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# 1/X+1/Y=40/319. Find X + Y. (1) X and Y are primes (2)

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1/X+1/Y=40/319. Find X + Y. (1) X and Y are primes (2) [#permalink]

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18 May 2004, 14:58
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1/X+1/Y=40/319. Find X + Y.

(1) X and Y are primes
(2) X>Y>1
Senior Manager
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18 May 2004, 15:20
mirhaque wrote:
1/X+1/Y=40/319. Find X + Y.

(1) X and Y are primes
(2) X>Y>1

(X+Y)/(XY) = 40/319

1. X and Y are primes.
case 1: X = Y, then 2/X = 40/319 or X = 319/20 (contradiction)
case 2: X <> Y, X, or Y, does not divide X+Y. Hence XY = 319, X+Y = 40.
or <X, Y> = <11, 29> or <29, 11>
Sufficient.

2. insufficient.

Re: DS:   [#permalink] 18 May 2004, 15:20
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