• Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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

basic math

This topic has 5 expert replies and 3 member replies
omegan3 Newbie | Next Rank: 10 Posts Default Avatar
Joined
06 Jun 2017
Posted:
8 messages

basic math

Post Sun Jun 11, 2017 11:05 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    In one of the MGMAT books:
    "If n is the product of 2,3, and a two-digit prime number, how many of its factors are greater than 6?"

    In the answer they say:
    "Because we have been asked for a concrete answer, we can infer that the answer will be the same
    regardless of which 2-digit prime we pick."

    Does anyone know why the answer doesn't depend on which 2-digit prime is picked?

    Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sun Jun 11, 2017 11:34 am
    Hi omegan3,

    There are a variety of different math 'rules' (patterns, Number Properties, etc.) that exist that most people don't realize are actually rules. Since GMAT questions are almost always based on a rule or pattern of some kind (and sometimes more than one), you can rely on the existence of those patterns and do the necessary work to get to the correct answer (although in DS questions, sometimes your work has to also focus on defining whether a combination of facts actually leads to a definitive pattern or not).

    For this prompt, the rules involved are based on 'prime factorization', but even if you don't recognize that at first, you can still answer the question that is asked.

    Let's start with the smallest two-digit prime number: 11.
    (2)(3)(11) = 66
    The factors of 66 are: 1 and 66, 2 and 33, 3 and 22, 6 and 11. Organized a different way, you can see them as...
    1
    2
    3
    11
    (2)(3) = 6
    (2)(11) = 22
    (3)(11) = 33
    (2)(3)(11) = 66

    In this list, you'll see the number 1, each individual prime, the product of each "pair" of primes and the product of all 3 primes. THAT pattern will always occur regardless of what the 2-digit prime is. By extension, you should notice that - of the 6 factors - exactly four will always be greater than 6 (re: the 2-digit prime, 2(prime), 3(prime) and (2)(3)(prime)). If you don't 'see it' yet, then try another 2-digit prime (such as 13 or 17) and track the results - the answer to the question WILL be the same.

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: omegan3, gmatdestroyer13
    Post Sun Jun 11, 2017 2:37 pm
    Broadly speaking, if a PS question asks for a concrete answer when the variable in question in unknowable (e.g. *some* 2-digit prime, but we'll never know which one), we have to infer that the answer would be the same no matter which value we pick, because otherwise there wouldn't be one (and only one) right answer to the question.

    Here's another example:

    PS #40 in OG2017:
    Quote:
    If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?

    (A) 0
    (B) 1
    (C) 2
    (D) 3
    (E) 5
    If there were different results for different values of n, then it would be impossible to answer the question.

    So, we know that we can just pick any value for n that fits, and see what result we get:

    n=5
    n^2 = 25
    25/12 give a remainder of 1.

    The answer must be B.

    _________________


    Ceilidh Erickson
    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


    Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
    Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

    Thanked by: omegan3, gmatdestroyer13
    Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
    omegan3 Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    06 Jun 2017
    Posted:
    8 messages
    Post Mon Jun 12, 2017 10:47 am
    Rich.C@EMPOWERgmat.com wrote:
    ..
    Rich
    Hello Rich,

    It's very nice to you to take the time to respond and help explain the reasoning.

    You gave a very thorough explanation which I found helpful!
    Thank you for that!



    Last edited by omegan3 on Mon Jun 12, 2017 10:52 am; edited 1 time in total

    omegan3 Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    06 Jun 2017
    Posted:
    8 messages
    Post Mon Jun 12, 2017 10:51 am
    ceilidh.erickson wrote:
    ..
    Hi Ceilidh,

    This seems like a useful way to think, a bit counter-intuitive for me, but I'll try to keep this reasoning in mind.

    I also liked that you were able to come up with a similar example to explain you point!

    Thank you.

    Post Mon Jun 12, 2017 12:22 pm
    omegan3 wrote:
    ceilidh.erickson wrote:
    ..
    Hi Ceilidh,

    This seems like a useful way to think, a bit counter-intuitive for me, but I'll try to keep this reasoning in mind.

    I also liked that you were able to come up with a similar example to explain you point!

    Thank you.
    My pleasure!

    _________________


    Ceilidh Erickson
    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


    Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
    Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

    Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

    GMAT/MBA Expert

    Post Sun Jul 23, 2017 2:47 pm
    Here's the simplest way, I think: call this prime p.

    Since our number = 2 * 3 * p, it has the following factors:

    1, 2, 3, p, 2*3, 2*p, 3*p, 2*3*p

    Since p is a two digit number, everything here with p in it will be (at least) two digits. So the factors p, 2p, 3p, and 6p are all greater than 6, giving us FOUR such factors.

    Thanked by: omegan3
    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!
    omegan3 Newbie | Next Rank: 10 Posts Default Avatar
    Joined
    06 Jun 2017
    Posted:
    8 messages
    Post Mon Jul 24, 2017 6:04 am
    Matt@VeritasPrep wrote:
    Here's the simplest way, I think: call this prime p.

    Since our number = 2 * 3 * p, it has the following factors:

    1, 2, 3, p, 2*3, 2*p, 3*p, 2*3*p

    Since p is a two digit number, everything here with p in it will be (at least) two digits. So the factors p, 2p, 3p, and 6p are all greater than 6, giving us FOUR such factors.
    Thank you dear for explaining, and sharing your knowledge with us.

    GMAT/MBA Expert

    Post Sun Aug 06, 2017 10:45 pm
    omegan3 wrote:
    Matt@VeritasPrep wrote:
    Here's the simplest way, I think: call this prime p.

    Since our number = 2 * 3 * p, it has the following factors:

    1, 2, 3, p, 2*3, 2*p, 3*p, 2*3*p

    Since p is a two digit number, everything here with p in it will be (at least) two digits. So the factors p, 2p, 3p, and 6p are all greater than 6, giving us FOUR such factors.
    Thank you dear for explaining, and sharing your knowledge with us.
    Certainly! I don't know if I deserve being 'dear', but hey, I'm flattered.

    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!

    Best Conversation Starters

    1 lheiannie07 116 topics
    2 LUANDATO 62 topics
    3 swerve 62 topics
    4 ardz24 61 topics
    5 AAPL 58 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    172 posts
    2 image description Scott@TargetTestPrep

    Target Test Prep

    154 posts
    3 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    131 posts
    4 image description EconomistGMATTutor

    The Economist GMAT Tutor

    127 posts
    5 image description GMATGuruNY

    The Princeton Review Teacher

    125 posts
    See More Top Beat The GMAT Experts