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What is shortcut in Number System for quantitative aptitude

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I want to Number System shortcut  for quantitative aptitude. Please give me answers.

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NUMBER SYSTEM SHORTCUTS FOR QUANTITATIVE APTITUDE
 
Natural Numbers - N (1,2,3,4,.........)
 
Whole Numbers - W(0,1,2,3,.....)
 
Prime Numbers - a number other than 1 , if it is divisible only by 1 and itself

 

prime numbers
 
=> the lowest prime no. is 2
 
=>2 is the only even prime no.
 
=> the lowest odd prime no. is 3.

=> the remainder when a prime no. p>=5 is divided by 6 is 1 or 5. however, if a no. on being divided by 6 gives remainder of 1 or 5 the no. need not be prime.

 
=> the remainder of the division of the square of a prime number p>= divided by 24 is 1.
 
=> for prime no. p>3, p2-1 is divisible by 24.
 
Divisibility rules
 
 
=> divisibility by 2: a no. is divisible by 2 if its last digit is 0 or divisible by 2.
 
=> divisibility by 3: a no. is divisible by 3 if the sum of its digits is divisible by three.
 
=> divisibility by 4: a no. is divisible by 4 if its last two digits are '00 or divisible by 4.
 
=> divisibility by 5: a no. is divisible by 5 if its last digit is 0 or 5.
 
=> divisibility by 6: a no. is divisible by 6 if it is divisible by 2 and 3 both.
 
=> divisibility by 7: a no. is divisible by 7 if the difference of the number of its thousands and the remainder of its division by 1000 is divisible by 7.
 
=> divisibility by 8: a no. is divisible by 8 if its last three digits are '000 or divisible by 8.
 
=> divisibility by 9: a no. is divisible by 9 if the sum of its digits is divisible by 9
 
=> divisibility by 11: a no. is divisible by 11 if the difference of the sum of the digits at even places and sum of the digits at odd places is zero or divisible by 11.
 
=> divisibility by 13: a no. is divisible by 13 if the difference of the number of its thousands and the remainder of its division by 1000 is divisible by 13.

 

Certain rules pertaining to number system

=> of n consecutive whole nos. a, a+1,.......a+n-1, one and only one is divisible by n.
 
=> 3n will always have an even no. of tens.e.g. 27,81, 243,729 etc.
 
=> a sum of five consecutive whole numbers will always be divisible by 5. e.g. 1+2+3+4+5=15/5=3
 
=> xy-yx is divisible by 9.
 
=> the product of three consecutive natural nos.is divisible by 6.
 
=> odd no.x odd no.=odd no.
 
=> odd no.x even no.=even no.
 
=> even no.x even no.=even no.
 
=> odd no.+ odd no.=even no.
 
=> odd no.- odd no.=even no.
 
=> odd no.+ even no.=odd no.
 
=> even no.+ even no.=even no.
 
=> even no.- even no.=even no.
 
=> the product of 'r' consecutive numbers is divisible by r!
 
if m and n are two numbers then (m+n)! is divisible by m!n!
 
if a and b are any two odd prime then a2-b2 is composite. also, a2+b2 is composite
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