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

 It is currently 17 Oct 2019, 08:30

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

If r and s are negative, is r/s less than 1 ?

Author Message
TAGS:

Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 442
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If r and s are negative, is r/s less than 1 ?  [#permalink]

Show Tags

07 Mar 2012, 16:24
3
6
00:00

Difficulty:

85% (hard)

Question Stats:

55% (02:33) correct 45% (02:48) wrong based on 125 sessions

HideShow timer Statistics

If r and s are negative, is r/s less than 1 ?

(1) r + 2s = s^2/r
(2) r/s is 2 less than s/r

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 58401
If r and s are negative, is r/s less than 1 ?  [#permalink]

Show Tags

07 Mar 2012, 16:37
1
1
If r and s are negative, is $$\frac{r}{s}$$ less than 1 ?

Since r and s are negative then either $$0<\frac{r}{s}<1$$ or $$\frac{r}{s}\geq{1}$$

(1) $$r + 2s = \frac{s^2}{r}$$. Divided both parts by $$s$$: $$\frac{r}{s}+2= \frac{s}{r}$$. We cannot have the second case because if $$\frac{r}{s}\geq{1}$$ then its reciprocal $$\frac{s}{r}\leq{1}$$ and it cannot equal to $$\frac{r}{s}+2=positive+2$$, hence $$0<\frac{r}{s}<1$$. Sufficient.

(2) $$\frac{r}{s}$$ is 2 less than $$\frac{s}{r}$$ --> $$\frac{r}{s}+2= \frac{s}{r}$$. The same info as above. Sufficient.

_________________
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 442
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: Integers R & S  [#permalink]

Show Tags

07 Mar 2012, 16:41
1
Sorry Bunuel - didn't get this buddy.

How did you get first line which says Since r & s are negative ......
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 58401
Re: Integers R & S  [#permalink]

Show Tags

07 Mar 2012, 16:43
1
enigma123 wrote:
Sorry Bunuel - didn't get this buddy.

How did you get first line which says Since r & s are negative ......

Since r and s are negative r/s>0, and then you can consider two cases: 0<r/s<1 and r/s>=1.
_________________
Intern
Joined: 21 Jan 2012
Posts: 2
Location: India
Schools: Kellogg '16 (S)
GPA: 3.95
WE: Consulting (Consulting)
Re: If r and s are negative, is r/s less than 1 ?  [#permalink]

Show Tags

18 Apr 2012, 08:42
1
A gives us $$r + 2s = s^2/r$$,
dividing by r we get ->$$1 + 2s/r = (s/r)^2$$
call s/r = a,
$$1 + 2a = a^2$$
$$a^2 - 2a = 1$$
adding 1 to both sides we get -> $$(a -1)^2 = 2$$
or a -1 = $$+\sqrt{2}$$ or a - 1 = $$-\sqrt{2}$$
since r and s are both -ve we know that s/r > 0 so a has to 1 + \sqrt{2}
=> $$s/r = 1+\sqrt{2}$$.
Sufficient.

B give us same statement as A, just substitute s/r = a you will end up with (a -1)^2 = 2 and use the same logic as above. So, B is sufficient

Hence D.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: If r and s are negative, is r/s less than 1 ?  [#permalink]

Show Tags

19 Apr 2012, 11:37
1
enigma123 wrote:
If r and s are negative, is $$\frac{r}{s}$$ less than 1 ?

(1) $$r + 2s = \frac{s^2}{r}$$

(2) $$\frac{r}{s}$$ is 2 less than $$\frac{s}{r}$$

Even though it has already been answered by Bunuel, I would like to point out some takeaways.

1. Dont be in a hurry to bring the fractions in integer form. Look at the options and see how variables are used in the options.
2. If r and s are both negative, it means r/s is positive i.e. > 0
3. If r/s is a positive fraction (non 1), one of r/s and s/r will be between 0 and 1 (the smaller one) and the other will be to the right of 1. (greater than 1)
4. It is possible that the two statements give the same data. It they do and if one stmnt alone is enough, both together will be enough. If one is not enough, neither are they enough together, nor is the other one enough alone.
_________________
Karishma
Veritas Prep GMAT Instructor

VP
Joined: 05 Mar 2015
Posts: 1007
If r and s are negative, is r/s less than 1 ?  [#permalink]

Show Tags

24 Mar 2016, 07:45
4
If r and s are negative, is r/s less than 1 ?

(1) r + 2s = s^2/r
(2) r/s is 2 less than s/r

(1) r + 2s - (s^2/r)=0
r^2-s^2=-2rs taking RHS part since r & s are -ve then -2rs must be negative
so r^2-s^2<0
r^2<s^2
taking root both sides IrI<IsI
as both are -ve so IrI=-r & IsI=-s
So, now we can write as -r<-s------> r>s
so r/s is always <1
eg. say r=-2 & s=-3 (as r>s and both are -ve)
now -2/-3 < 1
So suff..

(2) r/s is 2 less than s/r
r/s=s/r-2
rearranging we again get r^2-s^2=-2rs
similar reasoning as (1).
Suff..

Ans D
Non-Human User
Joined: 09 Sep 2013
Posts: 13242
Re: If r and s are negative, is r/s less than 1 ?  [#permalink]

Show Tags

30 Mar 2019, 04:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If r and s are negative, is r/s less than 1 ?   [#permalink] 30 Mar 2019, 04:48
Display posts from previous: Sort by