Problem Solving

Harmonic Mean of two numbers is the reciprocal of the Arithmetic Mean of the reciprocals of the two numbers, and Geometric Mean of two numbers is the positive square root of their product. If the Harmonic Mean of two numbers is to their Geometric Mean as 24 to 25, what is the ratio in numbers?
(A) 2/3 or 3/2
(B) 4/3 or 3/4
(C) 4/9 or 9/4
(D) 16/9 or 9/16
(E) 25/9 or 9/25

sanju09 wrote:Harmonic Mean of two numbers is the reciprocal of the Arithmetic Mean of the reciprocals of the two numbers, and Geometric Mean of two numbers is the positive square root of their product. If the Harmonic Mean of two numbers is to their Geometric Mean as 24 to 25. What is the ratio in numbers?
(A) 2/3 or 3/2
(B) 4/3 or 3/4
(C) 4/9 or 9/4
(D) 16/9 or 9/16
(E) 25/9 or 9/25

let a and b be the num

Harmonic mean = 2ab/(a+b) [ 1/2*(1/a +1/b)]
Geometric mean = Sqrt (ab)

HM/AM = 2ab/((a+b)*sqrt(ab) ) = 2*sqrt(ab)/(a+b) = 24/25

sqrt(ab)/a+b = 12/25

ab/(a+b)^2 = 144/625

(a+b)^2 /ab = 625/144

a^2+2ab+b^2/ab = 625/144

a/b+b/a+2 = 625/144

a/b+b/a = 337/144 (now you can solve this by quadratic equations)

or you can look at the answer and D is the only probability since 16*9 =144

so try the luck with D

16/9+9/16 =

256+81/144 = 337/144

Hence D

Does the GMAT tests Harmonic mean?

papgust wrote:Does the GMAT tests Harmonic mean?

GMAT tests what is already told.