• 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
  • 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
  • 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
  • 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
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider

Papgust's GMAT MATH FLASHCARDS directory

This topic has 9 expert replies and 136 member replies
Goto page Next
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653

Papgust's GMAT MATH FLASHCARDS directory

Post Thu Jun 03, 2010 6:26 pm
Greetings GMAT Aspirants!

I spoke to Eric whether i could share my flashcards with our community. Eric's instant reply was "Why not? It would be awesome to see the notes that you came up with".

Throughout my GMAT preparation, I have collected key core-concepts and tricks in my flashcards. No doubt, I had to spend atleast an hour to go through my flashcards everyday Smile. Eric and I are confident that these flashcards will help our community in some way or the other. Special thanks to Eric for allowing me to share these flashcards with you Smile

I would like to share these flashcards on a daily basis rather as a whole. Very simple reason is members can easily digest each and every concept and discuss on the concept by trying out a GMAT/Non-GMAT problem (It is very important to recognize an underlying concept in a GMAT problem and work through the problem). People tend to overlook some vital points if the flashcards are shared as a bunch.

Interested people can follow this thread and learn takeaways everyday which will definitely help you in your marathon preparation.

NOTE: My flashcards are in handwritten form in a notebook. My handwriting will not be readable by everybody here. So, the notebook will not be scanned and shared at one go as it serves no purpose at all. Kindly bear with me and get benefited by learning these points everyday. Will do my best to post as many points as possible whenever i logon to BTG.

Thanks!

Very good luck to ALL!! Happy Learning! Smile



Last edited by papgust on Sun Jun 06, 2010 1:55 am; edited 1 time in total

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Top Reply
Post Sun Jun 06, 2010 6:33 pm
Any number whose prime factorization contains even powers of primes, then the number must be a perfect square.

Any number whose prime factorization contains powers of primes with multiples of 3, then the number must be a perfect cube.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: binit
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Top Reply
Post Sun Jun 06, 2010 6:31 pm
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 ]

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: binit
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Sun Jun 06, 2010 6:33 pm
Any number whose prime factorization contains even powers of primes, then the number must be a perfect square.

Any number whose prime factorization contains powers of primes with multiples of 3, then the number must be a perfect cube.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: binit
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Sun Jun 06, 2010 6:31 pm
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 ]

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: binit
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Tue Jun 08, 2010 6:59 am
Simple Facts:

a^n - b^n:

1. ALWAYS divisible by a-b
2. If n is even, it is divisible by a+b
3. If n is odd, it is NOT divisible by a+b


a^n + b^n:

1. NEVER divisible by a-b
2. If n is odd, it is divisible by a+b
3. If n is even, it is NOT divisible by a+b

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Tue Jun 08, 2010 6:56 am
How to find REMAINDER for LARGE POWERS of numbers:


There are 2 ways to do so:

1. Pattern Method:

Example:

What is the remainder when 2^56 / 7 ?

Solution:
Remainder when 2^1 is divided by 7 is 2
Remainder when 2^2 is divided by 7 is 4
Remainder when 2^3 is divided by 7 is 1
Remainder when 2^4 is divided by 7 is 2 --> Repeats again.

The remainder repeats after 3 steps i.e. in the 4th step.

Now, Divide the power (or index) by 3 (no of steps after which remainder repeats) and compute a new remainder.

56 % 3 --> 2 (remainder)

Now, raise the base (2) to the power 2 (new remainder). 2^2 % 7 --> 4.

Thus, 4 is the remainder when 2^56 / 7.



2. Remainder Theorem Method: (NOT RECOMMENDED unless clear)

Example:

What is the remainder when 2^51 / 7 ?

Solution:
2^51 can be changed to (2^3)^17.
7 can be changed to (8-1) OR (2^3 - 1)

Substitute 'x' in place of 2^3,

x^17 / (x-1)

Remainder is f(1). Substitute 1 in 'x',

Remainder is 1.

Thus, 1 is the remainder when 2^51 / 7.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Tue Jun 08, 2010 6:44 am
Guys are indeed following the SC thread. I hope people are also following this thread. Let me continue to post flashcards.


REMAINDERS:


(I)

When 2 numbers are divided by same divisor and the remainders obtained are the same,
THEN
DIFFERENCE b/w 2 numbers is also divisible by that divisor.


(II)

When 2 positive numbers 'a' and 'b' are divided by the same divisor 'd' and remainders obtained are 'r1' and 'r2' respectively,
THEN
the remainders obtained when a+b is divided by d will be r1+r2

Quote:
NOTE: If r1+r2 >= d, compute (r1+r2) - d as the remainder.
(III)

When 2 positive numbers 'a' and 'b' are divided by the same divisor 'd' and the remainders obtained are 'r1' and 'r2' respectively,
THEN
the remainders obtained when a*b is divided by d will be r1*r2

Quote:
NOTE: If r1*r2 >= d, compute (r1*r2) / d as the remainder.
TAKEAWAY:

A remainder can NEVER be greater than or equal to the divisor.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Mon Jun 07, 2010 6:39 pm
Hello folks,

I'm not sure whether you guys are following the thread as there is no response or no interest shown by you.

Please let me know if i need to continue posting. Otherwise, i'll stop right here. It's a sheer waste of time if no one is getting benefited.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: ashrs
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Sun Jun 06, 2010 6:26 pm
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.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”



Last edited by papgust on Sun Jun 06, 2010 6:31 pm; edited 1 time in total

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: binit
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Sun Jun 06, 2010 6:24 pm
How to find number of factors for a POSITIVE INTEGER:

There are 2 approaches to find number of factors of an integer.

Approach #1: (Factor Pairs Method)

i. Let's take a non-perfect square number such as 32. Keep picking a number (start from 1) that divides 32 until you reach a number that is smaller than the quotient.

Small Large
1 32
2 16
4 8

Stop! If you take 8, you get 4 as quotient which is smaller than the number (8).
Therefore, there are 3*2 = 6 factor pairs or number of factors of 32.

ii. Let's take a perfect square number such as 36. Keep picking a number (start from 1) that divides 36 until you reach a number that is smaller than the quotient.

Small Large
1 36
2 18
3 12
4 9
6 6

Totally, there are 5*2 = 10 factor pairs or number of factors of 36. But, (6,6) gets repeated twice. So, deduct 1 from factor pairs i.e. 10-1 = 9 factor pairs or number of factors of 36.


Approach #2: (RECOMMENDED)

If N is expresses in terms of its prime factors as a^p * b^q * c^r, where p,q,r are positive integers, then N will have (p+1) * (q+1) * (r+1) positive factors.

Example:

i. 32 = 2^5.
No. of factors = (5+1) = 6.

ii. 1452 = 2^2 * 3 * 11^2
No. of factors = (2+1) * (1+1) * (2+1) = 18.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: GRV99, binit
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Sat Jun 05, 2010 7:54 pm
We are often faced to test the divisibility of some number in the exam. Following points may help you in simplifying the process,

Divisibility Tests:

To check whether a number (say n) is divisible

By 2: unit's place of n must be 0 (OR) unit's place of n must be divisible by 2.

By 3: Sum of the digits of n must be divisible by 3.

By 4: Last 2 digits (Unit's place and ten's place) of n are 0's (OR) Last 2 digits of n must be divisible by 4.

By 5: Unit's digit must be a 5 (OR) a 0.

By 6: n must be divisible by both 2 and 3 (Follow the method used for 2 and 3).

By 8: Last 3 digits (units, tens and hundredth place) of n are 0's (OR) Last 3 digits of n is divisible by 8.

By 9: Sum of the digits of n must be divisible by 9.

By 11: (Sum of the digits of n in odd places) - (Sum of the digits of n in even places) ==> Either 0 (OR) divisible by 11.

By 12: n must be divisible by both 3 and 4 (Follow the method used for 3 and 4).

By 25: Last 2 digits (units and tens place) of n are 0's (OR) Last 2 digits of n must be divisible by 25.

By 75: n must be divisible by both 3 and 25 (Follow the method used for 3 and 25).

By 125: Last 3 digits of n are 0's (OR) are divisible by 125.


Try out examples for each divisibility to grasp better.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: eaakbari, binit
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Sat Jun 05, 2010 7:40 pm
Warning: Some people may not find this approach comfortable. Some may find it comfortable. Please follow and practice only if you are comfortable with this approach. Otherwise, please ignore it.


Sometimes, we get one type of question in GMAT where we need to calculate units digit of integers raised to some power. I found a shortcut where you could save time by remembering some patterns.

How to find unit digit of powers of numbers:

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.

After dividing,
If remainder is 1, unit digit of number raised to the power 1.
If remainder is 2, unit digit of number raised to the power 2.
If remainder is 3, unit digit of number raised to the power 3.
If remainder is 0, unit digit of number raised to the power 4.

Pattern 2:
Unit's place that has digits - 0/1/5/6

Then, all powers of the number have same digit as unit's place.

For e.g., 6^1 = 6, 6^2 = 36, 6^3 = 216, 6^4 = 1296


Pattern 3:
Unit's place that has digit - 4

Then,
If power is odd --> unit's digit will be '4'
If power is even --> unit's digit will be '6'

Similarly,
Unit's place that has digit - 9

Then,
If power is odd --> unit's digit will be '9
If power is even --> unit's digit will be '1'


Example:
Let's take a long number - 122 ^ 94. Find unit's digit.

Unit's place is 2. So, it repeats every 4th term of the power.
So, divide the power by 4. 94 % 4 ==> 2 (remainder).

Raise the unit digit of the base number to the power (2 - remainder). 2^2 = 4.

Thus, 4 is the unit's digit of 122^94.


I found this approach very easy and comfortable. So, see how comfortable it is for you and apply.


Real GMAT Problem: OG-12 PS #190

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: eaakbari, binit, yb32
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Fri Jun 04, 2010 7:31 pm
There is one interesting cool fact to know. I remember applying this fact in actual GMAT. It's good to learn if you don't know.


Quote:
Product of any 2 numbers = Product of LCM and HCF of those 2 numbers

Product of any 2 fractions = Product of LCM and HCF of those 2 fractions
I will try to find and post a GMAT problem that uses this concept. Please feel free to post a question if you find it.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: binit
papgust Community Manager
Joined
10 Aug 2009
Posted:
1537 messages
Followed by:
240 members
Upvotes:
653
Post Fri Jun 04, 2010 7:27 pm
Most of you are comfortable with calculating LCM and HCF of 2 integers/numbers. But are you comfortable for doing the same with fractions? If you are not sure how to do for fractions, here is how you do.


How to calculate LCM and HCF of fractions:

Quote:
L.C.M of 2 fractions = L.C.M of NUMERATORS / H.C.F of DENOMINATORS

H.C.F of 2 fractions = H.C.F of NUMERATORS / L.C.M of DENOMINATORS
Try out an example if required.

_________________
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
http://www.beatthegmat.com/download-gmat-questions-with-expert-solutions-t59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
“Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life”

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: eaakbari, camlan1990, kartikc11

Best Conversation Starters

1 lheiannie07 116 topics
2 LUANDATO 67 topics
3 swerve 66 topics
4 ardz24 61 topics
5 AAPL 59 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

213 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

177 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

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

EMPOWERgmat

133 posts
5 image description GMATGuruNY

The Princeton Review Teacher

126 posts
See More Top Beat The GMAT Experts