Some important properties of numbers are given below :
Prime Number Series
Example:
2,3,5,7,11,.................
Exercise
41,43,47,53,61,71,73,81
In the above series all elements except 81 are prime numbers.so 81 is odd one.
Even Number Series
Example:
2,4,6,8,10,12,............
Odd Number Series:
Example:
1,3,5,7,9,11,...................
Exercise
3,5,7,12,17,19
In the above series except 12 all elements are odd
numbers.so 12 is the odd one.
Perfect Squares:
Example:
1,4,9,16,25,..............
Exercise
1,4,9,16,23,25,36
In the above series all elements except 23 are
perfect sqares.so 23 is odd one.
Perfect Cubes:
Example:
1,8,27,64,125,.................
Exercise
8,27,64,100,125,216,343
In the above series all elements except 100 are
perfect cubes.so 100 is odd one.
Multiples of Number Series:
Example:
3,6,9,12,15,..............are multiples of 3
Numbers in Arthimetic Progression(A.P):
Example:
13,11,9,7................
Numbers in G.P:
Example:
48,12,3,.....
SOME MORE PROPERTIES:
• If any series starts with 0,3,.....,generally the relation will be (n2-1).
• If any series starts with 0,2,.....,generally the relation will be (n2-n).
• If any series starts with 0,6,.....,generally the relation will be (n3-n).
• If 36 is found in the series then the series will be in n2 relation.
• If 35 is found in the series then the series will be in n2-1 relation.
• If 37 is found in the series then the series will be in n2+1 relation.
• If 125 is found in the series then the series will be in n3 relation.
• If 124 is found in the series then the series will be in n3-1 relation.
• If 126 is found in the series then the series will be in n3+1 relation.
• If 20,30 found in the series then the series will be in n2-n relation.
• If 60,120,210,........... is found as series then the series will be in n3-n relation.
• If 222,............ is found then relation is n3+n
• If 21,31,.......... is series then the relation is n2-n+1.
• If 19,29,.......... is series then the relation is n2-n-1.
• If series starts with 0,3,............ the series will be on n2-1 relation.
More Examples
(i) Find the odd one out.
835,734,642,751,853,981,532
Solution:
In the above series,the difference between third
and first digit of each element is equal to its middle digit.But 751 is
not in this pattern,so odd one.
(ii) Find the odd one out.
331,482,551,263,383,242,111
Solution:
In the above series,the product of first
and third digit of each element is equal to its middle digit. But 383
is not in this pattern,so odd one.
(iii) Find the odd one out.
2,5,10,50,500,5000
Solution:
In the above series,the pattern as follows:
1st term * 2nd term = 3rd term
2nd term * 3rd term = 4th term
3rd term * 4th term = 5th term
But 50*500=25000 which is not equal to
5000.
so 5000 is odd one.
(iv) Find the odd one out.
582,605,588,611,634,617,600
Solution:
In the above series, alternatively 23 is added
and 17 is subtracted from the terms.
So 634 is odd one
(v) Find the odd one out.
56,72,90,110,132,150
Solution:
The above series as follows:
7*8,8*9,9*10,10*11,11*12,12*13.
So it will be 56,72,90,110,132,156
so 150 is wrong.
(vi) Find the odd one out.
7,8,18,57,228,1165,6996
Solution:
A,A*1+1,B*2+2,C*3+3,............
so 288 is wrong.
(vii) Find the odd one out.
40960,10240,2560,640,200,40,10
Solution:
Go on dividing by 4 ,the series will be
40960,10240,2560,640,160,40,10.
So 200 is wrong.