Oddman Out and Series
Introduction:
In any type of problems,a set of numbers is given in such a way
that each one except one satiesfies a particular definite
property.The one which does not satisfy that characteristic is
to be taken out. Some important properties of numbers are
given below :
1.Prime Number Series
Example:
2,3,5,7,11,..............
2.Even Number Series
Example:
2,4,6,8,10,12,...........
3.Odd Number Series:
Example:
1,3,5,7,9,11,...........
4.Perfect Squares:
Example:
1,4,9,16,25,............
5.Perfect Cubes:
Example:
1,8,27,64,125,.................
6.Multiples of Number Series:
Example:
3,6,9,12,15,..............are multiples of 3
7.Numbers in Arthimetic Progression(A.P):
Example:
13,11,9,7................
8.Numbers in G.P:
Example:
48,12,3,.....
Some More Properties:
1. If any series starts with 0,3,.....,generally the relation
will be (n2-1).
2. If any series starts with 0,2,.....,generally the relation
will be (n2-n).
3. If any series starts with 0,6,.....,generally the relation
will be (n3-n).
4. If 36 is found in the series then the series will be in n2
relation.
5. If 35 is found in the series then the series will be in
n2-1 relation.
6. If 37 is found in the series then the series will be in n2+1
relation.
7. If 125 is found in the series then the series will be in n3
relation.
8. If 124 is found in the series then the series will be in n3-1
relation.
9. If 126 is found in the series then the series will be in n3+1
relation.
10. If 20,30 found in the series then the series will be in n2-n
relation.
11. If 60,120,210,........... is found as series then the series
will be in n3-n relation.
12. If 222,............ is found then relation is n3+n
13. If 21,31,.......... is series then the relation is n2-n+1.
14. If 19,29,.......... is series then the relation is n2-n-1.
15. If series starts with 0,3,............ the series will be on
n2-1 relation.
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Problems
1.Find the odd one out.3,5,7,12,17,19
SOLUTION:
The above series except 12 all elements are odd
numbers.so 12 is the odd one.
2.Find the odd one out.1,4,9,16,23,25,36
SOLUTION:
In the above series all elements except 23 are perfect sqares.
so 23 is odd one.
3.Find the odd one out.41,43,47,53,61,71,73,81
SOLUTION:
In the above series all elements except 81 are prime numbers.
so 81 is odd one.
4.Find the odd one out.1,4,9,16,20,36,49
SOLUTION:
In the above series all elements except 20 are perfect squares.
So 20 is odd one.
5.Find the odd one out.8,27,64,100,125,216,343
SOLUTION:
In the above series all elements except 100 are perfect cubes.
so 100 is odd one.
6. Find the odd one out.1,5,14,30,50,55,99
SOLUTION:
In the above series all elements in the pattern like 12,
12+22,12+22+32,................. But 50 is not in this
pattern,so odd one.
7.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.
8.Find the odd one out.385,4462,572,396,427,672,264
SOLUTION:
In the above series,the sum of first and third digit of each
element is equal to its middle digit.But 427is not in this
pattern,so odd one.
9.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.
10. Find the odd one out.2,5,10,17,26,37,50,64
SOLUTION:
In the above series,the elements are in the pattern of x2+1,
Where x is 1,2,3,4,5,6,7.but 82+1 is not equal to 64.It is
65.64 is odd one.
11.Find the odd one out. 19,28,39,52,67,84,102
SOLUTION:
In the above series,the elements are in the pattern of x2+3,
Where x is 4,5,6,7,8,9,10.but 102+3 is not equal to 102.
It is 103.so 102 is odd one.
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12.Find the odd one out.253,136,352,460,324,613,244
SOLUTION:
In the above series,the elements are in the pattern of x2+3,
Where x is 4,5,6,7,8,9,10.but 102+3 is not equal to 102.It is
103.so 102 is odd one.
13.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.
14.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.
15.Find the odd one out.46080,3840,384,48,24,2,1
SOLUTION:
In the above series,the terms are successively divided by
12,10,8,6,..... so 24 is not in this pattern.
so 24 is odd one.
16.Find the odd one out.5,16,6,16,7,16,9
SOLUTION:
In the above series,the terms at odd places are 5,6,7,8.......
and at even places is 16. So 9 is odd one.
17.Find the odd one out.6,13,18,25,30,37,40
SOLUTION:
In the above series,the difference between two successive terms
from the beginning are 7,5,7,5......... so 40 is odd one.
18.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.
19.Find the odd one out. 1,2,6,15,31,56,91
SOLUTION:
Add 1square ,2square ,....,6square to the terms.
so 91 is wrong.
20.Find the odd one out.105,85,60,30,0,-45,-90
SOLUTION:
Subtract 20,25,30,35,40,45 from the terms.
So 0 is odd one.
21.Find out the odd one out.3,10,21,36,55,70,105
SOLUTION:
The pattern in the series is
1*3, 2*5, 3*7, 4*9, 5*11, 6*13, 7*15.
So the series will be 3,10,21,36,55,78,105.
So 70 is wrong term in the series.
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22.Find out the odd one out. 4,9,19,39,79,160,319
SOLUTION:
Double the number and add 1 to it.
So the series will be 4,9,39,79,159,319. So 160 is wrong.
23.Find out the odd one out.10,14,28,32,64,68,132.
SOLUTION:
Alternatively add 4 and double the next term.
So 132 is wrong.
COmplex Problems
1.Find the missing term in the series:
4,-8,16,-32,64,( )
SOLUTION:
The terms are doubled and change the sign.
So the next term is -128
2.16,33,65,131,261,( )
SOUTION:
The terms are doubled and 1 is added.
So 261*1+1=522+1=523
So the missing term is 523.
3.2,6,12,20,30,42,56,( )
SOLUTION:
The pattern is
1 * 2 , 2 * 3 , 3 * 4 , 4 * 5 , 5 * 6 , 6 * 7 ,
7 * 8 , 8 * 9 .
So the series is 2,6,12,20,30,42,56,72.
So 72 is the missing term.
4. 8,24,12,36,18,54,( )
SOLUTION:
Numbers are alternatively multiplied by 3 and
divided by 2. So the next term is 54 / 2 = 27.
5. 165,195,255,285,345,( )
SOLUTION:
Each number is 15 multiplied by a prime number.
i.e the series is 15*11,15*13,15*17,15*19,15*23,15*29.
So series is 165,195,255,285,345,435.
So 435 is the missing term.
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6. 7,16,63,124,215,342,( ).
SOLUTION:
Numbers are 23 -1,33-1,43-1,....................so 83-1=511.
So 511 is the missing term.
7.2,4,12,48,240,( )
SOLUTION:
Go on multiplying by 2,3,4,5,6.
So the last term in the series is 240*6=1440.
8.8,7,11,12,14,17,17,22,( )
SOLUTION:
There are two series 8,11,14,17,20 and 7,12,17,22
So increasing by 3 and 5.So 20 the missing term.
9.71,76,69,74,67,72,( )
SOLUTION:
Alternately add 5 and subtract 7.
so the series is 71+5=76
10.10.2,5,9,19,37
SOLUTION:
Second number is one more than twice the first,Third
number is one less than twice the second,Forth is one
more than twice the third and so on.
So the next number is 2 * 37 + 1 = 74+1 = 75.
11. Find the wrong number in the given series.
3,8,15,24,34,48,63
SOLUTION:
The difference between consecutive terms are
respectively 5,7,9,11,13.
So 34 is the wrong number in the series.
12. 125,106,88,76,65,58,53
SOLUTION:
Subtract 24,21,18,15,12,9 from the numbers to get the
next number.
So 128 is wrong.
13. 1,1,2,6,24,96,720
SOLUTION:
Multiply with 1,2,3,4,5,6 to get the next number.
So 96 is wrong.
14 . 32,36,41,61,86,122,171,235
SOLUTION:
Second term = First term + 22
Third term = Second term + 32
Fourth term = Third term + 42
Fifth term = Forth term + 52
Sixth term = Fifth term + 62
Seventh term = Sixth term + 72
So the third term should be 45 instead of 41.
15 . 15,16,34,105,424,2124,12576
SOLUTION:
Second term = First term * 1 + 1 = 16
Third term = Second term * 2 + 2 = 34
Forth term = Third Term * 3 + 3 = 105
Fifth term = Forth term * 4 + 4 = 424
Sixth term = Fifth term * 5 + 5 =2125
Seventh term = Sixth term * 6 + 6 = 12576.
So 2124 is wrong.
16 . 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.
17.7,8,18,57,228,1165,6996
SOLUTION:
Let the numbers be A,B,C,D,E,F,G then
A,A*1+1,B*2+2,C*3+3,............
so 288 is wrong.
18. 19,26,33,46,59,74,91
SOLUTION:
Go on adding 7,9,11,13,15,17.
So 33 is wrong.
19 . 10,26,74,218,654,1946,5834.
SOLUTION:
Second term = first term * 3 – 4 = 26.
Third term = Second term * 3 – 4 =74
Forth term = Third term * 3 – 4 =218
Fifth term = Forth term * 3 – 4 =650
So 654 is wrong .
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