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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]

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10 Oct 2010, 05:29
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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?
[Reveal] Spoiler: OA

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Re: OG 10 Qn: 246 [#permalink]

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07 Jul 2013, 23:08
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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?

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.

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.
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Re: OG 10 Qn: 246 [#permalink]

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10 Oct 2010, 05:38
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?

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.

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Re: OG 10 Qn: 246 [#permalink]

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30 Nov 2010, 11:24
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]

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05 Jul 2013, 02:52
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]

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05 Jul 2013, 02:58
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]

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07 Jul 2013, 19:29
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?

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.

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: If rs#0, is 1/r + 1/s = 4 ? [#permalink]

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10 Aug 2014, 18:00
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]

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12 Aug 2014, 08:04
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 !!!!!

(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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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]

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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]

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17 Sep 2016, 06:40
A is correct.

(1) r+s = 4rs
=(r+s)/rs = 4 (divide both sides by rs)
=(1/s) + (1/r) = 4

SUFFICIENT

(2) r =s
=(1/s)+(1/s) = 4
=(2/s) = 4 --> 2 = 4s

INSUFFICIENT - this doesn't provide us with any information to prove the main eq
Re: If rs#0, is 1/r + 1/s = 4 ?   [#permalink] 17 Sep 2016, 06:40
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