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If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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04 Mar 2014, 00:23
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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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04 Mar 2014, 00:24



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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05 Mar 2014, 23:59
From the stem, the equation can be written as, is r + s = 4rs?
St1: r + s = 4rs
Directly gives the answer. Sufficient.
St2: r = 5
No information about s. Not sufficient.
Answer (A).



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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06 Mar 2014, 00:40
Question  1/r + 1/s = 4 ? Simplifying the above equation by multiplying both sides with 'rs' we get  r + s = 4rs The above simplified statement is what we have to prove now.
Now St1 : r + s = 4rs Directly gives us the answer. No brainer there. This statement is sufficient
St2: r = 5 Substituting we get 5+s = 20s We dont know the value of S, if S = 1 then 5+1 not equal to 20*1 not proven. If S = 5/19 then 5+ 5/19 = 20*5/19 proven. Thus this statement is not sufficient.
Thus the Answer is Option (A)



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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22 Jun 2014, 14:10
Hi guys,
Quick question, because it's a method I've been using and has seemed to work but I don't know if it is correct.
Could 1/r + 1/s =4 be rearranged to r + s = 1/4?



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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22 Jun 2014, 15:51



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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22 Jun 2014, 15:55
Bunuel wrote: carolinanmd wrote: Hi guys,
Quick question, because it's a method I've been using and has seemed to work but I don't know if it is correct.
Could 1/r + 1/s =4 be rearranged to r + s = 1/4? No, that's not correct. For example, \(\frac{1}{2} + \frac{7}{2} = 4\) but \(2 + \frac{2}{7} \neq{ \frac{1}{4}}\) The correct way is: \(\frac{1}{r}+\frac{1}{s}=4\); \(\frac{r+s}{rs}=4\) \(r+s=4rs\). Thanks! I figured that would be the right way.



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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10 Mar 2015, 19:48
I think the question is written incorrectly in the original post. If you look in the actual book the second statement is "r=s" not "r=5"



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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10 Mar 2015, 21:06
Hi soniasawhney, You are correct; there IS a typo in the original prompt. However, the given explanation is correct and Bunuel's solution appears to correct the error. Bunuel (or other Moderators), can you fix the typo? GMAT assassins aren't born, they're made, Rich
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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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11 Mar 2015, 04:24



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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25 Mar 2017, 05:36
Bunuel wrote: If rs#0, is 1/r + 1/s = 4 ?
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 I understand that statement 2 has several solutions for r and s  but why can't I just determine the value for r and s as as following: (2) r = s > replace r by s: 1/s + 1/s = 4 > multiply with s: 1 + 1 = 4s > divide by 4: 1/2 = s > replace s by 1/2: 1/ 1/2 + 1/ 1/2 = 4 > multiply with 1/2: 1+1 = 2 > this s = 1/2 is true, so r has to be 1/2 as well and 2nd statement is sufficient? Thanks! gentler



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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25 Mar 2017, 05:49
guenthermat wrote: Bunuel wrote: If rs#0, is 1/r + 1/s = 4 ?
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 I understand that statement 2 has several solutions for r and s  but why can't I just determine the value for r and s as as following: (2) r = s > replace r by s: 1/s + 1/s = 4 > multiply with s: 1 + 1 = 4s > divide by 4: 1/2 = s > replace s by 1/2: 1/ 1/2 + 1/ 1/2 = 4 > multiply with 1/2: 1+1 = 2 > this s = 1/2 is true, so r has to be 1/2 as well and 2nd statement is sufficient? Thanks! gentler When you do all these manipulations with 1/r + 1/s = 4, you should not forget that it's not given as a fact. 1/r + 1/s = 4 is a question. We want to know whether 1/r + 1/s = 4. So, you don't get there that s = 1/2. when you substitute r = s into the question (1/r + 1/s = 4), the question becomes "does s = 1/2?". Hope it's clear.
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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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25 Mar 2017, 09:33
Bunuel wrote: When you do all these manipulations with 1/r + 1/s = 4, you should not forget that it's not given as a fact. 1/r + 1/s = 4 is a question. We want to know whether 1/r + 1/s = 4. So, you don't get there that s = 1/2. when you substitute r = s into the question (1/r + 1/s = 4), the question becomes "does s = 1/2?".
Hope it's clear. Yes, all clear  thanks! I forgot that it wasn't a fact but a question.



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Re: If rs#0, is 1/r + 1/s = 4 ? [#permalink]
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25 Mar 2017, 11:38
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf rs#0, is 1/r + 1/s = 4 ? (1) r + s = 4rs (2) r = s Data Sufficiency Question: 124 Category: Algebra First and seconddegree equations Page: 162 Difficulty: 550 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! Interestingly, if someone don't make statement 1 sufficient, then s/he will mistakenly choose C in wrong way. But, the correct choice is . Thank you...
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