Last visit was: 24 Jun 2024, 00:55 It is currently 24 Jun 2024, 00:55
Toolkit
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 a > 0 and b > 0, is a/b > b/a ?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93968
Own Kudos [?]: 634430 [9]
Given Kudos: 82435
Retired Moderator
Joined: 26 Nov 2012
Posts: 473
Own Kudos [?]: 495 [0]
Given Kudos: 46
Intern
Joined: 09 Jul 2016
Posts: 22
Own Kudos [?]: 10 [0]
Given Kudos: 13
Manager
Joined: 21 Mar 2014
Status:It`s Just a pirates life !
Posts: 214
Own Kudos [?]: 34 [0]
Given Kudos: 246
Location: India
Concentration: Strategy, Operations
GMAT 1: 690 Q48 V36
GPA: 4
WE:Consulting (Manufacturing)
Re: If a > 0 and b > 0, is a/b > b/a ? [#permalink]
Bunuel wrote:
If a > 0 and b > 0, is a/b > b/a ?

(1) a = b - 2
(2) a/(4b) =1/5

I concur.My take is D.

statement 1: Since a and b are positive, min value of b > 2.

Statement 2: Rearrangement makes the equation (a/b) = 4/5 so (b/a) = 5/4.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6806
Own Kudos [?]: 30623 [3]
Given Kudos: 799
Re: If a > 0 and b > 0, is a/b > b/a ? [#permalink]
1
Kudos
2
Bookmarks
Top Contributor
Bunuel wrote:
If a > 0 and b > 0, is a/b > b/a ?

(1) a = b - 2
(2) a/(4b) =1/5

Target question: Is a/b > b/a ?

Given: a > 0 and b > 0

This is a great candidate for REPHRASING the target question: Is a/b > b/a ?
Since a and b are both POSITIVE, we can multiply both sides of the inequality by ab to get: Is a² > b²?

Nice Rules: If 0 < b < a, then and b² < a²
Conversely, if a and b are positive AND b² < a², then we can be certain that b < a

This allows us to REPHRASE our target question once more to get...
REPHRASED target question: Is b < a?

Once we're rephrased the target question like this, the statements are pretty easy to analyze.

Statement 1: a = b - 2
In other words, a is 2 less than b
So, we can be certain that a < b
In other words, it is definitely NOT the case that b < a
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: a/(4b) =1/5
Multiply both sides by 4b to get: a = (4/5)b
In other words, a is equal to 4/5 of b
Since it's given that a and b are positive, we can be certain that a < b
In other words, it is definitely NOT the case that b < a
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEOS

Retired Moderator
Joined: 10 May 2010
Posts: 796
Own Kudos [?]: 629 [0]
Given Kudos: 192
If a > 0 and b > 0, is a/b > b/a ? [#permalink]
Think Stmt 1 and Stmt 2 are contradicting each other a/b >1 in Stmt 1 and a/b < 1 in Stmt 2.
Math Expert
Joined: 02 Sep 2009
Posts: 93968
Own Kudos [?]: 634430 [0]
Given Kudos: 82435
Re: If a > 0 and b > 0, is a/b > b/a ? [#permalink]
AbhiJ wrote:
Think Stmt 1 and Stmt 2 are contradicting each other a/b >1 in Stmt 1 and a/b < 1 in Stmt 2.

For both a < b. How did you get that a > b for (1)? It says a = b - 2, so a < b.
Senior Manager
Joined: 15 Jan 2017
Posts: 257
Own Kudos [?]: 86 [0]
Given Kudos: 932
Re: If a > 0 and b > 0, is a/b > b/a ? [#permalink]
I tried with fractions and integers-- the question doesn't expressly say its not an integer.
1) St 1; if with integers, a = 8, b = 10 - 2 --> 8/10 < 5/4 A is suff, with a = 1/4 , b = 9/4 A suff
2) a = 4/5 b, which is suff for both integers and fractions

Ans D
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19044
Own Kudos [?]: 22475 [0]
Given Kudos: 286
Location: United States (CA)
Re: If a > 0 and b > 0, is a/b > b/a ? [#permalink]
Bunuel wrote:
If a > 0 and b > 0, is a/b > b/a ?

(1) a = b - 2
(2) a/(4b) =1/5

Solution:

Since both a and b are positive, a/b is greater than b/a if a > b and a/b is not greater than b/a if a ≤ b.

Statement One Only:

a = b - 2

Since a = b - 2, then a < b and therefore, a/b is not greater than b/a. Statement one alone is sufficient.

Statement Two Only:

a/(4b) = 1/5

Simplifying, we have a = 4b/5. Since both a and b are positive, this means a < b, and therefore, a/b is not greater than b/a. Statement two alone is sufficient.