• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If P is a set of integers and 3 is in P, is every positive m

This topic has 1 expert reply and 0 member replies

If P is a set of integers and 3 is in P, is every positive m

Post
If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

(1) For any integer in P, the sum of 3 and that integer is also in P.
(2) For any integer in P, that integer minus 3 is also in P.

What's the best way to determine which statement is sufficient? Can any experts show?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2666 messages
Followed by:
125 members
Upvotes:
1153
GMAT Score:
770
Post
ardz24 wrote:
If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

(1) For any integer in P, the sum of 3 and that integer is also in P.
(2) For any integer in P, that integer minus 3 is also in P.

What's the best way to determine which statement is sufficient? Can any experts show?
Statement 1: If we know that 3 is in the set, and that for every integer in the set, the sum of 3 plus that integer is also included, we know that 3 + 3 = 6 is in the set too. Similarly, we'd know that 6 + 3 = 9 is in the set and so forth. (More abstractly, if x is in the set, then x + 3 is in the set. If x + 3 is in the set, then x + 3 + 3 is in the set, and so forth. If x = 3, then we'd include every positive multiple of 3 you can conjure.) Thus we know that all positive multiples of 3 would be included. (Of course, this raises interesting philosophical questions about infinite sets, but you get the idea.) Statement 1 alone is sufficient

Statement 2: Well, we know that if 3 is in the set, then 3 - 3 = 0 is in the set. And we'd know that if 0 is in the set, then 0 - 3 = -3 is in the set. and so forth. But what if 3 is the largest element in the set? There's no way to know. All we know for sure is that 3, 0, -3, -6.... are included. This statement is not sufficient.

The answer is A

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 Ian Stewart 44 first replies
2 Brent@GMATPrepNow 34 first replies
3 Scott@TargetTestPrep 32 first replies
4 Jay@ManhattanReview 31 first replies
5 GMATGuruNY 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

139 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Ian Stewart

GMATiX Teacher

53 posts
4 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

51 posts
5 image description Jay@ManhattanReview

Manhattan Review

31 posts
See More Top Beat The GMAT Experts