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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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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Two numbers have a sum of 10 and a product of 20. What is the sum of t  [#permalink]

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13 Sep 2017, 00:45
00:00

Difficulty:

35% (medium)

Question Stats:

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

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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

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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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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

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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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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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13 Sep 2017, 02:22
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1
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):

$$\frac{10}{20}$$ = $$\frac{1}{2}$$

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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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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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