The geometric mean of (x 1, x 2, x 3,…. X n) is X and the geometric me

| The geometric mean of (x1, x2, x3,…. Xn) is X and the geometric mean of (y1, y2, y3,….Yn) is Y. Which of the following is/are correct?

1. The geometric mean of

(x1y1, x2y2, x3y3, …. Xnyn) is XY.

2. The geometric mean of

is

Select the correct answer using the code given below :

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 nor 2

Right Answer is: C

SOLUTION

Let us consider an example(x1,x2,x3,…..xn)

=(1, 2, 4, 2)

G.M = =2=X

and (y1,y2,y3,…..yn)

=(2,3,4,6) = =2(32)1/4

Y=2√3

Now GM of (x1y1,x2y2,x3y3…..xnyn)

G.M of (2,6,16,12) =  =4√3 XY

Hence statement 1 is correct

Now,

G.M of (x1/y1,x2/y2,x3/y3…..xn/yn)

G.M of (12,23,44,26)

=1/√3 =X/Y

Hence 2nd statement is also true

Both 1 and 3 are correct.

Leave a Comment

Your email address will not be published. Required fields are marked *