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In an electric circuit, two resistors with resistances . . .

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by M7MBA » Sat Dec 30, 2017 7:45 am
In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y?

(A) xy
(B) x + y
(C) 1/(x + y)
(D) xy/(x + y)
(E) (x + y)/xy

The OA is the option D.

I am really confused here. Experts, can you give me your explanation here? Thanks.
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by Brent@GMATPrepNow » Sat Dec 30, 2017 8:20 am
M7MBA wrote:In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y?

(A) xy
(B) x + y
(C) 1/(x + y)
(D) xy/(x + y)
(E) (x + y)/xy
The reciprocal of r is equal to the sum of the reciprocals of x and y
So, 1/r = 1/x + 1/y
We must solve this equation for r.

Take: 1/r = 1/x + 1/y
Rewrite the right side with a COMMON DENOMINATOR of xy: 1/r = y/xy + x/xy
Combine the two terms to get: 1/r = (y + x)/xy
Since we have two equivalent fractions, their reciprocals will also be equal.
That is: r/1 = xy/(y + x)
Or, r = xy/(y + x)

Answer: D

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Brent
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by Scott@TargetTestPrep » Sun Aug 25, 2019 5:45 pm
M7MBA wrote:In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y?

(A) xy
(B) x + y
(C) 1/(x + y)
(D) xy/(x + y)
(E) (x + y)/xy
We are given that the reciprocal of r is equal to the sum of the reciprocals of x and y. Thus we can say:

1/r = 1/x + 1/y

Getting a common denominator for the right side of the equation, we have:

1/r = y/xy + x/xy

1/r = (y + x)/xy

If we reciprocate both sides of the equation, we have:

r = xy/(y+x)

Answer: D

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