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Thursday, May 6, 2010

Linear algebraic equations with two variables

Linear equations with two variables are as follows:

15x + 7y = 52

To solve such a system of simultaneous equations such as

15x + 7y = 52-----------------------1
5x + 3y = 18------------------------2

We can do as follows:

Method-1:
After Multiplying equation-2 with "3", we will get

15x + 7y = 52-----------------------1
3x(5x + 3y = 18)------------------------3

=>

15x + 7y = 52-----------------------1
15x + 9y = 54------------------------3

By subtracting these two equation, we get
15x + 7y = 52
-15x - 9y = -54
-----------------
0 -2y = -2
=> y = -2/-2
=> y = 1

By putting this value of "y" in equation-1, we get
15x + 7y = 52
=> 15x + 7(1) = 52
=> 15x = 52-7
=> 15x = 45
=> x = 45/15 = 3

So, x = 3

Method-2:

15x + 7y = 52-----------------------1
5x + 3y = 18------------------------2

Take equation-2
5x + 3y = 18
=> x = (18-3y)/5

By putting this value of "x" in equation-1, we will get

15((18-3y)/5) + 7y = 52
=> 54-9y + 7y = 52
=> 54-2y = 52
=> -2y =-2
=> y = 1

By putting this value of "y" in equation-2, we get

x = (18-3)/5 = 15/5 = 3
=> x = 3

Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Barron's GRE

Kaplan GRE Exam 2010-2011 Premier with CD-ROM (Kaplan GRE Premier Program (W/CD))

Kaplan GRE Exam 2010: Strategies, Practice, and Review

Crash Course for the GRE, 3rd Edition (Graduate School Test Preparation)

Linear algebraic equations with one variable

Equations having one variable are easy to solve in finding the value of that variable.

Equivalent equations having the same solution, for example

x + 5 = 15,
3x+15=45
are two equivalent equations.

Both of these equations are true when the value of x is 10 and otherwise these are false equations.

Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Kaplan GRE Exam 2010-2011 Premier with CD-ROM (Kaplan GRE Premier Program (W/CD))

GRE: Practicing to Take the General Test 10th Edition (Practicing to Take the Gre General Test)

Barron's GRE with CD-ROM

Absolute value

The absolute value of any number "x" is denoted by |x| such that

|2| = 2 , |0| = 0

and |-4| =-(-4) = 4

It is to be noted that absolute value of a number cannot be negative.

Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Barron's GRE

Essential Words for the GRE (Barron's Essential Words for the GRE)

Kaplan GRE Exam 2010-2011 Premier with CD-ROM (Kaplan GRE Premier Program (W/CD))

Friday, April 30, 2010

Percent

The term percent represents per hundred or divided by one hundred such as

2% = 2/100 and
35% = 35/100

In order to find x% of y, where x and y are real numbers, we multiply x% with y. For example,

30% of 500 => 30/100 x 500 = 150

On the other hand, in order to find that, x is what %age of y, we divide x and y and multiply it with 100. Here x and y are real numbers. For example,

7 is what percent of 14?
Here 7 is divided by 14 and multiplied by 100
7/14 x 100 = 50 %

If we want to find the %age increase, We can do as follows
Suppose, there is a number 400 which is increased by 50 numbers and becomes 450. We can detect percent increase by this way

50/400 x 100 = 12.5%

In order to detect %age decrease, we can do as follows
Suppose there is a number 200 which is decreased by 20 numbers and becomes 180, we can calculate % decrease by

20/200 x 100 = 10%

To detect %age increase, Suppose x is a number and y is its final increased state (any number) and z = y - x

Here z/x x 100 and to%age decrease , x is a number and y is decreased number and z = x - y, so z/x x 100.

Here x=base.

In the above examples, 400 and 200 are bases.

Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Barron's GRE

Essential Words for the GRE (Barron's Essential Words for the GRE)

Kaplan GRE Exam 2010-2011 Premier with CD-ROM (Kaplan GRE Premier Program (W/CD))

GRE: Practicing to Take the General Test 10th Edition (Practicing to Take the Gre General Test)

Kaplan GRE Exam Math Workbook

Barron's GRE with CD-ROM

Kaplan GRE Exam 2009 Premier Program (w/ CD-ROM) (Kaplan Gre Exam Premier Live)

Thursday, April 29, 2010

Real numbers

These are numbers including integers and all the other numbers with values present between them such as 22/7, 2.5, square root of 5 etc.

Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Barron's GRE

Essential Words for the GRE (Barron's Essential Words for the GRE)

Kaplan GRE Exam 2010-2011 Premier with CD-ROM (Kaplan GRE Premier Program (W/CD))

Fractions

When one integer is divided by another, it is fraction for example

3/5 or 4/10 and many more.

Here in these examples 3 and 4 are numerators and 5 and 10 are denominators.

Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Barron's GRE

Essential Words for the GRE (Barron's Essential Words for the GRE)

Kaplan GRE Exam 2010-2011 Premier with CD-ROM (Kaplan GRE Premier Program (W/CD))

Factors and product

In the multiplication of two integers with each other these two integers are referred to as factors and the result of their multiplication is called as product.

For example in
5 x 2 = 10

5 and 2 are factors and 10 is product.

Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Barron's GRE

Essential Words for the GRE (Barron's Essential Words for the GRE)

Kaplan GRE Exam 2010-2011 Premier with CD-ROM (Kaplan GRE Premier Program (W/CD))

Integers

Integers are all of the counting numbers. They are represented by "I" i.e.
....,-3,-2,-1,0,1,2,3.....

They may be positive or negative. Integers that are multiples of 3 are called as even numbers or integers. Moreover 0 is also called as an even number/integer e.g.....,-6,-4,-2,0,2,4,6,......

The numbers other than these are odd integers.

Remainder is that integer which remains at the end of division of one number by another.

(This article give some study about the numbers in GRE preparation)
Further Reading:
Cracking the GRE, 2010 Edition (Graduate School Test Preparation)

Kaplan GRE Exam Vocabulary in a Box

Barron's GRE

Essential Words for the GRE (Barron's Essential Words for the GRE)