GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 May 2020, 12:25 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In an electric circuit, two resistors with resistances x and

Author Message
TAGS:

### Hide Tags

Manager  Joined: 02 Dec 2012
Posts: 172
In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

5
1
33 00:00

Difficulty:   15% (low)

Question Stats: 75% (01:05) correct 25% (01:16) wrong based on 1805 sessions

### HideShow timer Statistics

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
Math Expert V
Joined: 02 Sep 2009
Posts: 64242
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

2
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).

_________________
Manager  Joined: 03 Nov 2009
Posts: 54
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

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: 54
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

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: 12 Jan 2013
Posts: 137
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

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?
Math Expert V
Joined: 02 Sep 2009
Posts: 64242
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

2
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.
_________________
Manager  Joined: 12 Jan 2013
Posts: 137
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

1
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]

### Show Tags

1
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)]
Current Student B
Joined: 10 Mar 2013
Posts: 449
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A$) GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: In an electric circuit, two resistors with resistances x and [#permalink] ### Show Tags 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) EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 16738 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In an electric circuit, two resistors with resistances x and [#permalink] ### Show Tags 1 1 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 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ SVP  V Joined: 23 Feb 2015 Posts: 1886 In an electric circuit, two resistors with resistances x and [#permalink] ### Show Tags 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 Originally posted by Asad on 15 Oct 2015, 22:33. Last edited by Asad on 26 Jan 2017, 07:12, edited 3 times in total. Verbal Forum Moderator V Status: Greatness begins beyond your comfort zone Joined: 08 Dec 2013 Posts: 2446 Location: India Concentration: General Management, Strategy Schools: Kelley '20, ISB '19 GPA: 3.2 WE: Information Technology (Consulting) Re: In an electric circuit, two resistors with resistances x and y are con [#permalink] ### Show Tags 1/r = 1/x + 1/y => r = xy/(x+y) Please correct the OA provided Answer D . This question has already been discussed - in-an-electric-circuit-two-resistors-with-resistances-x-and-y-are-con-28295.html _________________ When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long SVP  V Joined: 23 Feb 2015 Posts: 1886 Re: In an electric circuit, two resistors with resistances x and y are con [#permalink] ### Show Tags skywalker18 wrote: 1/r = 1/x + 1/y => r = xy/(x+y) Please correct the OA provided Answer D . 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! EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 16738 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In an electric circuit, two resistors with resistances x and [#permalink] ### Show Tags 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 _________________ SVP  V Joined: 23 Feb 2015 Posts: 1886 In an electric circuit, two resistors with resistances x and [#permalink] ### Show Tags 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. Originally posted by Asad on 19 Oct 2015, 10:02. Last edited by Asad on 21 Apr 2020, 21:01, edited 1 time in total. Intern  Joined: 23 Mar 2016 Posts: 24 Schools: Tulane '18 (M$)
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

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)
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

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)

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director  P
Joined: 04 Sep 2015
Posts: 626
Location: India
WE: Information Technology (Computer Software)
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

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)
Director  G
Joined: 02 Sep 2016
Posts: 625
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 64242
Re: In an electric circuit, two resistors with resistances x and  [#permalink]

### Show Tags

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.
_________________ Re: In an electric circuit, two resistors with resistances x and   [#permalink] 04 Sep 2017, 02:27

Go to page    1   2    Next  [ 31 posts ]

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