In an electric circuit, two resistors with resistances x...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

In an electric circuit, two resistors with resistances x...

by swerve » Fri Dec 15, 2017 1:27 pm

In an electric circuit, two resistors with 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 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 OA is D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Dec 15, 2017 1:27 pm

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

by [email protected] » Fri Dec 15, 2017 3:40 pm

Hi swerve,

We're told that the reciprocal of R is equal to the SUM of the reciprocals of X and Y. This question can be solved with TESTing Values.

Based on the wording of the prompt, we can create the following equation:

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. There's only one answer that matches...

Final Answer: D

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

Contact Rich at [email protected]

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GMATWisdom: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Nov 29, 2017 4:38 pm; Thanked: 14 times

by GMATWisdom » Sat Dec 16, 2017 9:03 am

swerve wrote:In an electric circuit, two resistors with 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 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 OA is D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.

in the statement itself he is telling reciprocal of r is equal to the sum of reciprocals of x and y which means
1/r = 1/x + 1/y
or 1/r = (x+y)/xy
or r = xy/(x+y)
hence D the correct option.

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Sep 23, 2019 4:33 pm

swerve wrote:In an electric circuit, two resistors with 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 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 OA is D.

Please, can any expert explain this PS question for me? I don't understand why that is the correct answer. Thanks.

We are given that 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

Scott Woodbury-Stewart
Founder and CEO
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