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If rs#0, is 1/r + 1/s = 4 ?

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If rs#0, is 1/r + 1/s = 4 ? [#permalink] New post 10 Oct 2010, 04:29
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A
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If rs#0, is 1/r + 1/s = 4 ?

(1) r + s = 4rs
(2) r = s

[Reveal] Spoiler: OA and my Assumption
OA is "A". That's only A is sufficient. but I presume that that answer should be "C" because for me r=s , if I substitute in the equation then

1/r + 1/r = 2/r = 4
r = 1/2 and I am able to prove the condition. Although, OG has taken values of r and s to prove that 2nd condition is not sufficient, then why not try to put some values for r and s in the 1st option too?
Please help
[Reveal] Spoiler: OA

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Re: OG 10 Qn: 246 [#permalink] New post 10 Oct 2010, 04:38
Expert's post
zerotoinfinite2006 wrote:
If rs <> 0, is \frac{1}{r} + \frac{1}{s} = 4?

    r + s = 4rs
    r = s

Please note that <> in the question should be read as "Not Equal To".

[Reveal] Spoiler: OA and my Assumption
OA is "A". That's only A is sufficient. but I presume that that answer should be "C" because for me r=s , if I substitute in the equation then

1/r + 1/r = 2/r = 4
r = 1/2 and I am able to prove the condition. Although, OG has taken values of r and s to prove that 2nd condition is not sufficient, then why not try to put some values for r and s in the 1st option too?
Please help


Question: is \frac{1}{r}+\frac{1}{s}=4 --> is \frac{r+s}{rs}=4 --> is r+s=4rs?

(1) r+s=4rs, directly answers the question. Sufficient.
(2) r = s, the question becomes: is \frac{1}{r}+\frac{1}{r}=4 ? --> is r=\frac{1}{2}? but we dont' know whether r=\frac{1}{2}. Not sufficient.

Answer: A.
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Re: OG 10 Qn: 246 [#permalink] New post 30 Nov 2010, 10:24
Hi
if i go the algebric way on statement 1 i get it right but statement 2 i get it wrong so I am kinda confused
eg statement 2 sates r = s

so lets see 1/r + 1/s = 4
can be written as r + s = 4 rs
so replacing r we get 2s = 4s^2
s = 1/2
so statement 2 is also sufficient hence ans is D but this is not correct
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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink] New post 05 Jul 2013, 01:52
Hi Bunuel/Instructors,
I have ac confusion here in this Q.
as to How you & the OG deduce:

1/r +1/s as (r+s)/rs.

I know it is by taking LCM but one IMO shouldnt generalize it. As teh same holds true for 1/4+1/3 BUT CANNOT for 1/4 +1/12.

SO IMO: the solution should be: (from A)

r-s=4rs
=> s=4rs-r
=> r=s/(4s-1)

putting value in 1/r +1/s becomes (4s-1)/s + 1/s => 4s/s => 4

Please correct me OR let me know if my concepts are not correct as I want this to clear so that I can avoid any mistakes.

Thanks !! :?:
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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink] New post 05 Jul 2013, 01:58
Expert's post
p111 wrote:
Hi Bunuel/Instructors,
I have ac confusion here in this Q.
as to How you & the OG deduce:

1/r +1/s as (r+s)/rs.

I know it is by taking LCM but one IMO shouldnt generalize it. As teh same holds true for 1/4+1/3 BUT CANNOT for 1/4 +1/12.

SO IMO: the solution should be: (from A)

r-s=4rs
=> s=4rs-r
=> r=s/(4s-1)

putting value in 1/r +1/s becomes (4s-1)/s + 1/s => 4s/s => 4

Please correct me OR let me know if my concepts are not correct as I want this to clear so that I can avoid any mistakes.

Thanks !! :?:


Its' BASIC algebra:

\frac{1}{r}+\frac{1}{s}=\frac{s}{rs}+\frac{r}{rs}=\frac{s+r}{rs}.
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Re: OG 10 Qn: 246 [#permalink] New post 07 Jul 2013, 18:29
Bunuel wrote:
zerotoinfinite2006 wrote:
If rs <> 0, is \frac{1}{r} + \frac{1}{s} = 4?

    r + s = 4rs
    r = s

Please note that <> in the question should be read as "Not Equal To".

[Reveal] Spoiler: OA and my Assumption
OA is "A". That's only A is sufficient. but I presume that that answer should be "C" because for me r=s , if I substitute in the equation then

1/r + 1/r = 2/r = 4
r = 1/2 and I am able to prove the condition. Although, OG has taken values of r and s to prove that 2nd condition is not sufficient, then why not try to put some values for r and s in the 1st option too?
Please help


Question: is \frac{1}{r}+\frac{1}{s}=4 --> is \frac{r+s}{rs}=4 --> is r+s=4rs?

(1) r+s=4rs, directly answers the question. Sufficient.
(2) r = s, the question becomes: is \frac{1}{r}+\frac{1}{r}=4 ? --> is r=\frac{1}{2}? but we dont' know whether r=\frac{1}{2}. Not sufficient.

Answer: A.


Hi Bunuel,
Could you kindly explain statement 2 clearly. From the choice, we come to the conclusion that r=s=1/2. Cant this be sufficient to answer the question?
In that case, it should be (D) right.????
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Re: OG 10 Qn: 246 [#permalink] New post 07 Jul 2013, 22:08
Expert's post
avinashrao9 wrote:
Bunuel wrote:
zerotoinfinite2006 wrote:
If rs <> 0, is \frac{1}{r} + \frac{1}{s} = 4?

    r + s = 4rs
    r = s

Please note that <> in the question should be read as "Not Equal To".

[Reveal] Spoiler: OA and my Assumption
OA is "A". That's only A is sufficient. but I presume that that answer should be "C" because for me r=s , if I substitute in the equation then

1/r + 1/r = 2/r = 4
r = 1/2 and I am able to prove the condition. Although, OG has taken values of r and s to prove that 2nd condition is not sufficient, then why not try to put some values for r and s in the 1st option too?
Please help


Question: is \frac{1}{r}+\frac{1}{s}=4 --> is \frac{r+s}{rs}=4 --> is r+s=4rs?

(1) r+s=4rs, directly answers the question. Sufficient.
(2) r = s, the question becomes: is \frac{1}{r}+\frac{1}{r}=4 ? --> is r=\frac{1}{2}? but we dont' know whether r=\frac{1}{2}. Not sufficient.

Answer: A.


Hi Bunuel,
Could you kindly explain statement 2 clearly. From the choice, we come to the conclusion that r=s=1/2. Cant this be sufficient to answer the question?
In that case, it should be (D) right.????


The question asks: is \frac{1}{r}+\frac{1}{s}=4 ?

(2) says r = s. So, our questions becomes: is \frac{1}{r}+\frac{1}{r}=4? --> is r=\frac{1}{2}? Notice it's not given, in contrast we are asked to answer this.

Now, if r=\frac{1}{2}, then the answer is YES but if r\neq\frac{1}{2}, then the answer is NO. Do we know what r is actully equal to? No. So, this statement is NOT sufficient.

Hope it's clear.
_________________

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

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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink] New post 10 Aug 2014, 17:00
Hi Bunuel,
Could you kindly explain statement 2 clearly. From the choice, we come to the conclusion that r=s=1/2. Cant this be sufficient to answer the question?
In that case, it should be (D) right.????[/quote]

The question asks: is \frac{1}{r}+\frac{1}{s}=4 ?

(2) says r = s. So, our questions becomes: is \frac{1}{r}+\frac{1}{r}=4? --> is r=\frac{1}{2}? Notice it's not given, in contrast we are asked to answer this.

Now, if r=\frac{1}{2}, then the answer is YES but if r\neq\frac{1}{2}, then the answer is NO. Do we know what r is actully equal to? No. So, this statement is NOT sufficient.

Hope it's clear.[/quote]



Can you explain that please ?
if we applied the second answer's approach on statement one :

if r= 1/2 and s=1/2 …….. > then r+s=4rs = 1/2 + 1/2 = 4*1/2*1/2 …. but if r=2 and s=2 the …> 2+2 not equal to 4*2*2


this question is confusing !!!!!
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If rs#0, is 1/r + 1/s = 4 ? [#permalink] New post 12 Aug 2014, 07:04
Expert's post
shagalo wrote:
Can you explain that please ?
if we applied the second answer's approach on statement one :

if r= 1/2 and s=1/2 …….. > then r+s=4rs = 1/2 + 1/2 = 4*1/2*1/2 …. but if r=2 and s=2 the …> 2+2 not equal to 4*2*2


this question is confusing !!!!!


Your question is not clear.

(1) says that r + s = 4rs. Why are you plugging number for which r + s does not equal to 4rs ? Also, the question asks whether r + s = 4rs and (1) directly answers this. Why even plug?
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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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If rs#0, is 1/r + 1/s = 4 ?   [#permalink] 12 Aug 2014, 07:04
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