• EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist 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

The “primeness”

This topic has 4 expert replies and 0 member replies

The “primeness”

Post Sun Sep 24, 2017 4:02 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness?

    A) 10
    B) 12
    C) 14
    D) 15
    E) 18

    How will i start to solve this? Can any experts help me?

    OA C

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sun Sep 24, 2017 4:21 am
    lheiannie07 wrote:
    The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness?

    A) 10
    B) 12
    C) 14
    D) 15
    E) 18

    How will i start to solve this? Can any experts help me?

    OA C
    A) 10:

    Factors of 10 are: 1, 2, 4, 5, and 10; the largest prime factor = 5 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 5 - 2 = 3.

    B) 12:

    Factors of 12 are: 1, 2, 3, 4, 6, and 12; the largest prime factor = 3 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 3 - 2 = 1.

    C) 14:

    Factors of 14 are: 1, 2, 7, and 14; the largest prime factor = 7 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 7 - 2 = 5.

    D) 15:

    Factors of 15 are: 1, 3, 5, and 15; the largest prime factor = 5 and the smallest prime factor = 3; thus, the difference between the largest and the smallest prime factors = 5 - 3 = 2.

    E) 18:

    Factors of 18 are: 1, 2, 3, 6, 9, and 18; the largest prime factor = 3 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 3 - 2 = 1.

    The greatest difference is 5 for number 14 (option C).

    The correct answer: C

    Hope this helps!

    Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

    -Jay
    _________________
    Manhattan Review GMAT Prep

    Locations: New York | Hyderabad | Mexico City | Toronto | and many more...

    Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

    Thanked by: lheiannie07
    Post Mon Sep 25, 2017 3:52 pm
    Hi lheiannie07,

    This question literally tells you to use prime factorization on the each of the 5 answer choices - as we're looking for the answer with the largest DIFFERENCE between its largest and smallest prime factors.

    Answer A: 10 = (2)(5)
    Answer B: 12 = (2)(2)(3)
    Answer C: 14 = (2)(7)
    Answer D: 15 = (3)(5)
    Answer E: 18 = (2)(3)(3)

    Looking at these options, the largest difference isn't hard to spot...

    Final Answer: C

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: lheiannie07

    GMAT/MBA Expert

    Post Tue Sep 26, 2017 5:18 pm
    Find the prime factorization, then do largest prime - smallest prime.

    A: 10 = 2 * 5, largest - smallest = 5 - 2 = 3

    B: 12 = 2 * 2 * 3, largest - smallest = 3 - 2 = 1

    C: 14 = 2 * 7, largest - smallest = 7 - 2 = 5

    etc. etc. You get the idea Smile

    Thanked by: lheiannie07
    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!
    Post Fri Oct 13, 2017 10:56 am
    Quote:
    The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness?

    A) 10
    B) 12
    C) 14
    D) 15
    E) 18

    How will i start to solve this? Can any experts help me?
    Hi lheiannie07,
    Let's take a look at your question.
    The question states that the “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors.
    To find the greatest primeness, we will find the primeness of each number given one by one by finding its factors.

    Primeness of 10:
    Factors of 10 = 1, 2, 5, 10
    Smallest prime factor = 2
    Largest prime factor = 5
    Primeness of 10 = 5 - 2 = 3

    Primeness of 12:
    Factors of 12 = 1, 2, 3, 4, 6, 12
    Smallest prime factor = 2
    Largest prime factor = 3
    Primeness of 12 = 3 - 2 = 1

    Primeness of 14:
    Factors of 14 = 1, 2, 7, 14
    Smallest prime factor = 2
    Largest prime factor = 7
    Primeness of 14 = 7 - 2 = 5

    Primeness of 15:
    Factors of 15 = 1, 2, 3, 5, 15
    Smallest prime factor = 2
    Largest prime factor = 5
    Primeness of 15 = 5 - 2 = 3

    Primeness of 18:
    Factors of 18 = 1, 2, 3, 6, 9, 18
    Smallest prime factor = 2
    Largest prime factor = 3
    Primeness of 18 = 3 - 2 = 1

    We can see that 14 has the largest primeness, i.e. 5.

    Therefore, Option C is correct.
    Hope this helps.

    I am available, if you'd like any follow up.

    _________________
    GMAT Prep From The Economist
    We offer 70+ point score improvement money back guarantee.
    Our average student improves 98 points.

    Thanked by: lheiannie07
    Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.

    Best Conversation Starters

    1 Vincen 152 topics
    2 lheiannie07 61 topics
    3 Roland2rule 49 topics
    4 ardz24 40 topics
    5 LUANDATO 32 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    141 posts
    2 image description EconomistGMATTutor

    The Economist GMAT Tutor

    107 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    106 posts
    4 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    104 posts
    5 image description Matt@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts