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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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New post 10 Oct 2010, 05:29
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A
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D
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If rs#0, is 1/r + 1/s = 4 ?

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

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

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Re: OG 10 Qn: 246  [#permalink]

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New post 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".

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]

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New post 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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New post 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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New post 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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New post 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".

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]

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New post 07 Jul 2013, 23:08
1
1
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".

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

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New post 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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New post 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 !!!!!


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

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

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New post 06 May 2018, 13:25
Hey,
Im still confused about statement 2
if r=s then 1/s+1/s=4 then s and r =1/2
1/1/2+1/1/2=2+2=4
so I picked D Why is it A?
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Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

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New post 22 May 2018, 07:32
1
cocojatti92 wrote:
Hey,
Im still confused about statement 2
if r=s then 1/s+1/s=4 then s and r =1/2
1/1/2+1/1/2=2+2=4
so I picked D Why is it A?



2) if we put r=s we get

1/r +1/r=4
r=1/2

We get r as 1/2 but this is not our intention.we need to find 1/r+1/s which we are not getting .
That's why this statement 2 is insufficient

Give kudos if it helps

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

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New post 31 Jan 2019, 03:56
1
Hi guys,

I was also in trouble with statement (2) and reading the answers I understood. Since I see there are some still with problems, I will try to explain with my words:

The question is x≠0, is 1/r + 1/s = 4? Since it has a question mark, this is not a statement and you can not use it to prove the point. The best thing is to rephrase the question. Since the question wants to no if 1/r plus 1/s equals to 4, a yes or no to this question would be enough. Therefore, you can rephrase as: r=? and s=? (you need to know both to know it they equal 4 in the equation).

(2) number 2 says r=s; but you still don’t know whether r=s=1 what would lead you to 1+1=2≠4 or r=s=1/2 leading to 2+2=4. Since there are cases where the answer is yes and others where the answer is no, statement 2 does not answer your question.

(1) one gives your question as a statement, so it answers

A
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Re: If rs#0, is 1/r + 1/s = 4 ?   [#permalink] 31 Jan 2019, 03:56
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