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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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Joined: 07 Jun 2004
Posts: 599
Location: PA
If rs 0, does 1/r + 1/s = 1 (1) rs = 1 (2) s + r = 2.5 Did  [#permalink]

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12 Dec 2010, 08:05
2
9
00:00

Difficulty:

95% (hard)

Question Stats:

31% (02:30) correct 69% (02:12) wrong based on 200 sessions

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If rs ≠ 0, does 1/r + 1/s = 1

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

Did not understand the OA
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: DS Algebra  [#permalink]

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12 Dec 2010, 08:25
2
4
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.

Answer: D.
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##### General Discussion
Manager
Joined: 19 Apr 2010
Posts: 176
Schools: ISB, HEC, Said
Re: DS Algebra  [#permalink]

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14 Dec 2010, 03:28
Nice one... Certainly tricky
Manager
Status: Last few days....Have pressed the throttle
Joined: 20 Jun 2010
Posts: 57
WE 1: 6 years - Consulting
Re: DS Algebra  [#permalink]

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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.

Answer: D.

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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Consider giving Kudos if my post helps in some way

Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: DS Algebra  [#permalink]

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27 Dec 2010, 02:21
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.

Answer: D.

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

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20 Feb 2017, 22:04
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.

Answer: D.

In view of the above question, I have a question in mind. Can multiple of two numbers be equal to the sum of those two numbers in any way?
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Hasan Mahmud

Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: If rs 0, does 1/r + 1/s = 1 (1) rs = 1 (2) s + r = 2.5 Did  [#permalink]

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20 Feb 2017, 22:39
Mahmud6 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.

Answer: D.

In view of the above question, I have a question in mind. Can multiple of two numbers be equal to the sum of those two numbers in any way?

Yes. There are infinite solutions for non-integers.

For integers:

0 + 0 = 0*0
2 + 2 = 2*2.
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Posts: 9416
Re: If rs 0, does 1/r + 1/s = 1 (1) rs = 1 (2) s + r = 2.5 Did  [#permalink]

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30 May 2018, 19:39
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Re: If rs 0, does 1/r + 1/s = 1 (1) rs = 1 (2) s + r = 2.5 Did &nbs [#permalink] 30 May 2018, 19:39
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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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