Wednesday, 13 January 2016

Speed up your calculation in bank exam : Number System

Speed up your calculation in bank exam : Number System

Number System

Divisibility Rule:

“Divisible By” means “when you divide one number by another the result is a whole number
Examples:14 is divisible by 7, because 14÷7 = 2 exactly
But 15 is not divisible by 7, because 15÷7 = 2 1/7 (i.e., the result is not a whole number)
“Divisible by” and “can be evenly divided by” mean the same thing
These rules let you test if one number is divisible by another, without having to do too much calculation!
Divisible by If Examples
2 The last digit is even (0,2,4,6,8) 128 is
129 is not
3 The sum of the digits is divisible by 3 Shortcut :- cancel all the 9 and numbers which adding to 9.
381 (3+8+1=12, and 12÷3 = 4) Yes
217 (2+1+7=10, and 10÷3 = 3 1/3)No
4 The last 2 digits are divisible by 4 1312 is (12÷4=3)
7019 is not
5 The last digit is 0 or 5 175 is
809 is not
6 The number is divisible by both 2 and 3 114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No
7 If you double the last digit and subtract it from the rest of the number and the answer is: 0, ordivisible by 7
672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No
8 The last three digits are divisible by 8
109816 (816÷8=102) Yes
216302 (302÷8=37 3/4) No
9 The sum of the digits is divisible by 9
Shortcut :- cancel all the 9 and numbers which adding to 9.
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No
10 The number ends in 0 220 is
221 is not
11 Add and subtract digits in an alternating pattern (add first, subtract second, add third, etc). Then the answer must be: 0, or
divisible by 11
1364 (1−3+6−4 = 0) Yes
913 (9−1+3 = 11) Yes
3729 (3−7+2−9 = −11) Yes
987 (9−8+7 = 8) No
12 The number is divisible by both 3 and 4 648
(By 3? 6+4+8=18 and 18÷3=6 Yes.
By 4? 48÷4=12 Yes) Yes
Few extra Shortcuts for some divisibility rules by :-
1)6 —   2 *3 => number should be divisible by 2 and 3 both
2)12—3*4 => number should be divisible by 3 and 4both
3)20—4*5=> number should be divisible by 4 and 5 both
4)30—5*6=> number should be divisible by 5 and 6 both
5)42—6*7=> number should be divisible by 6 and 7 both
6)56—7*8=> number should be divisible by 7 and 8 both
7)72—8*9=> number should be divisible by 8 and 9 both
8)90—9*10=> number should be divisible by 9 and 10 both
Number of prime factor and Total factor
Suppose
T =pax qbx rc  where p ,q ,and r must be prime numbers and a,b,c are the powers of p ,q,and r.
Then  ,Total factors  = (a+1)(b+1)(c+1).
Total prime factors  = (a+b+c).
Remainder concept of few frequently asked model
even = what is remainder ?              x odd= what  is remainder ?
X+1                                                        x+1
even = 1 (when power is even )      x odd=  x  (when power is odd)
X+1                                                        x+1
Example :-
17200 = 1                                                 17257 = 17
17+1                                                       17+1
Cyclicity 

21=2 31=3 41=4 51=5 61=6 71=7 81=8 91=9

22=4 32=9 42=16 52=25 62=36 72=49 82=64 92=81

23=8 33=27 43=64 53=125 63=216 73=343 83=512 93=729

24=16 34=81 44=256 54=…….5 64=1296 74=2401 84=4096 94=….1

25=32 35=243 45=1024 55=…….5 65=7776 75=…..7 85=….8 95=….9

26=64 36=729 46=4096 56=……..5 66=46656 76=…….9 86=……4 96=….1

27=128 37=2187 47=16384 57=…….5 67=2..936 77=…….3 87=…….2 97=….9

28=256 38=6561 48=65536 58=……..5 68=  …..6 78=…….1 88=……6 98=….1









=>4           =>4            =>2           =>1           =>1            =>4            =>4          =>2
Example :-  what is unit digit of  423 = ?
Solution :-   4 cyclicity is 2 ,so  when we divide 23 by 2 ,we get remainder =1,
Which indicates means  41=4 , so unit digit of 423 is also will be 4.
So ,friends and students ,today through this article we have seen and learnt some important concept and useful shortcuts tricks which can really speed up your calculation in bank exam.

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