• PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas 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
  • 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
  • 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

if Y is the smallest positive integer (no. properties)

This topic has 2 expert replies and 2 member replies
mattnyc15 Junior | Next Rank: 30 Posts
Joined
17 Jul 2015
Posted:
26 messages
Thanked:
1 times

if Y is the smallest positive integer (no. properties)

Post Sun Nov 22, 2015 1:02 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Q: If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be:

    A: 2
    B: 5
    C: 6
    D: 7
    E: 14


    OA: E


    I know we break this down by primes, but I don't understand why we need to get the single prime factors and multiply. Maybe I don't fully understand the question? Why couldn't we say 6 (2x3) or even 2?

    I'd love an explanation here. Thanks!

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    theCEO Master | Next Rank: 500 Posts Default Avatar
    Joined
    17 Oct 2010
    Posted:
    363 messages
    Followed by:
    3 members
    Thanked:
    115 times
    Post Sun Nov 22, 2015 2:07 pm
    mattnyc15 wrote:
    Q: If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be:

    A: 2
    B: 5
    C: 6
    D: 7
    E: 14


    OA: E


    I know we break this down by primes, but I don't understand why we need to get the single prime factors and multiply. Maybe I don't fully understand the question? Why couldn't we say 6 (2x3) or even 2?

    I'd love an explanation here. Thanks!
    Let's see if this this helps.

    3,150 * y = a^2; in order for this to be true 3150*y must be a perfect square
    50 * 21 * 3 * y = a^2
    25 * 2 * 7 * 3 * 3 * y = a^2
    5^2 * 3^2 * 2 * 7 * y = a^2
    (5+3)^2 * 14y = a^2

    For the smallest possible integer and to be a perfect square y=14

    In other words when is the following equation true?
    3150y = (5+3+y)^2 = a^2

    It's true when y=14

    ans = e

    Post Sun Nov 22, 2015 2:25 pm
    mattnyc15 wrote:
    Q: If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be:

    A: 2
    B: 5
    C: 6
    D: 7
    E: 14


    OA: E


    Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime.
    For example, 36 = (2)(2)(3)(3)
    And 400 = (2)(2)(2)(2)(5)(5)
    Likewise, 3150y must have an EVEN number of each prime in its prime factorization.

    Aside: for more on this concept, watch our free video: http://www.gmatprepnow.com/module/gmat-integer-properties/video/829

    So, 3150y = (2)(3)(3)(5)(5)(7)y
    We have an EVEN number of 3's and 7's, but we have a single 2 and a single 7.
    If y = (2)(7), then we get a perfect square.

    That is: 3150y = (2)(2)(3)(3)(5)(5)(7)(7)

    So, if y = 14, then 3150y is a perfect square.

    Answer: E

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

    GMAT/MBA Expert

    Post Fri Nov 27, 2015 2:41 am
    I'd take 3150 and get it as close to a square as you can. If it's a square, it should have two identical roots, so let's shoot for that.

    3150 = 315 * 10
    = 63 * 5 * 10
    = 7 * 3 * 3 * 5 * 5 * 2

    Close! 3*3 and 5*5 are squares, so we're almost there: we're short a 7 and a 2. So if y gives us those factors, we're set, and y = 14.

    To see why this works, take y = 14.

    Then 3150*y = 3150 * 14 = (3 * 3 * 5 * 5 * 7 * 2) * 2 * 7, or (3*5*7*2)².

    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!
    vishnujthattil Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    12 Jan 2016
    Posted:
    2 messages
    Post Thu Jan 14, 2016 9:10 am
    [quote="mattnyc15"]Q: If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be:

    A: 2
    B: 5
    C: 6
    D: 7
    E: 14

    Since 3150 * y should be a perfect square, the resulting product must have 0 in the ten's place too. hence options B and D become invalid. further for option A it is visual calculation, 3150* 2= 6300 is not a perfect square. for option C, its 3 times 3150 * 2, i.e 6300*3=18900 again a visual calculation and it is not a perfect square. thus option E is correct. This Approach helps to save valuable time I believe!!!

    Best Conversation Starters

    1 Vincen 180 topics
    2 lheiannie07 61 topics
    3 Roland2rule 54 topics
    4 ardz24 44 topics
    5 VJesus12 14 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    155 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    105 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    101 posts
    4 image description Jay@ManhattanReview

    Manhattan Review

    82 posts
    5 image description Matt@VeritasPrep

    Veritas Prep

    80 posts
    See More Top Beat The GMAT Experts