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General Abilities Basic Arithmetic, Algebra and Geometry, Logical Reasoning and Analytical Ability, General Mental Ability

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  #11  
Old Wednesday, June 19, 2013
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Quote:
Originally Posted by VetDoctor View Post
Broadly speaking, there are two types of Integers.
1. Odd Integers
2.Even Integers

1. Odd Integers : Any number that cannot be divided by 2 is called an odd integer. For example : -3, -1, 1, 3, 5, 7, 9,11 and so on.
Properties of odd integers :
i. The difference between two consecutive odd integers is 2.
ii. If a is an odd integer, then the next consecutive odd integer will be a + 2.
iii. The sum of two odd integer is an even number.
iv. Product of two odd integers is an odd integer.
v. Division of an odd integer by another odd integer may not be an integer.

2. Even Integers : Any number that can be divided by 2 OR those integers that are multiple of 2 are even integers. For example. -4,-2, 0, 2, 4, 6 and so on.
Properties :
i. Difference between two even numbers is 2.
ii. If x is an even integer, then the next consecutive even integer will be x + 2.
iii. the sum of two even integers is an even integer.
iv. Product of two even integers is also an even integer.
v. Division of an even integer by another even integer may not be an integer.

Next topic will be Prime Numbers.
Good effort Brother, thank you so very much because I am also among those who do not know pinch of maths.
stay happy
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  #12  
Old Wednesday, June 19, 2013
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Prime Numbers : The numbers that can be divided by itself and by 1 only.
Examples : 2, 3, 7, 11, 13 , 17, 19 and so on.

Some important points for mcqs :
i. The only even Prime number is 2.
ii. 1 is NOT a prime number.
iii. Product of two Prime numbers can NEVER be a Prime number. Example 2 multiply by 3 = 6 which is NOT a Prime number.
iv. Sum of Prime number may OR may not be a prime number.
v. Difference between two Prime numbers may OR may not be a Prime number.

If you have any query then ask me without any hesitation.

Fractions and Decimals :
A number lying between zero and 1 OR between zero and -1 is a fraction .

A fraction is just another way of expressing division. the expression 12/17 is exactly the same thing as 12 divided by 17.
y/z = y divided by z.

In y/z, y is known as " Numerator " and z is known as " denominator"

Positive fraction = A number lying between zero and 1 is a positive fraction.
Negative fraction = A number lying between zero and -1 is a negative fraction.
Proper fraction = If Numerator is less than denominator in a fraction then is called as proper fraction.
Improper fraction = If the Numerator is greater than denominator is a fraction then it is called as improper fraction.
Mixed fraction = Combination of a whole number and a fraction. e.g 2 4/5. 2 is whole number and 4/5 is a fraction.

Common Factor :
Common factor of two or more numbers is a number that divides these number.
For example. Common factor of 6, and 8 is 2. why ?
Because 2 divides both 6 and 8.
# cannot be a common factor of 6 and 8 because 6 can be divided by 3 ( 6/3 =2) but 8 cannot be divided by 3. So 2 is the only common factor of 6 and 8.

Now the question is , how to find the common factor. This procedure is very simple.
Break down both the numbers to their prime factors to see what they have in common. then multiply the shared prime factors to find all the common factors.

Example : what are the common factors of 135 and 225 ?
answer : First of all find the prime factors of 135 and 225.
135 = 3*3*3*5 ( star denotes multiplication sign)
225 = 3*3*5*5
Now the shared numbers are = 3*3*5, ( common factors)
Thus aside from 3 and 5, the remaining common factors can be found by multiplying 3, 3 and 5 in every possible combination. e.g 3*3 =9
3*5= 15, 3*3*5= 45... means 9, 15, 45 and so on are common factors of 135 and 225


Regards

Last edited by Arain007; Thursday, June 20, 2013 at 09:43 PM. Reason: merged
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  #13  
Old Thursday, June 20, 2013
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Quote:
Originally Posted by VetDoctor View Post
Prime Numbers : The numbers that can be divided by itself and by 1 only.
Examples : 2, 3, 7, 11, 13 , 17, 19 and so on.

Some important points for mcqs :
i. The only even Prime number is 2.
ii. 1 is NOT a prime number.
iii. Product of two Prime numbers can NEVER be a Prime number. Example 2 multiply by 3 = 6 which is NOT a Prime number.
iv. Sum of Prime number may OR may not be a prime number.
v. Difference between two Prime numbers may OR may not be a Prime number.

If you have any query then ask me without any hesitation.

Fractions and Decimals :
A number lying between zero and 1 OR between zero and -1 is a fraction .

A fraction is just another way of expressing division. the expression 12/17 is exactly the same thing as 12 divided by 17.
y/z = y divided by z.

In y/z, y is known as " Numerator " and z is known as " denominator"

Positive fraction = A number lying between zero and 1 is a positive fraction.
Negative fraction = A number lying between zero and -1 is a negative fraction.
Proper fraction = If Numerator is less than denominator in a fraction then is called as proper fraction.
Improper fraction = If the Numerator is greater than denominator is a fraction then it is called as improper fraction.
Mixed fraction = Combination of a whole number and a fraction. e.g 2 4/5. 2 is whole number and 4/5 is a fraction.

Common Factor :
Common factor of two or more numbers is a number that divides these number.
For example. Common factor of 6, and 8 is 2. why ?
Because 2 divides both 6 and 8.
# cannot be a common factor of 6 and 8 because 6 can be divided by 3 ( 6/3 =2) but 8 cannot be divided by 3. So 2 is the only common factor of 6 and 8.

Now the question is , how to find the common factor. This procedure is very simple.
Break down both the numbers to their prime factors to see what they have in common. then multiply the shared prime factors to find all the common factors.

Example : what are the common factors of 135 and 225 ?
answer : First of all find the prime factors of 135 and 225.
135 = 3*3*3*5 ( star denotes multiplication sign)
225 = 3*3*5*5
Now the shared numbers are = 3*3*5, ( common factors)
Thus aside from 3 and 5, the remaining common factors can be found by multiplying 3, 3 and 5 in every possible combination. e.g 3*3 =9
3*5= 15, 3*3*5= 45... means 9, 15, 45 and so on are common factors of 135 and 225


Regards
Sir 5 is also a prime number.
Sir your work will only be helpful if you please continue this effort on.
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  #14  
Old Friday, June 21, 2013
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Quote:
Originally Posted by Tehman Khan View Post
Sir 5 is also a prime number.
Sir your work will only be helpful if you please continue this effort on.
You are right, 5 is also a Prime number.
INSHALLAH i shall continue this but the pace may be a bit slow because i have a full time job but i promise to deliver as much as i can. Secondly there may be some mistakes in my posts, so if anybody find any, he/she can highlight those mistakes.

The basics of math has been explained briefly in a book available in PDF format on this link.
http://www.cssforum.com.pk/css-dates...ning-test.html

If anyone has query regarding math or other subjects, he/she can post here.
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Old Friday, June 21, 2013
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any good book to tackle math ?
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  #16  
Old Friday, June 21, 2013
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Quote:
Originally Posted by maryam masood View Post
any good book to tackle math ?
Barron's GRE book OR Dogar's GAT GENERAL book.

Addition and subtraction of fractions :

Fractions having same denominator :
To add two or more fractions having the same denominator, simply add up the numerators and put the sum over the common denominator.
Example : 3/5 + 4/5 = 3+4 / 5 = 7/5

similarly subtraction
7/8 - 3/8 = 7-3/8 = 5/8

Fractions having different denominators :
All of the fractions should be given same denominator before addition OR subtraction. For getting common denominator multiply each fraction by a number that will give it a denominator in common with the other. an example will explain it better.
Example : 1/2 + 2/3 = ?

1/2 * 3/3 + 2/3 * 2/2 = 3/6 + 4/6 = 3+4/6 = 7/6

Multiplication of fractions :
To multiply fractions, just multiply the numerators and put the product over the product of denominators.
Example : 3/4 * 4/5 = 3*4/4*5 = 12/20 OR 3/5

Last edited by Arain007; Sunday, June 23, 2013 at 09:27 AM. Reason: merged
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  #17  
Old Saturday, June 22, 2013
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Quote:
Originally Posted by VetDoctor View Post
Addition and subtraction of fractions :

Fractions having same denominator :
To add two or more fractions having the same denominator, simply add up the numerators and put the sum over the common denominator.
Example : 3/5 + 4/5 = 3+4 / 5 = 7/5

similarly subtraction
7/8 - 3/8 = 7-3/8 = 5/8

Fractions having different denominators :
All of the fractions should be given same denominator before addition OR subtraction. For getting common denominator multiply each fraction by a number that will give it a denominator in common with the other. an example will explain it better.
Example : 1/2 + 2/3 = ?

1/2 * 3/3 + 2/3 * 2/2 = 3/6 + 4/6 = 3+4/6 = 7/6

Multiplication of fractions :
To multiply fractions, just multiply the numerators and put the product over the product of denominators.
Example : 3/4 * 4/5 = 3*4/4*5 = 12/20 OR 3/5
4/8 is the answer for subtraction sir ,, sir good job done highly appreciable,please.
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Old Saturday, June 22, 2013
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4/6 is the answer for subtraction sir ,, sir good job done highly appreciable,please.
Its 4/8, i think.
Thanx for correction brother.
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Old Monday, June 24, 2013
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Dividing fractions :
To divide one fraction by another, invert the second fraction and then multiply.
Example : 3/4 divide by 4/5
Solution : Invert the second fraction, i-e 5/4 and now multiply with 3/4.
3/4 * 5/4 = 15/16

Comparing fraction : Screening test may have some questions of comparing fractions like , compare 3/4, 7/8, 9/11, which one is the greatest fraction ?

solution : first take two fractions among the three given in the question.
3/4 and 7/8.
Multiply numerator of the first(3/4) with denominator of the second(7/8).
i-e 3 * 8 = 24,
similarly multiply numerator of the second(7/8) with the denominator of the first(3/4).
i-e 7 * 4 = 28.
since 28 is greater than 24 so 7/8 is greater than 3/4.

Similarly we can repeat the same procedure for the 7/8 and 9/11.
Numerator of 7/8 is multiplied with denominator of 9/11.
7 * 11 = 77
Numerator of 9/11 is multiplied with denominator of 7/8.
9 * 8 = 72
since 77 is greater than 72 so 7/8 is greater than 9/11.
so 7/8 is greatest of the three given fractions.

I am giving you a practice question.
which one is greatest fractions among 5/6, 8/9, 9/12 ?
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Old Monday, June 24, 2013
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Quote:
Originally Posted by VetDoctor View Post
Broadly speaking, there are two types of Integers.
1. Odd Integers
2.Even Integers

1. Odd Integers : Any number that cannot be divided by 2 is called an odd integer. For example : -3, -1, 1, 3, 5, 7, 9,11 and so on.
Properties of odd integers :
i. The difference between two consecutive odd integers is 2.
ii. If a is an odd integer, then the next consecutive odd integer will be a + 2.
iii. The sum of two odd integer is an even number.
iv. Product of two odd integers is an odd integer.
v. Division of an odd integer by another odd integer may not be an integer.

2. Even Integers : Any number that can be divided by 2 OR those integers that are multiple of 2 are even integers. For example. -4,-2, 0, 2, 4, 6 and so on.
Properties :
i. Difference between two even numbers is 2.
ii. If x is an even integer, then the next consecutive even integer will be x + 2.
iii. the sum of two even integers is an even integer.
iv. Product of two even integers is also an even integer.
v. Division of an even integer by another even integer may not be an integer.

Next topic will be Prime Numbers.
Sir i am not getting 5th point in which it has been said that division of an odd or even integer with respective integers results no integer how's that possible e.g,if 21 is divided by 7 both are odd integers result is 3 which is integer sir please clear this point
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