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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 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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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". 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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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) rs=4rs => s=4rsr => r=s/(4s1) putting value in 1/r +1/s becomes (4s1)/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



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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". 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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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". 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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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



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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 ?
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