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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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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, 00:45
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:48) correct 30% (02:11) wrong based on 47 sessions

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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, 02:18
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
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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, 02:19
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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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, 02:22
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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

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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 07 Feb 2019, 17:57
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Re: Two numbers have a sum of 10 and a product of 20. What is the sum of t   [#permalink] 07 Feb 2019, 17:57
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