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
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
- Abhishek009
- 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
Frame equations -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?
1/r = 1/x + 1/yLulaBrazilia 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 = (x+y)/xy
xy = r ( x + y )
Or, r = xy / x + y
Hence IMO answer is (D)
Abhishek
- Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Joined: Fri May 21, 2010 1:30 am
- Thanked: 335 times
- Followed by:98 members
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).
-Patrick
The answer is D. I go through the question in detail in the full solution below (taken from the GMATFix App).
-Patrick
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.
GMAT/MBA Expert
- [email protected]
- 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
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
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
GMAT/MBA Expert
- [email protected]
- 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
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
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
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
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]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews