NOTE: – MEANS MINUS
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.
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.
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
10.2,5,9,19,37
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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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.
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.
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
10.2,5,9,19,37
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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