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 →

Bet Sequence

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 233
Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members
Location: New York
Thanked: 7 times
by yellowho » Fri Feb 18, 2011 2:21 am
An inÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…nite. If S is an inÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The Â…rst ten integers in S are even.
(2) The di¤erence between each successive pair of
terms in S is a constant.

I don't understand why this is C.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members
Thanked: 127 times

by Night reader » Fri Feb 18, 2011 5:35 am
to make it more readable, add "fi" :)

The problem inquires about finite values of odd numbers. It does not put restrictions, numbers can be consecutive and non-consecutive, the same or not the same. The only restriction is numbers must be +ve integers.

st(1) that the first ten integers in S are even is Not Sufficient, as we get no relative data per odd-even and even-odd numbers in set S;
st(2) also Not Sufficient as we don't know the distribution of numbers in set S; the numbers may start even or odd; we know only that --> a(n+3)+ a(n+4) - a(n) - a(n+1) is const
Combined st(1&2) makes Sufficiency as we can arrange our set in infinite number of ways to keep odd numbers running, hence my answer is NO and Sufficient.

IOM C
yellowho wrote:An infiÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…finite. If S is an infiÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The fist ten integers in S are even.
(2) The difference between each successive pair of
terms in S is a constant.

I don't understand why this is C.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members
Location: Varanasi
Thanked: 11 times

by ankur.agrawal » Sat Feb 19, 2011 1:46 am
2) sufficient.

If difference is same between each successive pair then we can arrange our set in infinite number of ways to keep odd numbers running / we can even create sets without any odd nos. Both of them denies thats it is not a beta sequence. So should be sufficient.


yellowho wrote:An inÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…nite. If S is an inÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The Â…rst ten integers in S are even.
(2) The di¤erence between each successive pair of
terms in S is a constant.

I don't understand why this is C.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members
Thanked: 127 times

by Night reader » Sat Feb 19, 2011 3:15 am
@ankur, st(2) implies only difference between each successive pairs.
The question did not provide that the numbers must be even. It says S is an infinite number of positive integers.
Beta set --> 1,3,5,7,9,11,13,15 ... / differences (5+7-1-3=8, 9+11-5-7=8, 9+11-13-15=8...)
OR
Not Beta set --> 2,4,6,8,10,12...

statement (2) is Not Sufficient.
ankur.agrawal wrote:2) sufficient.

If difference is same between each successive pair then we can arrange our set in infinite number of ways to keep odd numbers running / we can even create sets without any odd nos. Both of them denies thats it is not a beta sequence. So should be sufficient.


yellowho wrote:An inÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…nite. If S is an inÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The Â…rst ten integers in S are even.
(2) The di¤erence between each successive pair of
terms in S is a constant.

I don't understand why this is C.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members
Location: Varanasi
Thanked: 11 times

by ankur.agrawal » Sat Feb 19, 2011 11:51 am
Oh Careless reading. Misinterpreted each successive pairs .

Thanks .
Night reader wrote:@ankur, st(2) implies only difference between each successive pairs.
The question did not provide that the numbers must be even. It says S is an infinite number of positive integers.
Beta set --> 1,3,5,7,9,11,13,15 ... / differences (5+7-1-3=8, 9+11-5-7=8, 9+11-13-15=8...)
OR
Not Beta set --> 2,4,6,8,10,12...

statement (2) is Not Sufficient.
ankur.agrawal wrote:2) sufficient.

If difference is same between each successive pair then we can arrange our set in infinite number of ways to keep odd numbers running / we can even create sets without any odd nos. Both of them denies thats it is not a beta sequence. So should be sufficient.


yellowho wrote:An inÂ…nite sequence of positive integers is called a "beta
sequence" if the number of odd integers in the sequence is
Â…nite. If S is an inÂ…nite sequence of positive integers, is S a
beta sequence?

(1) The Â…rst ten integers in S are even.
(2) The di¤erence between each successive pair of
terms in S is a constant.

I don't understand why this is C.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1