Difference between revisions of "2006 iTest Problems/Problem 2"

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==Solution==
 
==Solution==
  
The [[harmonic mean]] of two numbers is the reciprocal of the mean of the reciprocals of the two numbers.  The reciprocals of <math>10</math> and <math>20</math> are <math>\tfrac1{10}</math> and <math>\tfrac1{20}</math> and the mean of the two is <math>\tfrac3{40}</math>, so the harmonic mean is <math>\boxed{\textbf{(B) } \tfrac{40}{3}}</math>
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The [[harmonic mean]] of two numbers is the reciprocal of the mean of the reciprocals of the two numbers.  The reciprocals of <math>10</math> and <math>20</math> are <math>\tfrac1{10}</math> and <math>\tfrac1{20}</math> and the mean of the two is <math>\tfrac3{40}</math>, so the harmonic mean is <math>\boxed{\textbf{(B) } \tfrac{40}{3}}</math>.
  
 
==See Also==
 
==See Also==
  
 
{{iTest box|year=2006|num-b=1|num-a=3|ver=[[2006 iTest Problems/Problem U1|U1]] '''•''' [[2006 iTest Problems/Problem U2|U2]] '''•''' [[2006 iTest Problems/Problem U3|U3]] '''•''' [[2006 iTest Problems/Problem U4|U4]] '''•''' [[2006 iTest Problems/Problem U5|U5]] '''•''' [[2006 iTest Problems/Problem U6|U6]] '''•''' [[2006 iTest Problems/Problem U7|U7]] '''•''' [[2006 iTest Problems/Problem U8|U8]] '''•''' [[2006 iTest Problems/Problem U9|U9]] '''•''' [[2006 iTest Problems/Problem U10|U10]]}}
 
{{iTest box|year=2006|num-b=1|num-a=3|ver=[[2006 iTest Problems/Problem U1|U1]] '''•''' [[2006 iTest Problems/Problem U2|U2]] '''•''' [[2006 iTest Problems/Problem U3|U3]] '''•''' [[2006 iTest Problems/Problem U4|U4]] '''•''' [[2006 iTest Problems/Problem U5|U5]] '''•''' [[2006 iTest Problems/Problem U6|U6]] '''•''' [[2006 iTest Problems/Problem U7|U7]] '''•''' [[2006 iTest Problems/Problem U8|U8]] '''•''' [[2006 iTest Problems/Problem U9|U9]] '''•''' [[2006 iTest Problems/Problem U10|U10]]}}

Latest revision as of 02:24, 27 November 2018

Problem

Find the harmonic mean of 10 and 20.

$\mathrm{(A)}\, 15\quad\mathrm{(B)}\, \frac{40}{3}$

Solution

The harmonic mean of two numbers is the reciprocal of the mean of the reciprocals of the two numbers. The reciprocals of $10$ and $20$ are $\tfrac1{10}$ and $\tfrac1{20}$ and the mean of the two is $\tfrac3{40}$, so the harmonic mean is $\boxed{\textbf{(B) } \tfrac{40}{3}}$.

See Also

2006 iTest (Problems)
Preceded by:
Problem 1
Followed by:
Problem 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 U1 U2 U3 U4 U5 U6 U7 U8 U9 U10
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