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

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by swerve » Fri Dec 15, 2017 1:27 pm
In an electric circuit, two resistors with 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 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 D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.
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by [email protected] » Fri Dec 15, 2017 3:40 pm
Hi swerve,

We're told that the reciprocal of R is equal to the SUM of the reciprocals of X and Y. This question can be solved with TESTing Values.

Based on the wording of the prompt, we can create the following equation:

1/R = 1/X + 1/Y

We're asked for the value of R in terms of X and Y

If X = 2 and Y = 3, then we have...

1/R = 1/2 + 1/3

1/R = 3/6 + 2/6 = 5/6

R = 6/5

So we need an answer that = 6/5 when X = 2 and Y = 3. There's only one answer that matches...

Final Answer: D

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by GMATWisdom » Sat Dec 16, 2017 9:03 am
swerve wrote:In an electric circuit, two resistors with 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 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 D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.
in the statement itself he is telling reciprocal of r is equal to the sum of reciprocals of x and y which means
1/r = 1/x + 1/y
or 1/r = (x+y)/xy
or r = xy/(x+y)
hence D the correct option.
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by Scott@TargetTestPrep » Mon Sep 23, 2019 4:33 pm
swerve wrote:In an electric circuit, two resistors with 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 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 D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.
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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