Resistors connected in parallel

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 116
Joined: Tue Mar 31, 2009 10:50 am
Followed by:1 members

Resistors connected in parallel

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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

User avatar
Master | Next Rank: 500 Posts
Posts: 359
Joined: Wed Mar 11, 2009 4:37 am
Location: Kolkata, India
Thanked: 50 times
Followed by:2 members

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)
Abhishek

User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

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).

Image

-Patrick
  • Ask me about tutoring.

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews