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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 04 Mar 2014, 00:23
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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

Data Sufficiency
Question: 124
Category: Algebra First- and second-degree equations
Page: 162
Difficulty: 550


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

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New post 04 Mar 2014, 00:24
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SOLUTION

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

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New post 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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New post 06 Mar 2014, 00:40
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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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New post 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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New post 22 Jun 2014, 15:51
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:
\(\frac{1}{r}+\frac{1}{s}=4\);

\(\frac{r+s}{rs}=4\)

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

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New post 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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New post 10 Mar 2015, 19:48
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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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New post 10 Mar 2015, 21:06
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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?

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

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

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New post 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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New post 25 Mar 2017, 11:38
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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

Data Sufficiency
Question: 124
Category: Algebra First- and second-degree equations
Page: 162
Difficulty: 550


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each 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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Re: If rs#0, is 1/r + 1/s = 4 ?   [#permalink] 25 Mar 2017, 11:38
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