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

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Math Expert
Joined: 02 Sep 2009
Posts: 51184
If the sum of two numbers is 6, and the sum of their reciprocals is 15  [#permalink]

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23 Aug 2018, 23:19
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Difficulty:

25% (medium)

Question Stats:

88% (01:18) correct 12% (02:25) wrong based on 33 sessions

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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

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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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23 Aug 2018, 23:24
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 = $$\frac{16}{5}$$.

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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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23 Aug 2018, 23:40
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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24 Aug 2018, 00:13
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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24 Aug 2018, 01:37
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.

If the sum of two numbers is 6, and the sum of their reciprocals is 15 &nbs [#permalink] 24 Aug 2018, 01:37
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