BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Papgust's GMAT MATH FLASHCARDS directory

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Fri Jun 11, 2010 5:55 am
Although this is not very important, it is fun to simply know this point.


If p is a prime number, then for any integer n,
(n^p - n) is ALWAYS divisible by p.


Example:
p = 3, n = 2

(2^3 - 2) is divisible by 3
OR
6 is divisible by 3
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Fri Jun 11, 2010 7:13 pm
"Number Properties" flashcards are over by now.

I will start posting flashcards in "Inequalities".
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Fri Jun 11, 2010 7:15 pm
If x > y,
then x - y > 0 AND x = y + k (Where k > 0)


If x < y,
then x - y < 0 AND [x = y - k (Where k > 0) OR x = y + k (Where k < 0)]
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Fri Jun 11, 2010 7:25 pm
If x > y and 'k' is a real number,
then
x + k > y + k (Irrespective of the value of k)
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Fri Jun 11, 2010 7:27 pm
I.
If x > y and k > 0,
then
k*x > k*y AND x/k > y/k


II.
If x > y and k < 0,
then
k*x < k*y AND x/k < y/k
[-- Inequality reverses when k < 0 --]
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Fri Jun 11, 2010 7:32 pm
(IMPORTANT)

If x and y are both POSITIVE/NEGATIVE
AND x > y

THEN

1/x < 1/y


Examples:
1. x = 3, y = 2, x > y
So, 1/3 < 1/2

2. x = -2, y=-3, x > y
So, -1/2 < -1/3
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sat Jun 12, 2010 8:32 am
If a1 > b1, a2 > b2, ... an > bn,
Then
(a1 + a2 + ... an) > (b1 + b2 + ... bn)


If a1 > b1, a2 > b2, ... an > bn,
Then
(a1 * a2 * ... an) > (b1 * b2 * ... bn) --- [ONLY When all values of a and b are POSITIVE]
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sat Jun 12, 2010 8:35 am
If ax^2+bx+c > 0, where a > 0,
Then
x DO NOT LIE between xL and xU

(xL and xU are lower and upper limits of x respectively)


If ax^2+bx+c < 0, where a > 0,
Then
x LIES between xL and xU

(xL and xU are lower and upper limits of x respectively)
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sat Jun 12, 2010 8:41 am
i. If | X1 | > | X2 |, Then X1 > X2 OR - X1 > X2


ii. If | X1 | < | X2 |, Then X1 < X2 OR - X1 < X2
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
Master | Next Rank: 500 Posts
Posts: 186
Joined: Fri May 28, 2010 1:05 am
Thanked: 11 times

by jube » Sat Jun 12, 2010 1:54 pm
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.
Didn't know this - thanks a ton! I'm really loving your flashcard threads! thanks!
Top
Master | Next Rank: 500 Posts
Posts: 186
Joined: Fri May 28, 2010 1:05 am
Thanked: 11 times

by jube » Sat Jun 12, 2010 2:02 pm
thanks a ton for all the stuff on remainders - it REALLY helps!
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sat Jun 12, 2010 7:20 pm
jube wrote:thanks a ton for all the stuff on remainders - it REALLY helps!
Really glad to hear that my flashcards are helping you. Thank you very much! Stay tuned to this thread for more.
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sat Jun 12, 2010 7:23 pm
|x - a| < r, where a is a positive real number and a is a fixed real number,
then
a-r < x < a+r



|x - a| > r, where a is a positive real number and a is a fixed real number,
then
x < a-r (OR) x > a+r
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sat Jun 12, 2010 7:26 pm
Golden Rule:
When a NEGATIVE value is multiplied both sides in an INEQUALITY, then the INEQUALITY SIGN reverses/flips.


Example:
-1/x > -3/14

When -ve is multipled both sides,

1/x < 3/14 [-- Not only does the number sign changes, but also the inequality sign --]
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
User avatar
Community Manager
Posts: 1537
Joined: Mon Aug 10, 2009 6:10 pm
Thanked: 653 times
Followed by:252 members

by papgust » Sat Jun 12, 2010 7:34 pm
Always Remember to:

Plug in the solutions back to the absolute equations to see whether it satisfies, whenever you get multiple solutions while solving absolute equations (A very useful takeaway especially for solving DS questions)


Example:
Solve, |x| = 3x - 2.

i. x = 3x - 2
2x = 2
x = 1.

ii. -x = 3x - 2
4x = 2
x = 1/2.

You get 2 solutions 1 and 1/2. DO NOT CONCLUDE that there are 2 solutions and move on. Plug in both solutions back to the original equation (|x| = 3x - 2) and see whether the equation holds.

Sub. x = 1 in |x| = 3x - 2,
Equation SATISFIES!

Sub. x = 1/2 in |x| = 3x - 2,
Equation DOES NOT SATISFY!

Hence, x = 1 is the ONLY solution.
Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.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"
Top
Post new topic Post Reply