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If the sum of two numbers is 6, and the sum of their reciprocals is 15

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Posts: 49271
If the sum of two numbers is 6, and the sum of their reciprocals is 15  [#permalink]

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New post 24 Aug 2018, 00:19
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

90% (01:17) correct 10% (02:23) wrong based on 30 sessions

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Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
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If the sum of two numbers is 6, and the sum of their reciprocals is 15  [#permalink]

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New post 24 Aug 2018, 00:24
Let the number be X and Y.
Given, X+Y = 6.

and \(\frac{1}{X}\)+\(\frac{1}{Y}\) = \(\frac{15}{8}\).

\(\frac{X+Y}{XY}\) = \(\frac{15}{8}\)

Substituting X+Y = 6.

We get \(\frac{6}{XY}\) = \(\frac{15}{8}\) or XY = \(\frac{16}{5}\).

C is the answer.
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If the sum of two numbers is 6, and the sum of their reciprocals is 15  [#permalink]

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New post 24 Aug 2018, 00:40
Bunuel wrote:
If the sum of two numbers is 6, and the sum of their reciprocals is 15/8, what is the product of the two numbers?

A. 5/24
B. 5/16
C. 16/5
D. 25/4
E. 45/4


Given , the sum of two numbers is 6.
If one number is n, then the other number is 6-n.

To find:- n*(6-n)

Given, the sum of their reciprocals is 15/8
Or, \(\frac{1}{n}+\frac{1}{6-n}=\frac{15}{8}\)
Or, \(\frac{6}{n(6-n)}=\frac{15}{8}\)
Or, \(n*(6-n)=\frac{8*6}{15}=\frac{16}{5}\)

Ans. (C)
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Re: If the sum of two numbers is 6, and the sum of their reciprocals is 15  [#permalink]

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New post 24 Aug 2018, 01:13
Bunuel wrote:
If the sum of two numbers is 6, and the sum of their reciprocals is 15/8, what is the product of the two numbers?

A. 5/24
B. 5/16
C. 16/5
D. 25/4
E. 45/4
C
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If the sum of two numbers is 6, and the sum of their reciprocals is 15  [#permalink]

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New post 24 Aug 2018, 02:37
Bunuel wrote:
If the sum of two numbers is 6, and the sum of their reciprocals is 15/8, what is the product of the two numbers?

A. 5/24
B. 5/16
C. 16/5
D. 25/4
E. 45/4


Let the numbers be x and y.

x + y = 6

\(\frac{1}{x}\) +\(\frac{1}{y}\) = \(\frac{15}{8}\)

\(\frac{x + y}{xy}\) = \(\frac{15}{8}\)

8(x + y) = 15xy

8(6) = 15xy

xy = \(\frac{48}{15}\)

xy = \(\frac{16}{5}\).................This is what we are looking for. the product of 2 numbers.

The best answer is C.
If the sum of two numbers is 6, and the sum of their reciprocals is 15 &nbs [#permalink] 24 Aug 2018, 02:37
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