The harmonic mean of n numbers is the reciprocal of the arithmetic

Question

﻿The harmonic mean of n numbers is the reciprocal of the arithmetic mean of their reciprocals. What is the harmonic mean of 2, 4, 6, and 12 ?

A. 1/6

B. 1/4

C. 1

D. 4

E. 6

gmatophobia · Accepted Answer

Arithmetic Mean of  (\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{12})

The LCM of the denominator = 12

Mean = Sum / Number of terms

Sum =  \frac{6 + 3 + 2 + 1 }{ 12} = \frac{12}{12} = 1

Average =  \frac{1}{4}

Harmonic Mean = 1/(1/4) = 4

Option D

averagedude23 · Answer

This problem took my mind behind the woodshed.

zachadam1999 · Answer

4?

4/ .5 +.25 + 0.167 + 0.083 =4

4/ 1/2+1/4+1/6+1/12

I’m not sure if this is correct… needs verification

Posted from my mobile device

JeffTargetTestPrep · Answer

The arithmetic mean of the reciprocals is:

(1/2 + 1/4 + 1/6 + 1/12)/4 = (12/12)/4 = 1/4

Since the reciprocal of the arithmetic mean of the reciprocals is 4/1 = 4, the harmonic mean is 4.

Answer: D

KanikaJain · Answer

The harmonic mean of n numbers is the reciprocal of the arithmetic mean of their reciprocals. What is the harmonic mean of 2, 4, 6, and 12 ?

A. 1/6

B. 1/4

C. 1

D. 4

E. 6

AM: (1/2 + 1/4 + 1/6 + 1/12)/4

= ((6+3+2+1)/12)/4
= 1/4

HM = 4

lawyeroffduty · Answer

can anyone please share some more question on this topic, and also should i develop conceptual clarity on this topic as i haven't studied this under the arithmetic? please let me know and thank you in advance

Bunuel · Answer

The question tests statistics and number properties. Are you looking for questions on statistics and number properties?

If you’re referring to harmonic mean questions, then on the GMAT you won’t get a question on harmonic mean without the question itself defining what it is. So the questions on harmonic mean are quite rare, and even if you get them, the question will provide the definition.

The harmonic mean of n numbers is the reciprocal of the arithmetic

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The harmonic mean of n numbers is the reciprocal of the arithmetic

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