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Mean of the reciprocals

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by sanju09 » Thu Jan 28, 2010 12:02 am
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
Last edited by sanju09 on Thu Jan 28, 2010 11:15 pm, edited 1 time in total.
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by ajith » Thu Jan 28, 2010 12:21 am
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
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by papgust » Thu Jan 28, 2010 12:57 am
Does the GMAT tests Harmonic mean?
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by sanju09 » Thu Jan 28, 2010 2:24 am
papgust wrote:Does the GMAT tests Harmonic mean?
GMAT tests what is already told.
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by Ian Stewart » Thu Jan 28, 2010 10:26 am
papgust wrote:Does the GMAT tests Harmonic mean?
I could imagine a GMAT question which told you, in the question, what the 'harmonic mean' is, and then asked a simple question about it (simpler than the one in the post above), but you certainly don't need to study anything about harmonic means for your test. In the *very* unlikely event that you see it on test day, all the information you need will be given to you in the question itself; otherwise almost no one would have a decent chance of answering the question.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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