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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: 41886

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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13 Sep 2017, 01:45
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79% (01:18) correct 21% (02:50) wrong based on 28 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
[Reveal] Spoiler: OA

_________________

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

Senior Manager
Joined: 02 Jul 2017
Posts: 252

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

Location: India
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, 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

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

Intern
Joined: 13 Sep 2017
Posts: 1

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

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, 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.

Sent from my iPhone using GMAT Club Forum mobile app

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

Director
Joined: 22 May 2016
Posts: 806

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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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):

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

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

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