• 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
  • 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
  • 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
  • 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
  • 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
  • examPAL
    Most awarded test prep in the world
    Now free for 30 days

    Available with Beat the GMAT members only code

    MORE DETAILS
    examPAL

Papgust's GMAT MATH FLASHCARDS directory

This topic has 9 expert replies and 136 member replies
Goto page Previous
binit Master | Next Rank: 500 Posts Default Avatar
Joined
07 Mar 2015
Posted:
111 messages
Followed by:
1 members
Upvotes:
8
Post Sun Mar 08, 2015 12:04 am
papgust wrote:
If N is a perfect square, then the number of factors of N will ALWAYS be an ODD number.

If N is a NON-perfect square, then the number of factors of N will ALWAYS be an EVEN number.
Hello Sir, thanks a lot for ur essential help in prepping. Just one query, can we extend the theory for NON-perfect square to "all positive integers except squares"? Cos it's just one odd power that's needed to make the number of factors even. Pls give ur insight.

  • +1 Upvote Post
  • Quote
  • Flag
binit Master | Next Rank: 500 Posts Default Avatar
Joined
07 Mar 2015
Posted:
111 messages
Followed by:
1 members
Upvotes:
8
Post Sun Mar 08, 2015 12:26 am
papgust wrote:
How to find Sum of all factors of a POSITIVE integer:

If N is expressed in terms of its prime factors as a^p * b^q * c^r, where p,q,r are positive integers, then the sum of all factors of N is

[ (a^(p+1) - 1) / a-1 ] * [ (b^(q+1) - 1) / b-1 ] * [ (c^(r+1) - 1) / c-1 ]
Thanks a ton for this utterly useful formula. This is just awesome.

  • +1 Upvote Post
  • Quote
  • Flag
run3 Newbie | Next Rank: 10 Posts
Joined
11 Apr 2016
Posted:
1 messages
Post Mon Apr 11, 2016 7:07 pm
Very nice post and right to the point. I am not sure if this is actually the best place to ask but do you folks have any idea where to hire some professional writers? Thanks in advance Smile

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Jul 05, 2017 12:07 am
run3 wrote:
Very nice post and right to the point. I am not sure if this is actually the best place to ask but do you folks have any idea where to hire some professional writers? Thanks in advance Smile
What sort of writer? There are so many freelancers out there, and plenty of sites on which they advertise.

  • +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!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Jul 05, 2017 12:07 am
binit wrote:
papgust wrote:
How to find Sum of all factors of a POSITIVE integer:

If N is expressed in terms of its prime factors as a^p * b^q * c^r, where p,q,r are positive integers, then the sum of all factors of N is

[ (a^(p+1) - 1) / a-1 ] * [ (b^(q+1) - 1) / b-1 ] * [ (c^(r+1) - 1) / c-1 ]
Thanks a ton for this utterly useful formula. This is just awesome.
But the fun part is proving it! Smile

How would we know that such a formula works?

  • +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!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Jul 05, 2017 12:11 am
Piggybacking on my last post, a more memorable formula (in my opinion) is

(a- + a-⁻¹ + ... + a¹ + 1) * (b' + b'⁻¹ + ... + b¹ + 1) * (cʳ + cʳ⁻¹ + ... + c¹ + 1)

I prefer this one - it shows a little more clearly where the formula comes from.

  • +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!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Jul 05, 2017 12:14 am
drkomal2000 wrote:
papgust wrote:
Pattern 1:
Unit's place that has digits - 2/3/7/8

Then, unit's digit repeats every 4th value. Divide the power (or index) by 4.
Hi Papgust
Thanks a lot for your notes. Can you or anyone from the community give me example of the pattern 1? I know you gave one example but Its confusing for me.
powers of 2: 2, 4, 8, 16, 32, 64, 128, 256, ...

  • +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!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Jul 05, 2017 12:15 am
drkomal2000 wrote:
papgust wrote:
Pattern 1:
Unit's place that has digits - 2/3/7/8

Then, unit's digit repeats every 4th value. Divide the power (or index) by 4.
Hi Papgust
Thanks a lot for your notes. Can you or anyone from the community give me example of the pattern 1? I know you gave one example but Its confusing for me.
powers of 3: 3, 9, 27, 81, 243, 729, 2187, 6561, ...

  • +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!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Jul 05, 2017 12:17 am
drkomal2000 wrote:
papgust wrote:
Pattern 1:
Unit's place that has digits - 2/3/7/8

Then, unit's digit repeats every 4th value. Divide the power (or index) by 4.
Hi Papgust
Thanks a lot for your notes. Can you or anyone from the community give me example of the pattern 1? I know you gave one example but Its confusing for me.
powers of 7: 7, 49, 343, 2401, 16807, 117649, 823543, 5764801, ...

  • +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!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Jul 05, 2017 12:19 am
drkomal2000 wrote:
papgust wrote:
Pattern 1:
Unit's place that has digits - 2/3/7/8

Then, unit's digit repeats every 4th value. Divide the power (or index) by 4.
Hi Papgust
Thanks a lot for your notes. Can you or anyone from the community give me example of the pattern 1? I know you gave one example but Its confusing for me.
powers of 8: 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, ...

  • +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!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
12 Sep 2012
Posted:
2640 messages
Followed by:
113 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post Wed Jul 05, 2017 12:22 am
drkomal2000 wrote:
papgust wrote:
Pattern 1:
Unit's place that has digits - 2/3/7/8

Then, unit's digit repeats every 4th value. Divide the power (or index) by 4.
Hi Papgust
Thanks a lot for your notes. Can you or anyone from the community give me example of the pattern 1? I know you gave one example but Its confusing for me.
Once we're armed with those, we can use the powers of an integer to determine the units digit. For instance, suppose I ask for the units digit of 3²³. We know that the units digits cycle in a block of 4: 3, 9, 7, 1, 3, 9, 7, 1, ...

With that in mind, we only need to know the remainder when 23 is divided by 4. That remainder is 3, meaning that its units digit will be the third in the cycle {3, 9, 7, 1} and that 3²³ ends in 7. At the risk of sounding like the dorkiest math teacher you had ... too cool!

  • +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!

Best Conversation Starters

1 lheiannie07 108 topics
2 Roland2rule 63 topics
3 ardz24 63 topics
4 LUANDATO 50 topics
5 AAPL 42 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

152 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

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

EMPOWERgmat

104 posts
4 image description Scott@TargetTestPrep

Target Test Prep

96 posts
5 image description Max@Math Revolution

Math Revolution

87 posts
See More Top Beat The GMAT Experts