It is currently 23 Jun 2017, 17:17

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# I'm going to make a sticky thread where the very very basic

Author Message
TAGS:

### Hide Tags

SVP
Joined: 03 Jan 2005
Posts: 2233
I'm going to make a sticky thread where the very very basic [#permalink]

### Show Tags

03 Mar 2005, 12:15
26
KUDOS
19
This post was
BOOKMARKED
I'm going to make a sticky thread where the very very basic mathematical principles are collected for everybody's reference. Please feel free to discuss and add to what I have here.
Attachments

MathBasicPrinciples.doc [46.5 KiB]

_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Last edited by HongHu on 17 Aug 2005, 08:57, edited 1 time in total.
SVP
Joined: 03 Jan 2005
Posts: 2233
Cancelling out "common terms" on both sides [#permalink]

### Show Tags

08 Mar 2005, 10:44
7
KUDOS
1
This post was
BOOKMARKED
Cancelling out "common terms" on both sides of an equation

You need to be very careful when you do algebra derivations. One of the common mistake is to divide both side by "a common term". Remember you can only do this safely if the "common term" is a constant. However you CAN't do it if it contains a variable.

Example:

x(x-2)=x
You can't cancel out the x on both side and say x=3 is the solution. You must move the x on the right side to the left side.
x(x-2)-x=0
x(x-2-1)=0
The solutions are: x=0 and x=3
The reason why you can't divided both sides by x is that when x is zero, you can't divide anything by zero.

Equally important if not more, is that you CAN'T multiple or divide a "common term" that includes a variable from both side of an inequality. Not only it could be zero, but it could also be negative in which case you would need to flip the sign.

Example:

x^2>x
You CAN'T divided both sides by x and say x>1. What you have to do is to move the right side to the left:
x^2-x>0
x(x-1)>0
Solution would be either both x and x-1 are greater than zero, or both x and x-1 are smaller than zero. So your solution is: x>1 or x<0

Example:

x>1/x
Again you CAN'T multiply both sides by x because you don't know if x is positive or negative. What you have to do is to move the right side to the left:
x-1/x>0
(x^2-1)/x>0
If x>0 then x^2-1>0 =>x>1
If x<0 then x^2-1<0 =>x>-1
Therefore your solution is x>1 or 0>x>-1.
You could also break the original question to two branches from the beginning:
x>1/x
if x>0 then x^2>1 =>x>1
if x<0 then x^2<1 => x>-1
Therefore your solution is x>1 or 0>x>-1.

Last edited by HongHu on 26 Mar 2005, 22:08, edited 3 times in total.
SVP
Joined: 03 Jan 2005
Posts: 2233

### Show Tags

03 Mar 2005, 12:17
5
KUDOS
4
This post was
BOOKMARKED
Basic rules for inequalities:
(in the example: a>b>0, c>d>0)

You need to flip signs when both side are multiplied by a negative number:
-a<-b, -c<-d

You need to flip signs when 1 is divided by both side:
1/a<1/b, 1/c<1/d

You can only add or multiply them when their signs are in the same direction:
a+c>b+d
ac>bd

You can only apply substractions and divisions when their signs are in the opposite directions:
a>b, d<c
a-d>b-c
a/d>b/c
(You can't say a/c>b/c. It is WRONG)

Deal with negative numbers:
-a<-b<0, -c<-d<0
Then
-a-c<-b-d<0
-a-(-d)<-b-(-c)
However the sign needs to be flipped one more time if you are doing multiplication or division (because you are multiplying/dividing a negative number):
(-a)*(-c)>(-b)*(-d)
(-a)/(-d)>(-b)/(-c)

For example:
If x<-4, y<-2, we know that xy>8, but we don't know how x/y compare to (-4)/(-2)=2 since you can only do division when their signs are in different directions
If x>-4 and y<-2 then x/y<2 but we don't know how xy is compared to 8 since we can only do multiplication when their signs are the same direction.

It is easier to do the derivation, though, if you first change them to postive. For example:
If x<-4, y<-2, then -x>4, -y>2, xy>8
If x<-4, y<2, then -x>4, y<2, -x/y>2, x/y<-2

Last edited by HongHu on 14 Mar 2005, 08:21, edited 3 times in total.
Manager
Joined: 11 Jan 2005
Posts: 57
Location: Mexico City

### Show Tags

11 Mar 2005, 11:59
4
KUDOS
and for 11 which i got on an OG problem recently

Start with the units digit, add every other digit and remember this number. Form a new number by adding the digits that remain. If the difference between these two numbers is divisible by 11, then the original number is divisible by 11.

Examples:
Is the number 824472 divisible by 11? Starting with the units digit, add every other number:2 + 4 + 2 = 8. Then add the remaining numbers: 7 + 4 + 8 = 19. Since the difference between these two sums is 11, which is divisible by 11, 824472 is divisible by 11.

Is the number 49137 divisible by 11? Starting with the units digit, add every other number:7 + 1 + 4 = 12. Then add the remaining numbers: 3 + 9 = 12. Since the difference between these two sums is 0, which is divisible by 11, 49137 is divisible by 11.
Intern
Joined: 02 Aug 2009
Posts: 8

### Show Tags

05 Aug 2009, 11:14
3
KUDOS
Here's one :

Divisibility test for 7

For any number: double the units digit and subtract it from the remaining digits. If the resultant
number is divisible by 7 then the number is divisible by 7.

To illustrate take : 343
Double the units digit 3 ---- > 6
and subtract it from 34 ---- > 34 - 6 = 28, which is divisible by 7
therefore 343 is divisible by 7.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

### Show Tags

13 Mar 2005, 23:53
2
KUDOS
Sometime back, someone asked me how to find the GCF and LCM. Thought it'll be useful to throw it in this thread so members preparing for gmat and need a quick refresh can go through this.

GCF -> Greatest Common Factor
-> Largest possible common factor between numbers

LCM -> Lowest Common Multiple
-> Largest possible common multiple between numbers

To find the GCF/LCM, you will need to do prime-factorization. This means reducing a number to its prime-factor form.

E.g. 1

GCF/LCM of 4,18

4 = 2*2
18= 2*3*3

To find the GCF, take the multiplication of the common factors (pick the lowest power of the common factors) In this case, GCF = 2.

To find the LCM, take the multiplication of all the factors (pick the higest power of the common factors). In this case, LCM=2*2*3*3=36

E.g. 2

GCF/LCM of 4,24

4 = 2*2
24 = 2*2*2*3

GCF = 2*2 = 4
LCM = 2*2*2*3 = 24
SVP
Joined: 03 Jan 2005
Posts: 2233

### Show Tags

03 Mar 2005, 12:16
1
KUDOS
Even and Odd
Definition: Suppose k is an integer. If there exists an integer r such that k=2r+1, then k is an odd number. If there exists an integer r such that k=2r, then k is an even number.
Explanation: as long as an integer can be divided by 2, it is an even number.
Zero is an even number.

Positive and Negative
Definition: A positive number is a real number that is greater than zero. A negative number is a real number that is smaller than zero.
Zero is not positive, nor negative.

Last edited by HongHu on 09 Mar 2005, 15:58, edited 2 times in total.
SVP
Joined: 03 Jan 2005
Posts: 2233

### Show Tags

09 Mar 2005, 09:32
1
KUDOS
You need to first make sure you are clear about the concept before you go happily plugging numbers in. What I'm trying to do in these topped thead is exactly this: to collect some basic concepts at which everybody needs to be crystal clear.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

### Show Tags

10 Mar 2005, 23:58
1
KUDOS
1
This post was
BOOKMARKED
I'll add on some more over a period of time, but here are for starters:

Divisibility rules: - Know them well

Integer is divisible by:
2 - Even integer
3 - Sum of digits are divisible by 3
4 - Integer is divisible by 2 twice or Last 2 digits are divisible by 4
5 - Last digit is 0 or 5
6 - Integer is divisbile by 2 AND 3
8 - Integer is divisible by 2 three times
9 - Sum of digits is divisible by 9
10 - Last digit is 0

Some other things to note:
- If 2 numbers have the same factor, then the sum or difference of the two numbers will have the same facor.

(e.g. 4 is a factor of 20, 4 is also a factor of 80, then 4 will be a factor of 60 (difference) and also 120 (sum))

- Remember to include '1' if you're asked to count the number of factors a number has
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

### Show Tags

13 Mar 2005, 19:39
1
KUDOS

Adding on to the odd/even rule honghu wrote...

Adding/subtracting two odds or two evens --> even
Add/ Subtract an odd and an even --> od

Multiplication with at no even number --> odd
** Even number in a multiplication will always ensure an even product

Interesting properties:
- Adding n consecutive integers will yield a sum that is divisible by n (i.e. n will be a factor of the sum)

E.g. Adding 3,4,5,6 will give a sum with 4 as a factor
Adding 2,3,4 will give a sum with 3 as a factor

Basic principles dervied from adding, n, n+1, n+2 etc..

- Adding a consecutive set of odd integers will result in sum that is a multiple of the number of integers

E.g. Adding 2,4,6,8,10 --> sum will be multiple of 5 (sum=30)
Adding 1,3,5 --> sum will be multiple of 3 (sum=9)

- An even integer in a multiplication --> product divisible by 2
- 2 even integers in a multiplication --> product divisible by 4
etc
Intern
Joined: 20 Dec 2004
Posts: 5
Location: Russia

### Show Tags

04 Mar 2005, 05:32

do you, guys, know what the "line test method" is, which is discussed here

http://www.gmatclub.com/phpbb/viewtopic ... equalities

Did those guys mean just picking numbers or ..?
VP
Joined: 25 Nov 2004
Posts: 1483

### Show Tags

05 Mar 2005, 22:29
Hong, pls do note/correct the typo.

HongHu wrote:
Positive and Negative
Definition: A positive number is a real number that is greater than zero. A positive number is a real number that is smaller than zero. Zero is not positive, nor negative.
Director
Joined: 21 Sep 2004
Posts: 607

### Show Tags

09 Mar 2005, 07:34
Manager
Joined: 11 Jan 2005
Posts: 57
Location: Mexico City

### Show Tags

09 Mar 2005, 09:03
I really struggle with the number property stuff. i guess i didn't pay enough attention back in 9th grade. do you have any broader suggestions if you will. i always try plugging but a lot of times, you lead oyuirself down the wrong path.
Manager
Joined: 15 Feb 2005
Posts: 246
Location: Rockville

### Show Tags

09 Mar 2005, 12:56
Hong thanks for this thread, has been a big help!
Director
Joined: 05 Jan 2005
Posts: 557

### Show Tags

14 Mar 2005, 01:17
HongHu wrote:
Basic rules for inequalities:
(in the example: a>b, c>d)

You can only add or multiply them when their signs are in the same direction:
a+c>b+d
ac>bd

HongHu: If a= -2, b= -3, c= -1, and d= -2 then ac<bd

Quote:
You can only apply substractions and divisions when their signs are in the opposite directions:
a>b, d<c
a-d>b-c
a/d>b/c
(You can't say a/c>b/c. It is WRONG)

Again: If a= -4, b= -5, c= -1, and d= -2, then a/d<b/c (not a/d>b/c like you posted).
SVP
Joined: 03 Jan 2005
Posts: 2233

### Show Tags

14 Mar 2005, 08:05
Good point. Negative numbers need to flip the signs again. I'll edit the post. Thanks!
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

### Show Tags

14 Mar 2005, 17:29

- You can combine exponents of the same base or same exponents only in multiplication and division

Operations involving the same expoennts:
- Keep the exponent, multiply or divide the bases

E.g. Same exponent - multiplication

(2^3)(5^3) = 10^3

E.g. Same exponent - division

(10^2)/(5^2) = 2^2

Operations involving the same bases:
- Keep the base, add or subtract the exponent (add for multiplication, subtract for division)

E.g. Same base - multiplication

(5^3)(5^6) = 5^(3+6) = 5^9

E.g. Same base - division

(6^3)(6^2) = 6^1 = 6
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

### Show Tags

15 Mar 2005, 11:14
alright, some more as I've promised....

Working with absolute numbers:
When solving for absolute equations, be sure to test both positive and negative values since the absolute number only represent the distance from 0 on the number line.

For instance, |x| = 2 could be x=-2 or x=2

Here's one way to solve absolue inequalities:

|x-4| < 9
We need to solve both positive and negative x

Solving for positive: x-4 < 9 --> x <13
Solving for negative:
-x+4 < 9 --> - x < 5 --> x>-5 (dividing by negative number, switch the sign)

So now we have -5<x<13

Last edited by ywilfred on 23 Mar 2005, 20:14, edited 1 time in total.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

### Show Tags

15 Mar 2005, 11:47
Building on a post by Antmavel about sum of a series...

A quick way to find the sum of the a series where each preceding term is incremented by the same number would be to find the middle term and multiply it by the number of terms.

The middle term can be found at taking the average of the first and last term. Or for the case of Antmavel's question where there are ten terms, you just need to work up to the 5th and 6th term then find the middle of the these two numbers.

E.g. Sum of 4,8,12,16,20
Middle term: 12
Number of terms: 5
Sum = 12*5=60
15 Mar 2005, 11:47

Go to page    1   2   3   4   5   6   7    Next  [ 131 posts ]

Similar topics Replies Last post
Similar
Topics:
25 24 Very Imp++....Questions........ 11 29 Aug 2013, 23:18
Very Helpful Review on Permutations and Combinations 0 09 Jun 2011, 10:16
1 Finding Gmatclub Tests very hard 10 18 Jun 2015, 05:06
Very confused PS 6 12 Feb 2010, 19:14
Display posts from previous: Sort by

# I'm going to make a sticky thread where the very very basic

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.