BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

q114, OG QR 1st ed

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
GMAT Instructor
Posts: 1302
Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members
Location: Toronto
Thanked: 539 times
GMAT Score:800

by Testluv » Wed Oct 20, 2010 9:59 pm
Hi,

in a data sufficiency question involving inequalities, start thinking about signs (pos vs neg).

The question is:

Is 1/(a-b)<b-a?

We should note that (a-b) and (b-a) will have opposite signs (or if they are both zero, then no sign).

(1) tells us that a<b. When we subtract something large from something smaller, the result is negative. Thus, 1/(a-b) is negative. And when we subtract something small from something larger, the result is positive. Thus, (b-a) is positive. Thus, the question becomes:

Is (-ve)<(+ve)?

The answer is "definitely yes", and so (1) is sufficient. Eliminate B, C, and E.

(2) tells us that |a-b|>1. "|a-b|" means the distance between "a" and "b" on the number line. So, the distance between a and b on the number line is greater than 1. So, for example, a could be 4 and b could be 2, in which case 1/(a-b) is positive and (b-a) is negative, and the question becomes:

Is (+ve)<(-ve)? and the answer is "no".

However, it could also be the other way around: a could be 2 and b could be 4 (the distance between them is still greater than 1, so we are satisfying the statement). But in this case the answer to the question is "yes".

Because we can get both a "yes" and "no" answer, (2) is not sufficient.

(1) is sufficient by itself; (2) is not; choose A.
Kaplan Teacher in Toronto
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members
Location: Milpitas, CA
Thanked: 447 times

by Rahul@gurome » Wed Oct 20, 2010 10:03 pm
The question is Is 1/(a-b) < (b-a)?
Consider first (1) alone.
It says a<b.
Or a-b<0.
Or a-b is negative.
So even 1/(a-b) is negative.
Also b-a>0.
Or b-a is positive.
So obviously, since a negative quantity is less than a positive quantity, 1/(a-b) < (b-a).
So (1) alone is sufficient.
Next consider (2) alone.
It says 1 < la-bl.
It means a-b > 1 or a-b < -1.
So a-b can be either positive or negative and we cannot say definitely whether 1/(a-b) < (b-a) or not.
Or (2) alone is not sufficient.
The correct answer is (A).
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members
Thanked: 29 times

by diebeatsthegmat » Thu Oct 21, 2010 10:10 am
Rahul@gurome wrote:The question is Is 1/(a-b) < (b-a)?
Consider first (1) alone.
It says a<b.
Or a-b<0.
Or a-b is negative.
So even 1/(a-b) is negative.
Also b-a>0.
Or b-a is positive.
So obviously, since a negative quantity is less than a positive quantity, 1/(a-b) < (b-a).
So (1) alone is sufficient.
Next consider (2) alone.
It says 1 < la-bl.
It means a-b > 1 or a-b < -1.
So a-b can be either positive or negative and we cannot say definitely whether 1/(a-b) < (b-a) or not.
Or (2) alone is not sufficient.
The correct answer is (A).
my speed is so bad for math... i am dumb these days... but rahul, can i solve the problem like this:
1/(a-b)<(b-a) <=> 1/(a-b)+(a-b) <0 <=> [1+(a-b)^2]/(a-b)<0
now i will have to see if [1+(a-b)^2]/(a-b)<0
1. a<b
because (a-b)^2>0 with all a, b so 1+(a-b)^2>0 with all a and b
and a-b <0 so sufficient
2. 1<|a-b|
a-b>1 or a-b<-1
no conclusion about this, thus sufficient
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members
Location: Milpitas, CA
Thanked: 447 times

by Rahul@gurome » Thu Oct 21, 2010 7:36 pm
my speed is so bad for math... i am dumb these days... but rahul, can i solve the problem like this:
1/(a-b)<(b-a) <=> 1/(a-b)+(a-b) <0 <=> [1+(a-b)^2]/(a-b)<0
now i will have to see if [1+(a-b)^2]/(a-b)<0
1. a<b
because (a-b)^2>0 with all a, b so 1+(a-b)^2>0 with all a and b
and a-b <0 so sufficient
2. 1<|a-b|
a-b>1 or a-b<-1
no conclusion about this, thus sufficient
What you have done is also correct. It is ultimately the same thing.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1