In an electric circuit, two resistors with resistances x and y are con

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).

Answer: D.
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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

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.
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Hi All,

While this question looks a little "crazy", it 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

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

The answer is D.
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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.
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Bunuel as per this wording "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" i did this 1/r = 1/x + 1/y and chose C

can you explan how you got this ? --> r=xy/(x + y)

thanks !

It's very simple algebraic manipulation.

1/r = 1/x + 1/y

1/r = (x + y)/(xy)

xy = r*(x + y)

r = xy/(x + y)
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Hi all,

Can anyone advise why its not good logic to flip the reciprocals as the first step?

Hi HiItsAlif,

The 'math step' that you're thinking about is NOT mathematically correct. For example:

1/2 = 1/3 + 1/6

However, if you 'flip' the reciprocals, you end up with...

2 = 3 + 6

...which is not correct.

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