Number Series Methods shortcut tricks
Number Series shortcut tricks are very important thing to know for your
exams. Time takes a huge part in competitive exams. If you manage your time
then you can do well in those exams. Most of us miss that part. Few examples on
number series shortcuts is given in this page below. These
shortcut tricks cover all sorts of tricks on Number Series. We request all aspirants
to read all examples carefully. These examples will help you to understand
shortcut tricks on Number Series.Now we will discuss some basic ideas of Number Series. On the basis of these ideas we will learn trick and tips of shortcut number series. If you think that how to solve number series questions using number series shortcut tricks, then further studies will help you to do so.
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What is Number Series ?
Number series is a form of numbers in a certain sequence, where some numbers are mistakenly put into the series of numbers and some number is missing in that series, we need to observe first and then find the accurate number to that series of numbers.
Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks are comes into action.
In competitive exams number series are given and where you need to find missing numbers and mistakenly put into the series numbers. The number series are come in different types. At first you have to decided what type of series are given in papers then according with this you have to use shortcut tricks as fast as you can.
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Different types of Number Series
There are some format of series which are given in Exams.
Perfect Square Series
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Perfect square series is a arrangement of numbers in a certain order, where some numbers Series are based on square of a number which is in same order you need to place one square number that is missing in that given series, we need to observe and find the accurate number to the series of numbers.
This type of problem are given in Quantitative Aptitude which is a very essential in banking exam. It is simple to work on perfect square root numbers you can easily obtain the result of perfect square number. How you get easily by Perfect square numbers missing term by memorize square and square root numbers shortcut tricks .
The square of same number and the square result of a number which is equal to the square of another same element. In mathematical world, a square number or perfect square is number of an integer positive integer that is the square of an same integer number always and the numbers are non-negative.
In other words, we say it is the result of product of multiplication of some positive integer numbers with itself always. For example, we consider 4 is a result of square numbers, since it as 2 × 2 in normal way.
The normal representation of square numbers is n2 and that is similar with products of n × n, but it is similar with exponentiation of n2 ,
In Square numbers are positive number. So we can explain it that a positive number is a square number, where its square roots are always integers positive numbers. so For example, √4 = ±2, so 4 is a square number.
Here we see the some examples that how the perfect square are arranged how the missing square series are arranged.
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Example 1: 841, ?, 2401, 3481, 4761
Answer : 292, 392, 492, 592, 692
Example 2: 1, 9, 25, ?, 81, 121
Answer : 12, 32, 52, 72, 92, 112
Example 3: 289, 225, 169, ?, 81
Answer: 172, 152, 132, 112, 92
Example 4: 441, 484, 529, 576, ?,
Answer: 441 = 212, 484 = 222, 529 = 232, 576 = 242 ,625 = 252.
Example 5: 121, 144, 169, ?, 225
Answer: 121 = 112, 144 = 122, 169 = 132, 196 = 142, 225 = 152.
Example 6: ?, 2116, 2209, 2304, 2401, 2500
Answer: 2025 = 452, 2116 = 462, 2304 = 482, 2401 = 492, 2500 = 502
Example 7: 961, 1024, ?, 1156, 1225
Answer: 961 = 312, 1024= 322, 1089 = 332, 1156 = 342, 1225 = 352.
Example 8: 36, ?, 64, 81, 100, 121
Answer: 36 = 62, 49 = 72, 64 = 82, 81 = 92, 100 = 102, 121 = 112.
Example 9: 121 , 169 , ? , 289 , 361
Answer : 112 = 121 , 132 = 169 , 152 = 225 , 172 = 289 , 192 = 361.
Example 10: 121 , 484 , 1089 , 1936 , ? , 4356
Answer : 112 = 121 , 222 = 484 , 332 = 1089 , 442 = 1936 , 552 = 3025 , 662 = 4356.
Example 11: 961 , 1024 , 1089 , ? 1225
Answer : 312 , 322 , 332 , 342 , 352
Example 12: 1849 , ? , 2025 , 2116 , 2209
Answer : 432 , 442 , 452 , 462 , 472
Example 13 : 2500 , 2401 , 2304 , ? , 2116 , 2025
Answer : 502 , 492 , 482 , 472 , 462 , 452
Perfect Cube Series
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Perfect cube series is a arrangement of numbers in a certain order,where some numbers this Types of Series are based on cube of a number which is in same order and one cube number is missing in that given series.
we need to observe and find the accurate number to the series of numbers. This type of problem are given in Quantitative Aptitude which is a very essential paper in banking exam.Under below given some more example for your better practice.
All numbers are arranged in sequence order. we need to observe and find the accurate number to this type series of numbers. Here we learn the perfect cube series of Example.
This type of problem are given in Quantitative Aptitude which is a very essential in banking exam. Under below given some more example for your better practice.
In perfect cube series number is a combination of cube number are arranged. In example 1) 1331, 1728, 2197, ? where you need to count them in a one step or two step calculation for obtain the difference common result according with the series of ratio numbers .
At first you can calculate missing number in ratio series and that you place the actual missing number in the ? or missing place. Be prepared when you calculate differences because it is either one or two step calculation. So when you calculate and get result of two difference numbers you need follow some step wise.
At first calculate the first number cube value and second number cube value if all number are maintain a sequential order cube value then follow same steps which is carry up to last and after that you get actual missing number by finding the common value when you put the missing number you have noticed that all series numbers are common difference in between them.
This kind of missing series calculation you go thorough some common calculation shortcut tricks using cube and cube shortcut tricks, or you memorize the 1 to 30 cube series number value.
In this type series example questions, it is sounds hard, but it really isn’t. Get it? Once you have done this, by practice with more example then you just easily can do in your way as well competitive and as in bank exam also . So, each of our examples are given below.
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Perfect Cube Series:
Example 1: 3375, ?, 24389, 46656, 79507
Answer : 153, 223, 293, 363, 433
(Each cube digit added with seven to become next cube number)
Example 2: 729, 6859, 24389, ?, 117649, 205379
Answer : 93, 193, 293, 393, 493, 593
Example 3: 1000, 8000, 27000, 64000, ?
Answer: 103, 203, 303, 403, 503
Example 4: 1331 , ? , 35937 , 85184 , 166375
Answer : 113 , 223 , 333 , 443 , 553
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Example 5: 125, ?, 343, 512, 729, 1000
Answer : 125 = 53 , 216 = 63, 343 = 73, 512 = 83, 729 = 93, 1000 = 103.
Example 6: 1 , 9 , 125 , 343 , ? , 729
Answer : 13 , 33 , 53 , 73 , 83 , 93
Example 7: 125, ?, 343, 512, 729, 1000
Answer: 125 = 53, 216 = 63, 343 = 73, 512 = 83, 729 = 93, 1000 = 103.
Example 8: 8 , 64 , ? , 512 , 1000 , 1728
Answer : 23 , 43 , 63 , 83 , 103 , 123
Example 9: 4096, 4913, 5832, ?, 8000
Answer: 4096 = 163, 4913 = 173, 5832 = 183, 6859 = 193, 8000 = 203.
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Example 10: 1331 , ? , 29791 , 68921 132651
Answer : 113 , 213 , 313 , 413 , 513
Example 11: 1331, 1728, 2197, ?
Answer: 1331 = 113, 1728 = 123, 2197 = 133, 2744 = 143.
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Example 12: 1728, 1331, ?, 729, 512
Answer: 1728 = 123, 1331 = 113, 1000 = 103, 729 = 93, 512 = 83.
Example 13: 1000 , 8000 , ? ,64000 , 125000
Answer : 103 , 203 , 303 , 403 , 503
Example 14: 125000 , 64000 , ? , 8000 , 1000
Answer : 503 , 403 , 303 , 203 , 103
Mixed Series
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Mixed Number series is a arrangement of numbers in a certain order. How you
know that the given series is mixed series, notice that this type of
series are more then one different order which arranged in alternatively in a
single series or created according to any non conventional rule.Find the accurate number to the blank or ? mark series of numbers using calculation. This type of problem are given in Quantitative Aptitude which is a very essential in banking exam.Under below given some more example for your better practice.
In mixed Series a mixed number is a combination of number in another way it is not a sequential number series number that you have arranged. In example 1, 111, 220, 438, ?, 1746 where you need to count them in a one step or two step calculation for obtain the difference common result according with the series of mixed numbers .
At first you can calculate missing number in mixed series and that you place the actual missing number in the ? or missing place. Be prepared when you calculate differences because it is either one or two step calculation. So when you calculate and get two difference numbers result you need follow some step wise.
At first calculate the first and second number common difference then follow same steps another two number differences calculation which is carry up to last and after that you get actual missing number by finding the common difference when you put the missing number you have noticed that all series number are common difference in between them.
This kind of missing series calculation you go through some common calculation shortcut tricks square or division, cube, addition, multiplication.
In this type series example questions, it is sounds hard, but it really isn’t. Get it? Once you have done this, by practice with more example then you just easily can do in your way as well competitive and as in bank exam also. So, each of our examples are given below.
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Example 1: 180, 179,183, 156, 172, ?Answer : – 13, + 23, -33, +43, -53
Example 2: 6, ?, 33, 69, 141, 285
Answer : x 2 + 3, x 2 + 3, x 2 + 3, x 2 + 3, x 2 + 3, x 2 + 3
Example 3:
4, 16, 64, 256, 1024, ?
Answer: Multiply each number by 4 to get the next number.
4 x 4 = 16
16 x 4 = 64
64 x 4 = 256
256 x 4 = 1024
1024 x 4 = 4096
Example 4:
8, 16, 24, 40, 64, ?
Answer:
8 + 8 = 16
16 + 8( add previous ) = 24
24 + 16( add previous ) = 40
40 + 24( add previous ) = 64
64 + 40( add previous ) = 104
Examples 5:
24, ?, 208, 622, 1864
Answer:
from 24 to ? we get using this 24 x 3 = 72 – 2 = 70, Similarly we follow next steps
from 70 to 208 we get using this 70 x 3 = 210 – 2 = 208,
from 208 to 622 we get using this 208 x 3 = 624 – 2= 622,
from 622 to 1864 we get using this 622 x 3 = 1866 – 2 = 1864.
So the missing number is 70
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Examples 6: 111, 220, 438, ?, 1746
Answer:
from 111 to 220 we get using this 111 x 2 = 222 – 2 = 220,similarly we follow next steps
from 220 to 438 we get using this 220 x 2 = 440 – 2 = 438,
from 438 to ? we get using this 438 x 2 = 876 – 2 = 874,
from 874 to 1746 we get using this 874 x 2 = 1748 – 2 = 1746.
So the missing number is 874
Examples 7:
11, 24, 50, 102, 206, ?
Answer:
11 x 2 = 22 +2 = 24,
24 x 2 = 48 + 2 = 50,
50 x 2 = 100 + 2 = 102,
102 x 2 = 204 + 2 = 206,
206 x 2 = 412 + 2 = 414.
So the missing number is 414.
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Example 8:0, 6, 24, 60, 120, 210, ?
Answer :
The given series is : 13 – 1, 23 – 2, 33 – 3, 43 – 4, 53 – 5, 63 – 6,
So the missing term = 73 – 7 = 343 – 7 = 336 .
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Example 9:11, 14, 19, 22, 27, 30, ?
Answer :
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 30 + 5 = 35 .
Example 10:
6, 12, 21, ? , 48
Answer :
The pattern is + 6, + 9, + 12, +15 ………..
So the missing term is = 21 + 12 = 33 .
Example 11:
18, 22, 30, ? ,78, 142
Answer :
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 .
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Example 12:589245773, 89245773, 8924577, 924577, ?
Answer :
The pattern is The digits are removed one by one from the beginning and the end in order alternately, So to obtain the subsequent terms of the missing series is = 92457 .
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Example 13:8, 35, ? , 143, 224, 323
Answer :
The pattern is (32 – 1), (62 – 1),………., (122 – 1), (152 – 1), (182 – 1)
So the missing term is = (92 – 1 ) = 81 – 1 = 80 .
Example 14:
3, 7, 23, 95, ?
Answer :
The pattern is ( x 2 + 1 ),( x 3 + 2) , ( x 4 + 3 ) , ……….
So the missing term is = 95 x 5 + 4 = 479 .
Geometric Series:
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Geometric Number series is a arrangement of numbers in a certain order,
where some numbers are this type of series are based on ascending or
descending order of numbers and each continues number is obtain by
multiplication or division of the previous number with a static number.we need to observe and find the accurate number to the series of numbers. This type of problem are given in Quantitative Aptitude which is a very essential in banking exam. Under below given some more example for your better practice.
In geometric series number is a combination of number arranged. In example 1) 5, 45, 405, 3645, ? where you need to count them in a one step or two step calculation for obtain the difference common result according with the series of numbers.
At first you can calculate missing number in geometric series and that you place the actual missing number in the ? or missing place. Be prepared when you calculate differences because it is either one or two step calculation. So when you calculate and get result of two difference numbers you need follow some step wise.
At first calculate the first number 5 with 9 and second number value we get that is 45 then again second number calculate multiply with 9 and get the third number and follow same steps which is carry up to last and after that you get actual missing number by finding the common value when you put the missing number you have noticed that all series numbers are common 9 which multiply with number and get next number difference.
This kind of missing series calculation you go thorough some common calculation shortcut tricks using cube multiplication division addition cube square shortcut tricks.
In this type series example questions, it is sounds hard, but it really isn’t. Get it? Once you have done this, by practice with more examples then you just easily can do in your way as well competitive and as in bank exam also. So, each of our examples are given below.
Example 1: 3, ?, 21, 51, 162,
Answer : 3 x 0 +9 = 12, 12 x 1 + 9 = 21, 21 x 2 + 9 = 51, 51 x 3 + 9 = 162
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Examples 2: 5, 45, 405, 3645, ?Answer: 5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.
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Examples 3: 73205, 6655, 605, 55, ?Answer: 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205.
Example 4: 21, 84, 336, ?, 5376
Answer: 21 x 4 = 84, 84 x 4 = 336, 336 x 4 = 1344, 1344 x 4 = 5376
Example 5: 9, 54, ?, 1944, 11664
Answer: 9 x 6 = 54, 54 x 6 = 324, 324 x 6 = 1944, 1944 x 6 = 11664.
Example 6: 5, 35, ?, 1715, 12005,
Answer: 5 x 7 = 35, 35 x 7 = 245, 245 x 7 = 1715, 1715 x 7 = 12005.
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Example 7: 25, 100, ?, 1600, 6400Answer: 25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.
Example 8: 6, 18, 54, ?, 486, 1458
Answer: 6 x 3 = 18, 18 x 3 = 54, 54 x 3 = 162, 162 x 3 = 486, 486 x 3 = 1458.
Example 9: 15, 30, 60, 120, ?
Answer: 15 x 2 = 30, 30 x 2 = 60, 60 x 2 = 120, 120 x 2 = 240
Example 10: 19, ?, 475, 2375, 11875
Answer: 19 x 5 = 95, 475 x 5 = 2375, 2375×5 = 11875,
Example 11: 3, 48, ?, 768, 3072
Answer: 3 x 4 = 12, 12 x 4 = 48, 48 x 4 = 192, 192 x 4 = 768, 768 x 4 = 3072
Two stage Type Series:
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A two stage Arithmetic series is one in which the formation of
arithmetic series are obtain from differences of continuous numbers themselves.Example 1: i. 3, 9, 18, 35, 58,——
ii. 6, 9, 17, 23,———-
Number
Series questions:
1) In each of
the following questions a number series is given with one term missing. Choose
the correct alternative that will continue the same pattern and fill in the
blank spaces.
2, 7, 14, 23, ?,
47
A. 31
B. 28
C. 34
D. 38
Answer : C.
The given
sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7
+ 7 = 14, 14 + 9 = 23
Missing Number =
23 + 11 = 34.
2) 4, 6, 12, 14,
28, 30, ?
A. 32
B. 64
C. 62
D. 60
Answer : D.
The given
sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The
pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60
3) 4, 9, 13, 22,
35, ?
A. 57
B. 70
C. 63
D. 75
Answer : A.
Sum of two
consecutive numbers of the series gives the next number.
4) 11, 13, 17,
19, 23, 29, 31, 37, 41, ?
A. 43
B. 47
C. 51
D. 53
Answer : A.
The series
consists of prime numbers.
5) 15, 31, 63,
127, 255, ?
A.
513
B.
511
C.
523
D.
517
Answer : B.
Each number is
double of the preceding one plus 1.
6) 5, 11, 17,
25, 33, 43, ?
A. 49
B. 51
C. 52
D. 53
Answer : D.
The sequence is
+6, +6, +8, +8, +10, ....
7) 9, 12, 11,
14, 13, ?, 15
A. 12
B. 16
C. 10
D. 17
Answer : B.
Alternatively, 3
is added and one is subtracted.
8) 0.5, 0.55,
0.65, 0.8, ?
A.
0.7
B.
0.9
C.
0.95
D. 1
Answer : D.
The pattern is +
0.05, + 0.10, + 0.15, .....
9) 1, 4, 9, 16,
25, ?
A. 35
B. 36
C. 48
D. 49
Answer : B.
The sequence is
a series of squares, 12, 22, 32, 42, 52....
10) 2, 1, (1/2),
(1/4), ?
A.
(1/3)
B.
(1/8)
C.
(2/8)
D.
(1/16)
Answer : B.
This is a simple
division series; each number is one-half of the previous number.
In each of the
following questions a number series is given with one term missing. Choose the
correct alternative that will continue the same pattern and fill in the blank
spaces.
11) 1, 4, 27,
16, ?, 36, 343
A.
125
B. 50
C. 78
D.
132
Answer : A.
The series
consists of cubes of odd numbers and square of even numbers.
12) 20, 19, 17,
?, 10, 5
A. 15
B. 14
C. 13
D. 12
Answer : B.
The Pattern is -
1, - 2, -3, ...
13) 7, 10, 8,
11, 9, 12, ?
A. 13
B. 12
C. 10
D. 7
Answer : C.
This is a simple
alternating addition and subtraction series. In the first pattern, 3 is added;
in the second, 2 is subtracted.
14) 6, 11, 21,
36, 56, ?
A. 51
B. 71
C. 81
D. 41
Answer : C.
The pattern is +
5, + 10, + 15, + 20,....
15) 2, 3, 5, 7,
11, ?, 17
A. 15
B. 14
C. 13
D. 12
Answer : C.
The series
consists of prime numbers starting from 2.
16) 36, 34, 30,
28, 24, ?
A. 26
B. 23
C. 22
D. 20
Answer : C.
This is an
alternating number subtraction series. The pattern is -2, -4, -2, ....
17) 13, 35, 57,
79, 911, ?
A.
1145
B.
1113
C.
1117
D.
1110
Answer : B.
The terms are
formed by joining together consecutive odd numbers in order. i.e. 1 and 3, 3
and 5, 5 and 7, 7 and 9, 9 and 11,....
18) 6, 11, 21,
36, 56, ?
A. 65
B. 78
C. 81
D. 97
Answer : C.
The pattern is +
5, + 10, + 15, + 20,...
19) 53, 53, 40,
40, 27, 27, ?
A. 14
B. 12
C. 16
D. 18
Answer : A.
First, each
number is repeated, then 13 is subtracted to arrive at the next number.
20) 11, 10, ?,
100, 1001, 1000, 10001
A.
1000
B.
121
C.
111
D.
101
Answer : D.
The pattern is -
1, × 10 + 1, - 1, × 10 + 1, - 1, × 10 + 1, ....
In each of the
following questions a number series is given with one term missing. Choose the
correct alternative that will continue the same pattern and fill in the blank
spaces.
21) 1, 6, 13,
22, 33, ?
A. 35
B. 46
C. 38
D. 49
Answer : B.
The pattern is +
5, + 7, + 9, + 11,....
22) 21, 9, 21,
11, 21, 13, 21, ?
A. 15
B. 17
C. 23
D. 25
Answer : A.
In this
alternating repetition series, the number 21 is interpolated. If you exclude
21, the series increases by 2, beginning with the number 9.
23) 10, 14, 26,
42, 70, ?
A. 86
B. 98
C.
114
D.
126
Answer : C.
Each term of the
series, except the first two terms, is 2 more than the sum of the preceding two
terms.
24) 1, 9, 17,
33, 49, 73, ?
A. 78
B. 85
C. 91
D. 97
Answer : D.
The pattern is +
8, + 8, + 16, + 24,...
25) 31, 29, 24,
22, 17, ?
A. 15
B. 23
C. 13
D. 25
Answer : A.
This is a simple
alternating subtraction series, with a pattern -2, -5, -2, -5 ....
26) 1, 9, 25,
49, 81, ?
A.
100
B.
121
C.
144
D.
169
Answer : B.
The series
consists of squares of consecutive prime numbers.
27) 5, 9, 17,
29, 45, ?
A. 65
B. 56
C. 74
D. 57
Answer : A.
The pattern is +
4, + 8, + 12, + 16, ....
28) 14, 28, 20,
40, 32, 64, ?
A. 56
B. 46
C. 58
D. 48
Answer : A.
This is an
alternating multiplication and subtracting series with a pattern x2, -8, x2,
-8.
29) 2, 6, 12,
20, 30, 42, 56, ?
A. 63
B. 67
C. 69
D. 72
Answer : D.
The pattern is 1
× 2, 2 × 3, 3 × 4, 4 × 5, 6 × 7, 7 × 8,....
30) 3, 7, 15,
31, 63, ?
A. 89
B.
127
C.
142
D.
158
Answer : B.
Each number in
the series is the preceding number multiplied by 2 and then increased by 1.
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