + d + e + f}{6} = 16$

So,

$a + b + c + d + e + f = 16 \times 6 = 96$

Now,

G.M. Of First Four Of Them Is 8

So,

Mean of first four numbers =

$\frac{a + b + c + d}{4} = 8$

$a + b + c + d = 8 \times 4 = 32$

Now,

So, the sum of the other two numbers will be

= sum of six numbers - the sum of first four numbers = 96 - 32 = 64

So,

Mean of last two numbers =

$\frac{e+f}{2} =\frac{64}{2} = 32$

Henceforth, the means of Other Two is 32.

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