the reciprocal

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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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Source: Beat The GMAT — Problem Solving | Tue Feb 16, 2010 6:15 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

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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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

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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