In an electric circuit, two resistors with resistances x and

BTGmoderatorLU wrote:In an electric circuit, two resistors with resistance 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 reciprocal of r is equal to the sum of the reciprocals of x and y
So, 1/r = 1/x + 1/y
We must solve this equation for r.

Take: 1/r = 1/x + 1/y
Rewrite the right side with a COMMON DENOMINATOR of xy: 1/r = y/xy + x/xy
Combine the two terms to get: 1/r = (y + x)/xy
Since we have two equivalent fractions, their reciprocals will also be equal.
That is: r/1 = xy/(y + x)
Or, r = xy/(y + x)

Answer: D

Cheers,
Brent

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: D

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