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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] New post 12 Dec 2010, 08:05
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

8% (00:00) correct 92% (00:57) wrong based on 25 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] New post 12 Dec 2010, 08:25
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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.

Answer: D.

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Re: DS Algebra [#permalink] New post 14 Dec 2010, 03:28
Nice one... Certainly tricky
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Re: DS Algebra [#permalink] New post 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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Re: DS Algebra [#permalink] New post 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.

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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: DS Algebra   [#permalink] 27 Dec 2010, 02:21
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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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