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# if xy != 0, is (1/x + 1/y) = 2 ? 1) x=y 2) x+y = 2xy Any

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if xy != 0, is (1/x + 1/y) = 2 ? 1) x=y 2) x+y = 2xy Any [#permalink]  20 Sep 2010, 11:57
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if xy != 0, is (1/x + 1/y) = 2 ?
1) x=y
2) x+y = 2xy

Any idea ?

Thanks
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Re: Algebra DS [#permalink]  20 Sep 2010, 12:05
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tatane90 wrote:
if xy != 0, is (1/x + 1/y) = 2 ?
1) x=y
2) x+y = 2xy

Any idea ?

Thanks

Is \frac{1}{x}+ \frac{1}{y}= 2? --> is \frac{x+y}{xy}=2? --> is x+y=2xy?

(1) x=y --> question becomes is 2x=2x^2? --> reduce by 2x (we can safely do this as x\neq{0}) --> is x=1? We don't know that. Not sufficient.

(2) x+y = 2xy --> directly gives us the YES answer to the question. Sufficient.

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Re: Algebra DS [#permalink]  20 Sep 2010, 13:38
tatane90 wrote:
if xy != 0, is (1/x + 1/y) = 2 ?
1) x=y
2) x+y = 2xy

Any idea ?

Thanks

1. say x=y=2 xy=4 1/2+1/2 != 2
BUT x=y=1 xy=1 1/1 +1/1 = 2! so INSUFF

2.
you could see it another way - if x and y are the same then their sum equals to 2x or 2y and that cant be 2xy. the only way to be 2xy is if one of them is 1. so..
1 +y = 2(1)y = 1+y =2y. so y has to be 1 to satisfy 2y there fore 1/1 +1/1 =2 so SUFF
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Re: Algebra DS [#permalink]  20 Sep 2010, 18:20
tatane90 wrote:
if xy != 0, is (1/x + 1/y) = 2 ?
1) x=y
2) x+y = 2xy

Any idea ?

Thanks

1. (1/x + 1/y)
= x+y/xy
=2y/y^2
=2/y
Insufficient.

2. x+y/xy
=2xy/xy
=2

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Re: Algebra DS [#permalink]  20 Sep 2010, 18:53
tatane90 wrote:
if xy != 0, is (1/x + 1/y) = 2 ?
1) x=y
2) x+y = 2xy
Thanks

(1) x = y

1/x + 1/y = 1/x + 1/x = 2/x can't tell if 2/x = 2
1/x + 1/y = 1/y + 1/y = 2/y can't tell if 2/y = 2
insufficient

(2) x + y = 2xy

Divide both sides by x:
>> 1 + y/x = 2y
Divide both sides by y:
>> 1/y + 1/x = 2
sufficient

Ans B
Re: Algebra DS   [#permalink] 20 Sep 2010, 18:53
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