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# If rs 0, does 1/r + 1/s = 1 (1) rs = 1 (2) s + r = 2.5 Did

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If rs 0, does 1/r + 1/s = 1 (1) rs = 1 (2) s + r = 2.5 Did [#permalink]  12 Dec 2010, 08:05
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Difficulty:

95% (hard)

Question Stats:

17% (03:12) correct 83% (01:11) wrong based on 48 sessions
If rs ≠ 0, does 1/r + 1/s = 1

(1) rs = 1
(2) s + r = 2.5

Did not understand the OA
[Reveal] Spoiler: OA

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Re: DS Algebra [#permalink]  12 Dec 2010, 08:25
1
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Expert's post
rxs0005 wrote:
If rs ≠ 0, does 1/r + 1/s = 1

(1) rs = 1
(2) s + r = 2.5

Did not understand the OA

Is $$\frac{1}{r}+\frac{1}{s}=1$$?

(1) rs = 1 --> $$s=\frac{1}{r}$$ --> question becomes: is $$\frac{1}{r}+r=1$$ --> is $$r^2-r+1=0$$, no real $$r$$ satisfies this equation (equation has no real roots), so the answer is NO. Sufficient.
(2) s + r = 2.5 --> $$s=2.5-r$$ --> question becomes: is $$\frac{1}{r}+\frac{1}{2.5-r}=1$$ --> is $$2r^2-5r+5=0$$, no real $$r$$ satisfies this equation (equation has no real roots), so the answer is NO. Sufficient.

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Re: DS Algebra [#permalink]  14 Dec 2010, 03:28
Nice one... Certainly tricky
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Status: Last few days....Have pressed the throttle
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Re: DS Algebra [#permalink]  27 Dec 2010, 02:14
Bunuel wrote:
rxs0005 wrote:
If rs ≠ 0, does 1/r + 1/s = 1

(1) rs = 1
(2) s + r = 2.5

Did not understand the OA

Is $$\frac{1}{r}+\frac{1}{s}=1$$?

(1) rs = 1 --> $$s=\frac{1}{r}$$ --> question becomes: is $$\frac{1}{r}+r=1$$ --> is $$r^2-r+1=0$$, no real $$r$$ satisfies this equation (equation has no real roots), so the answer is NO. Sufficient.
(2) s + r = 2.5 --> $$s=2.5-r$$ --> question becomes: is $$\frac{1}{r}+\frac{1}{2.5-r}=1$$ --> is $$2r^2-5r+5=0$$, no real $$r$$ satisfies this equation (equation has no real roots), so the answer is NO. Sufficient.

A simpler approach would be:
Question is whether -> 1/r + 1/s = 1 or r+s/rs=1....(eq.1)

Stmt 1 -> rs=1 , substituting in (eq.1)

r+s=1 or 1/r+1/s = 1 -> Sufficient

Stmt 1 -> s+r=2.5 , substituting in (eq.1)

2.5/rs=1 => rs=2.5

or 1/r+1/s = 1 -> Sufficient

Ans - D
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Posts: 30376
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Re: DS Algebra [#permalink]  27 Dec 2010, 02:21
Expert's post
oldstudent wrote:
Bunuel wrote:
rxs0005 wrote:
If rs ≠ 0, does 1/r + 1/s = 1

(1) rs = 1
(2) s + r = 2.5

Did not understand the OA

Is $$\frac{1}{r}+\frac{1}{s}=1$$?

(1) rs = 1 --> $$s=\frac{1}{r}$$ --> question becomes: is $$\frac{1}{r}+r=1$$ --> is $$r^2-r+1=0$$, no real $$r$$ satisfies this equation (equation has no real roots), so the answer is NO. Sufficient.
(2) s + r = 2.5 --> $$s=2.5-r$$ --> question becomes: is $$\frac{1}{r}+\frac{1}{2.5-r}=1$$ --> is $$2r^2-5r+5=0$$, no real $$r$$ satisfies this equation (equation has no real roots), so the answer is NO. Sufficient.

A simpler approach would be:
Question is whether -> 1/r + 1/s = 1 or r+s/rs=1....(eq.1)

Stmt 1 -> rs=1 , substituting in (eq.1)

r+s=1 or 1/r+1/s = 1 -> Sufficient

Stmt 1 -> s+r=2.5 , substituting in (eq.1)

2.5/rs=1 => rs=2.5

or 1/r+1/s = 1 -> Sufficient

Ans - D

Answer to the question is indeed D, but I wonder what do the red parts mean in your simpler solution?
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Re: DS Algebra   [#permalink] 27 Dec 2010, 02:21
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