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Manager  Joined: 02 Dec 2012
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In an electric circuit, two resistors with resistances x and  [#permalink]

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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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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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1
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 wording is a bit confusing, though basically we are told that 1/r = 1/x + 1/y, from which it follows that r=xy/(x + y).

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Posts: 55
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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1
1
From the statements:
x+y = r --> 1
1/r = 1/x+1/y --> 2

From 1 and 2

So 1/r = (x+y)/xy,

r = xy/(x+y)

Ans - D
Manager  Joined: 03 Nov 2009
Posts: 55
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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From the statements:
x+y = r --> 1
1/r = 1/x+1/y --> 2

From 1 and 2

So 1/r = (x+y)/xy,

r = xy/(x+y)

Ans - D
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Posts: 142
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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Bunuel 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 wording is a bit confusing, though basically we are told that 1/r = 1/x + 1/y, from which it follows that r=xy/(x + y).

Could you explain this more in depth?

I interpret it as:

" r is the combined of x and y" --> r = x + y

"the reciprocal of r is equal to the sum of the reciprocals of x and y" ---> 1/r = (1/x) + (1/y)

" What is r in terms of x and y?" ---> 1 = [(1/x) + (1/y)] * r ----> r = 1 * [(x/1) + (y/1)] ---> r = x + y

Where's the flaw in my calculation?
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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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aeglorre wrote:
Bunuel 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 wording is a bit confusing, though basically we are told that 1/r = 1/x + 1/y, from which it follows that r=xy/(x + y).

Could you explain this more in depth?

I interpret it as:

" r is the combined of x and y" --> r = x + y

"the reciprocal of r is equal to the sum of the reciprocals of x and y" ---> 1/r = (1/x) + (1/y)

" What is r in terms of x and y?" ---> 1 = [(1/x) + (1/y)] * r ----> r = 1 * [(x/1) + (y/1)] ---> r = x + y

Where's the flaw in my calculation?

$$\frac{1}{r} = \frac{1}{x} + \frac{1}{y}$$;

$$\frac{1}{r} = \frac{y+x}{xy}$$;

$$r=\frac{xy}{x+y}$$.

Hope it's clear.
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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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Bunuel wrote:

$$\frac{1}{r} = \frac{1}{x} + \frac{1}{y}$$;

$$\frac{1}{r} = \frac{y+x}{xy}$$;

$$r=\frac{xy}{x+y}$$.

Hope it's clear.

Bunuel, this is still not clear to me.

I remember asking this very same question (in another thread) about a week ago. Quite obviously there are flaws in my fundamental understanding of concepts in regards to addition of algebraic fractions. Can you direct me to some guide or tutorial that in a simple but efficient way explains these concepts?

Or rather, if you - as you read this - instantly understand where my flaws are and what rule/law/fundamental error I need to "fix", I would be very thankfull if you could explain to me what understanding I lack for algebraic addition of fractions.

By the way, thank you for all of your help!
Intern  Joined: 17 Feb 2014
Posts: 1
In an electric circuit, two resistors with resistances x and  [#permalink]

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aeglorre wrote:
Bunuel 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 wording is a bit confusing, though basically we are told that 1/r = 1/x + 1/y, from which it follows that r=xy/(x + y).

Could you explain this more in depth?

I interpret it as:

" r is the combined of x and y" --> r = x + y

"the reciprocal of r is equal to the sum of the reciprocals of x and y" ---> 1/r = (1/x) + (1/y)

" What is r in terms of x and y?" ---> 1 = [(1/x) + (1/y)] * r ----> r = 1 * [(x/1) + (y/1)] ---> r = x + y

Where's the flaw in my calculation?

The steps should be as follows:

-> 1 = [(1/x)+(1/y)] * r
-> r = 1 / [(1/x)+(1/y)]
-> r = 1/ [(y+x)/xy] ... addition in denominator
-> r = 1/ [(x+y)/xy]
-> r = 1/1 * [xy/(x+y)] ... dividing fraction using reciprocal (flipping)
-> r= [xy/(x+y)]
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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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after some manipulations you get 1/R = x+y/xy you can just reverse this equation to get R --> R = xy/x+y
And yes, if a question is whether we can just reverse the equation -- 1/2 = 2/4 --> 2/1 = 4/2 (Both parts =2)
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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Hi All,

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.

Answer A: XY = (2)(3) = 6 NOT a match
Answer B: X+Y = 2+3 = 5 NOT a match
Answer C: 1/(X+Y) = 1/5 NOT a match
Answer D: XY/(X+Y) = 6/5 This IS a match
Answer E: (X+Y)/XY = 5/6 NOT a match

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In an electric circuit, two resistors with resistances x and  [#permalink]

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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 reciprocal of the sum 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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Originally posted by Asad on 15 Oct 2015, 23:33.
Last edited by Asad on 26 Jan 2017, 08:12, edited 3 times in total.
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Re: In an electric circuit, two resistors with resistances x and y are con  [#permalink]

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1/r = 1/x + 1/y
=> r = xy/(x+y)
Please correct the OA provided

This question has already been discussed - in-an-electric-circuit-two-resistors-with-resistances-x-and-y-are-con-28295.html
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Re: In an electric circuit, two resistors with resistances x and y are con  [#permalink]

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skywalker18 wrote:
1/r = 1/x + 1/y
=> r = xy/(x+y)
Please correct the OA provided

This question has already been discussed - in-an-electric-circuit-two-resistors-with-resistances-x-and-y-are-con-28295.html

My given answer is correct (B)....So, try for the second time!
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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Hi iMyself,

Your "version" of the prompt differs from the one listed in the OGs (so it was either transcribed incorrectly or purposely changed).

In the OGs, the prompt states that "the reciprocal of R is equal to the SUM of the RECIPROCALS of X and Y."

In the post here, the prompt states that "the reciprocal of R is equal to the RECIPROCAL of the SUM of X and Y."

EVERYTHING else (including the 5 answer choices) is exactly the same though, so I'm led to believe that this question was mis-transcribed. With this transcription error, the "correct" answer would change though - it would become .

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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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EMPOWERgmatRichC wrote:
Hi iMyself,

Your "version" of the prompt differs from the one listed in the OGs (so it was either transcribed incorrectly or purposely changed).

In the OGs, the prompt states that "the reciprocal of R is equal to the SUM of the RECIPROCALS of X and Y."

In the post here, the prompt states that "the reciprocal of R is equal to the RECIPROCAL of the SUM of X and Y."

EVERYTHING else (including the 5 answer choices) is exactly the same though, so I'm led to believe that this question was mis-transcribed. With this transcription error, the "correct" answer would change though - it would become .

GMAT assassins aren't born, they're made,
Rich

I've intentionally changed the question pattern. But, there is still something missing in your calculation or thinking. _________________
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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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1/r = 1/x + 1/y
1/r = y/y(1/x)+x/x(1/y)
1/r = (y/xy) + (x/xy)
1/r = (y+x/xy)
r=(xy/x+y)
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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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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

Solution:

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)

The answer is D.
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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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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

1/r=(1/x)+(1/y)=xy/(x+y)
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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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Bunuel

Why are we not considering r= x+y as it is mentioned that r is the combined resistance? Is it because we don't know how they are connected.
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Re: In an electric circuit, two resistors with resistances x and  [#permalink]

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Shiv2016 wrote:
Bunuel

Why are we not considering r= x+y as it is mentioned that r is the combined resistance? Is it because we don't know how they are connected.

The question clearly gives the relationship between r, x, and y and it is NOT r = x + y: the reciprocal of r is equal to the sum of the reciprocals of x and y.
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