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Two numbers have a sum of 10 and a product of 20. What is the sum of t

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V
Joined: 02 Sep 2009
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Kudos [?]: 128688 [0], given: 12182

Two numbers have a sum of 10 and a product of 20. What is the sum of t [#permalink]

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New post 13 Sep 2017, 01:45
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A
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D
E

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79% (01:18) correct 21% (02:50) wrong based on 28 sessions

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Kudos [?]: 128688 [0], given: 12182

Senior Manager
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Joined: 02 Jul 2017
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Re: Two numbers have a sum of 10 and a product of 20. What is the sum of t [#permalink]

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New post 13 Sep 2017, 03:18
Let 2 numbers be a and b.
Given: a+b =10 and a*b =20

Find : \(\frac{1}{a} + \frac{1}{b}\)

as a+b=10 and ab =20

=>\(\frac{a+b}{ab} =\frac{10}{20}\)

=>\(\frac{a}{ab} + \frac{b}{ab} =\frac{1}{2}\)

=>\(\frac{1}{b} +\frac{1}{a} = \frac{1}{2}\) = Answer

Answer : D

Kudos [?]: 59 [0], given: 59

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Re: Two numbers have a sum of 10 and a product of 20. What is the sum of t [#permalink]

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New post 13 Sep 2017, 03:19
The two numbers are 5+sqroot(5) and 5-sqroot(5) solving the reciprocals of the two numbers the answer is 1/2.


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Kudos [?]: 258 [0], given: 546

Two numbers have a sum of 10 and a product of 20. What is the sum of t [#permalink]

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New post 13 Sep 2017, 03:22
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Bunuel wrote:
Two numbers have a sum of 10 and a product of 20. What is the sum of the reciprocals of the two numbers?

A. 1/10
B. 1/8
C. 1/4
D. 1/2
E. 2

x + y = 10
xy = 20

What is the sum of the reciprocals of the two numbers?

\(\frac{1}{x}\) + \(\frac{1}{y}\) = \(\frac{(x + y)}{xy}\)

Substituting values from above for (x + y) and (xy):

\(\frac{10}{20}\) = \(\frac{1}{2}\)

Answer
[Reveal] Spoiler:
D

Kudos [?]: 258 [0], given: 546

Two numbers have a sum of 10 and a product of 20. What is the sum of t   [#permalink] 13 Sep 2017, 03:22
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