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the reciprocal

by sanju09 » Tue Feb 16, 2010 6:15 am
Harmonic Mean of two numbers is the reciprocal of the Arithmetic Mean of the reciprocals of the two numbers. The Harmonic Mean of p and q is 1, then q is equal to

(A) 2 p/ (2 p - 1)
(B) 2 p/ (2 p + 1)
(C) 1/ (2 p)
(D) p/ (2 p - 1)
(E) p/ (2 p + 1)
Last edited by sanju09 on Tue Feb 16, 2010 11:37 pm, edited 1 time in total.
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by ajith » Tue Feb 16, 2010 6:36 am
sanju09 wrote:Harmonic Mean of two numbers is the reciprocal of the Arithmetic Mean of the reciprocals of the two numbers. The Harmonic Mean of p and q is 1, then q is equal to

(A) 2 a/ (2 a - 1)
(B) 2 a/ (2 a + 1)
(C) 1/ (2 a)
(D) a/ (2 a - 1)
(E) a/ (2 a + 1)
The answer choices feature 'a' which is not mentioned in the question, I assume a=p.

HM = 1/(1/p+1/q)/2 = 2pq/(p+q) =1

p+q= 2pq
p = 2pq-q
p = q (2p-1)
q= p/(2p-1)

D
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by sanju09 » Tue Feb 16, 2010 6:43 am
ajith wrote:
sanju09 wrote:Harmonic Mean of two numbers is the reciprocal of the Arithmetic Mean of the reciprocals of the two numbers. The Harmonic Mean of p and q is 1, then q is equal to

(A) 2 a/ (2 a - 1)
(B) 2 a/ (2 a + 1)
(C) 1/ (2 a)
(D) a/ (2 a - 1)
(E) a/ (2 a + 1)
The answer choices feature 'a' which is not mentioned in the question, I assume a=p.

HM = 1/(1/p+1/q)/2 = 2pq/(p+q) =1

p+q= 2pq
p = 2pq-q
p = q (2p-1)
q= p/(2p-1)

D
please take a as p, I'll edit that on the next day.
The mind is everything. What you think you become. -Lord Buddha



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by gmatmachoman » Tue Feb 16, 2010 6:46 am
Agreed... D
If u wuld have missed the term "reciprocals of numbers P&Q" and instead took reciprocal of arithemetic mean of P& Q, then u wuld land up with q=(2-p)
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