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Resistors connected in parallel

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by LulaBrazilia » Mon Mar 17, 2014 8:28 am

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Answers

A

B

C

D

E

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Difficulty—

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
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by Abhishek009 » Mon Mar 17, 2014 8:35 am
LulaBrazilia 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?
Frame equations -
LulaBrazilia wrote: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?
1/r = 1/x + 1/y

1/r = (x+y)/xy

xy = r ( x + y )

Or, r = xy / x + y

Hence IMO answer is (D)
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Resistors connected in parallel

by Patrick_GMATFix » Mon Mar 17, 2014 8:39 am
Do not confuse "r is the combined resistance of the two resistors" with "r is the sum of x and y". It is the next sentence that gives us the equation we need. "the reciprocal of r is the sum of the reciprocals of x and y" means that 1/r = 1/x + 1/y

The answer is D. I go through the question in detail in the full solution below (taken from the GMATFix App).

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by [email protected] » Tue Mar 18, 2014 12:02 am
Hi LulaBrazilia,

This question can be solved with TESTing Values.

We're told that the reciprocal of R is equal to the SUM of the reciprocals of X and Y. This means....

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.

The only answer that matches is D

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by [email protected] » Tue Mar 18, 2014 12:03 am
Hi LulaBrazilia,

This question can be solved with TESTing Values.

We're told that the reciprocal of R is equal to the SUM of the reciprocals of X and Y. This means....

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.

The only answer that matches is D

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Rich
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by Jeff@TargetTestPrep » Tue Jul 17, 2018 3:41 pm
LulaBrazilia 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 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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