If r> 0 and s>0, is r/s < s/r ?
1. r/3s = 1/4
2. s = r + 4
OA - D
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Algebra - Ratios
This topic has expert replies
-
anirudhbhalotia
- Master | Next Rank: 500 Posts
- Posts: 123
- Joined: Tue Nov 23, 2010 7:18 pm
- Location: Mumbai, India
- Thanked: 5 times
- Followed by:4 members
GMAT/MBA Expert
-
Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Statement 1: (r/3s) = 1/4anirudhbhalotia wrote:If r> 0 and s>0, is r/s < s/r ?
1. r/3s = 1/4
2. s = r + 4
Implies, (r/s) = 3/4 => (s/r) = 4/3
Hence, (r/s) < (s/r)
Sufficient
Statement 2: s = (r + 4)
Dividing both side by r, (s/r) = 1 + (4/r) > 1
And dividing both side by s, 1 = (r/s) + (4/s) => (r/s) = 1 - (4/s) < 1
Hence (r/s) < (s/r)
Sufficient
The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
-
MAAJ
- Master | Next Rank: 500 Posts
- Posts: 243
- Joined: Sun Jul 12, 2009 7:12 am
- Location: Dominican Republic
- Thanked: 31 times
- Followed by:2 members
- GMAT Score:480
For the second statement you can also do this:
(r/s) < (s/r) ?
Because they are both positive, you can cross-multiply
r²< s² ?
Statement 2 tell us that s= r+4 so:
r² < (r+4)² ?
Because "r" is a positive number, r² will always by less than (r+4)², making this statement sufficient.
(r/s) < (s/r) ?
Because they are both positive, you can cross-multiply
r²< s² ?
Statement 2 tell us that s= r+4 so:
r² < (r+4)² ?
Because "r" is a positive number, r² will always by less than (r+4)², making this statement sufficient.
"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."
-
anirudhbhalotia
- Master | Next Rank: 500 Posts
- Posts: 123
- Joined: Tue Nov 23, 2010 7:18 pm
- Location: Mumbai, India
- Thanked: 5 times
- Followed by:4 members
Cool!MAAJ wrote:For the second statement you can also do this:
(r/s) < (s/r) ?
Because they are both positive, you can cross-multiply
r²< s² ?
Statement 2 tell us that s= r+4 so:
r² < (r+4)² ?
Because "r" is a positive number, r² will always by less than (r+4)², making this statement sufficient.
Was a bit confused as to how did Anurag suffice the 2nd statement!
-
ankur.agrawal
- Master | Next Rank: 500 Posts
- Posts: 261
- Joined: Wed Mar 31, 2010 8:37 pm
- Location: Varanasi
- Thanked: 11 times
- Followed by:3 members
MAAJ wrote:For the second statement you can also do this:
(r/s) < (s/r) ?
Because they are both positive, you can cross-multiply
r²< s² ?
Statement 2 tell us that s= r+4 so:
r² < (r+4)² ?
Because "r" is a positive number, r² will always by less than (r+4)², making this statement sufficient.
For the statement 2 we can do this:
s=r+4: putting this value:
r/r+4<r+4/r. From this it is clear that LHS will be <1 & RHS will be >1.
-
vikrambansal
- Senior | Next Rank: 100 Posts
- Posts: 38
- Joined: Thu Mar 19, 2015 2:32 am
- Location: India
- Followed by:1 members
- GMAT Score:550
Can we simplify r/s < s/r
= r^2 < s^2 (cross multiply. No change in inequality as both r & s are +ve)
= r < s (taking square root)
= r^2 < s^2 (cross multiply. No change in inequality as both r & s are +ve)
= r < s (taking square root)
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Perfect!vikrambansal wrote:Can we simplify r/s < s/r
= r^2 < s^2 (cross multiply. No change in inequality as both r & s are +ve)
= r < s (taking square root)
The KEY is that r and s are both POSITIVE
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
