GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jan 2019, 20:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52285
If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

03 Mar 2014, 23:23
1
5
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:06) correct 19% (01:25) wrong based on 719 sessions

### HideShow timer Statistics

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:
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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

03 Mar 2014, 23:24
3
5
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.

_________________
##### General Discussion
Manager
Joined: 04 Jan 2014
Posts: 117
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

05 Mar 2014, 22:59
From the stem, the equation can be written as, is r + s = 4rs?

St1: r + s = 4rs

St2: r = 5

No information about s. Not sufficient.

Intern
Status: Never Give up!!!
Joined: 02 Aug 2012
Posts: 47
Location: India
Concentration: Finance, General Management
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

05 Mar 2014, 23:40
1
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)
Intern
Joined: 31 Mar 2014
Posts: 10
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

22 Jun 2014, 13:10
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?
Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

22 Jun 2014, 14:51
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:
$$\frac{1}{r}+\frac{1}{s}=4$$;

$$\frac{r+s}{rs}=4$$

$$r+s=4rs$$.
_________________
Intern
Joined: 31 Mar 2014
Posts: 10
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

22 Jun 2014, 14:55
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.
Intern
Joined: 14 Oct 2013
Posts: 45
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

10 Mar 2015, 18:48
1
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"
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13347
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

10 Mar 2015, 20:06
1
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
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

11 Mar 2015, 03:24
soniasawhney wrote:
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"

______________
Edited. Thank you.
_________________
Intern
Joined: 18 Mar 2017
Posts: 38
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

25 Mar 2017, 04:36
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.

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
Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

25 Mar 2017, 04:49
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.

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.
_________________
Intern
Joined: 18 Mar 2017
Posts: 38
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

25 Mar 2017, 08:33
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.
Director
Joined: 23 Feb 2015
Posts: 592
GMAT 1: 720 Q49 V40
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

### Show Tags

25 Mar 2017, 10:38
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:
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...
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Re: If rs#0, is 1/r + 1/s = 4 ? &nbs [#permalink] 25 Mar 2017, 10:38
Display posts from previous: Sort by