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 →

An infinite sequence of positive integers is called an "

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 212
Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member
Location: India
Thanked: 5 times
by sachin_yadav » Tue Dec 06, 2011 9:54 am
An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?

(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.

Answer is E

Got it, but not sure. So, can anyone please explain in detail, how answer is E ?

Regards
Sachin
Never surrender
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

by Ian Stewart » Tue Dec 06, 2011 11:39 am
sachin_yadav wrote:An infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. If S is an infinite sequence of positive integers, is S an alpha sequence?

(1) The first ten integers in S are even.
(2) An infinite number of integers in S are odd.
A sequence is just a list of numbers in order. We can create two sequences which satisfy both statements here, one of which will have an infinite number of even values, and one of which will have a finite number of even values. We can just make the first ten values of our sequence all equal to 8, say, just to ensure Statement 1 is true. The remaining values could just be all of the positive integers, in which case we will have an infinite number of even values and an infinite number of odd values:

8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11....

or we can make the remaining values just the odd positive integers only, in which case we will only have ten even values in our sequence:


8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 3, 5, 7, 9, 11, 13, 15, 17, ....

So even with both statements we have no way of knowing if there is an infinite number of even values in the sequence, and the answer is E.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 212
Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member
Location: India
Thanked: 5 times

by sachin_yadav » Tue Dec 06, 2011 12:26 pm
Thanks Ian

Regards
Sachin
Never surrender
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 425
Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members
Thanked: 56 times
GMAT Score:690

by LalaB » Wed Dec 07, 2011 12:16 pm
we are told that an infinite sequence of positive integers is called an "alpha sequence" if the number of even integers in the sequence is finite. to answer to the q. we need 2 things to be true- 1. the sequence is infinite 2. the number of even integers in this sequence is finite.
the 1st one is already told in the q. so ,we need to prove the 2nd one.

(1) it could be enough, if we were told that "The first ten integers in S are even, and no other even numbers exist." since in an original post it was said only about 1st 10 integers, we have no info about other integers.as a result, they can be even or odd. so , (1) is insuff

(2) it could be enough, if we were told that "all numbers of sequence S are odd." since (2) says only about some integers, no conclusion can be made about all integers.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 934
Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members
Location: AAMCHI MUMBAI LOCAL
Thanked: 63 times

by [email protected] » Wed Mar 14, 2012 10:17 pm
The only thing you have to be careful is that you do not assume that the sequence is in AP. If you assume that or if it is given in the question, then the answer comes out to be D and not E.

Just changed a scenario a bit and found that the answer turns out to be D...

Hope this was helpful in some ways...
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1