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 →

arithmetic operations

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Senior | Next Rank: 100 Posts
Posts: 64
Joined: Sun Jul 24, 2011 9:11 am
Thanked: 13 times
GMAT Score:610

by sumgb » Mon Dec 12, 2011 8:16 am
IMO A

we need to find b - a >= 2* 3^n - 2*2^n

from I - we get, b - a = 3*3^n - 2*2^n which is more than 2* 3^n - 2*2^n given that n > 0 and an int.

from II - no info abt a or b. Hence insuff.

whats the OA and OE?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members
Location: Utrecht, The Netherlands
Thanked: 318 times

by neelgandham » Mon Dec 12, 2011 9:02 am
If n is a positive integer, is the value of b-a at least twice the value of 3^n-2^n?
Rephrasing the question to Is b-a > 2*(3^n-2^n), i.e Is b-a > (2*(3^n))-(2*(2^n)) ?
1) a=2^n+1 and b=3^n+1
b-a = 3^(n+1) - 2^(n+1) = (3*(3^n))-(2*(2^n)) = (3^n) + (2*(3^n))-(2*(2^n)) > (2*(3^n))-(2*(2^n))
because (3^n) + Number A > Number A
Sufficient!
2) n=3
Is b-a > 3^3-2^3 = 19
Insufficient!, because you don't know the values of b and a

Answer A IMO
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Mon Dec 12, 2011 9:37 am
n>0, Is (b-a)>=2(3^n-2^n)
st(1) a=2^n+1 and b=3^n+1 imply b-3^n=a-2^n, b-a=(3^n-2^n). Since n>0 (3^n-2^n) is also +ve. Sufficient, as we can answer No.
st(2) n=3 doesn't tell anything about a and b, Not Sufficient.

a
romitvsingh wrote:if n is a positive integer, is the value of b-a at least twice the value of 3^n-2^n?

1) a=2^n+1 and b=3^n+1

2) n=3
Success doesn't come overnight!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Dec 12, 2011 2:48 pm
romitvsingh wrote:if n is a positive integer, is the value of b-a at least twice the value of 3^n-2^n?
Statement 1: a=2^n+1 and b=3^n+1
Let n=1.
Then a=2² and b=3², so b-a = 3²-2².
Twice the value of 3^n-2^n = 2(3¹-2¹) = 2(3¹) - 2².
Is the value of b-a at least twice the value of 3^n-2^n?
3²-2² ≥ 2(3¹) - 2²
3² ≥ 2(3)
3 ≥ 2.
YES.

Increasing the value of n will simply increase the value of each exponent by the same amount.
If n=2, each exponent will increase by 1:
3³- 2³ ≥ 2(3²) - 2³
3³ ≥ 2(3²)
3 ≥ 2.

Thus, regardless of the value of n, the left-hand side will always be greater than the right-hand side.
SUFFICIENT.

Statement 2: n=3
No information about b-a.
INSUFFICIENT.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1