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

 It is currently 27 Jun 2019, 01:29 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If rs#0, is 1/r + 1/s = 4 ?

Author Message
TAGS:

Hide Tags

Manager  Joined: 17 Aug 2010
Posts: 50
If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

3
7 00:00

Difficulty:   15% (low)

Question Stats: 76% (01:04) correct 24% (01:37) wrong based on 365 sessions

HideShow timer Statistics 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?

_________________
I don't want kudos.. I want to see smile on your face if I am able to help you.. which is priceless.
Math Expert V
Joined: 02 Sep 2009
Posts: 55804
Re: OG 10 Qn: 246  [#permalink]

Show Tags

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?

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.

_________________
Manager  Joined: 28 Aug 2010
Posts: 170
Re: OG 10 Qn: 246  [#permalink]

Show Tags

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
Intern  Joined: 29 Aug 2012
Posts: 4
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

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 !! Math Expert V
Joined: 02 Sep 2009
Posts: 55804
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

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:

$$\frac{1}{r}+\frac{1}{s}=\frac{s}{rs}+\frac{r}{rs}=\frac{s+r}{rs}$$.
_________________
Intern  Joined: 02 Feb 2012
Posts: 24
GPA: 4
Re: OG 10 Qn: 246  [#permalink]

Show Tags

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?

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,
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.????
Math Expert V
Joined: 02 Sep 2009
Posts: 55804
Re: OG 10 Qn: 246  [#permalink]

Show Tags

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?

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,
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.
_________________
Intern  Joined: 15 Jan 2013
Posts: 48
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

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 !!!!!
Math Expert V
Joined: 02 Sep 2009
Posts: 55804
If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

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 !!!!!

(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?
_________________
Current Student B
Status: DONE!
Joined: 05 Sep 2016
Posts: 368
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

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
Intern  B
Joined: 28 Aug 2016
Posts: 6
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

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?
Director  P
Joined: 02 Oct 2017
Posts: 729
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

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

Posted from my mobile device
_________________
Give kudos if you like the post
Intern  Joined: 31 Jan 2019
Posts: 2
Re: If rs#0, is 1/r + 1/s = 4 ?  [#permalink]

Show Tags

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.

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

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