Number Series Completion:
What is Number Series ?
Number series based
questions are arrangement of numbers in
a certain order, where some numbers are wrongly put into the series of numbers
and some number is missing in that series, we need to observe and find the
accurate number to the series of numbers.
Number Series Methods
Number Series shortcut tricks are very important thing to
know for your exams. These shortcut tricks cover all sorts of tricks on Number
Series. These examples will help you to understand shortcut tricks on Number
Series.
Some Famous Variety of Series based pattern:
(Please note, in each of the following n =1,2,3,4….)
Example
|
Remarks
|
1,2,3,4…..
|
Series of
consecutive numbers
|
1, 4,9,16,….
|
Square of
consecutive numbers
|
1,8, 27, 64….
|
Cube of
consecutive Numbers
|
2, 6, 12,20….
|
Square of number
PLUS that number itself
|
2,5,10, 17, ….
|
Square of number
PLUS 1
|
2, 10, 30,68
|
Cube of number
PLUS that number itself
|
2,9, 28,65,126
|
Cube of number
PLUS 1
|
0, 2,6, 12,20
|
Square of number
MINUS that number itself
|
0,6,24,60,120…..
|
Cube of
number MINUS that number itself
|
0,3,8,15, 24,….
|
Square of number
MINUS 1
|
0,7,26,63,….
|
Cube of number
MINU
|
Different types of Number Series:
1. Perfect Square
Series: 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.
Example 1: 441, 484, 529, 576, ?,
Answer: 441 = 212, 484 = 222, 529 = 232, 576 = 242 ,625 =
252.
Example 2: 121, 144, 169, ?, 225
Answer: 121 = 112, 144 = 122, 169 = 132, 196 = 142, 225 =
152.
2. Perfect Cube Series
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.
Example 1 : 125, ?, 343, 512, 729, 1000
Answer : 125 = 53 , 216 = 63, 343 = 73, 512 = 83, 729 = 93,
1000 = 103.
Example 2 : 1 , 9 , 125 , 343 , ? , 729
Answer : 13 , 33 , 53 , 73 , 83 , 93
3. Geometric Series:
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 successive number is obtain
by multiplying or dividing the previous number with a fixed number.
Examples 1: 5, 45, 405, 3645, ?
Answer: 5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 =
32805.
Examples 2: 73205, 6655, 605, 55, ?
Answer: 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x
11 = 73205.
4. Addition or Subtraction:
Number or pattern of number may be added or subtracted in
each term to obtain the next term.
Example1:
3,6,9,12,15,…?
Hint: You can easily identify that 3 is added in each term
to get the next term.
Ans: 18
Example2:
4,6,9,13,18…?
Hint: Difference between successive number as… 2,3,4,5 and
next will be 6
Ans : 18+6 =24
Example3:
13,11,9,7,5…?
Hint: decreasing order pattern where Difference between
successive numbers is 2.
Ans: 3
5. Multiplication or Division:
Example 1:
4,8,24,96,…?
Hint:
4x2=8
8x3=24
24x4=96
96x5= 480
Ans: 480.
Example 2:
480,96,24,8…?
Hint:
From right to left:
8x3=24
24x4=96
96x5=480
Hence , “number” x 2= 8
Number= 4( answer).
6. Mixed Series:
Q. Which number would replace # mark in the series: 7, 12,19, #, 39
Solution: The given series follows a pattern of : +5, +7,
+9, +11 ……
i.e. 7+5 = 12,
12+7=19, 19+9 =28 28+11 =39
answer: 28
Q. Which is the number that comes next in the following
sequence:
4,
6,12,14,28,30, ( )…….
Solution: The given sequence is a combination of two series as:
Series1: 4,12,28,( )……
Series2: 6,14,30
The pattern followed in both the series is: +8 , +16, +32,
+64….
Hence the answer is 28 +( ) = ? 28 +(+32 ) = 60
Answer= 60
Q. Which is the number that comes next in the following
sequence:
1, 3,3,6,7,9 ?
, 12, 21.
Solution: The given sequence is a combination of two series as:
Series1: 1,3,7,(? ), 21 ……
Series2: 3,6,9,12…
The pattern followed in Series1 is +2, +4, +6, +8…
The pattern followed in Series2 is +3, +3, +3, +3…
Hence the answer is : 7+ (? ) = 7+ (6 )
= 13
Answer : 13
Practice Questions:
1.In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
1, 4, 9, 16, 25, x
Options: A. 35
B. 36 C. 48
D. 49
2. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
20, 19, 17, x , 10, 5
Options: A. 12
B. 13 C. 14 D. 15
3. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
2, 3, 5, 7, 11, x, 17
Options: A. 12
B. 13 C. 14 D. 15
Hint : Clearly, the given series consists of prime numbers
starting from 2. The prime number after 11 is 13.
So, 13 is the missing number.
4. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
6, 11, 21, 36, 56,
Options: A. 42
B. 51 C. 81 D. 91
5. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
1, 6, 13, 22, 33,
Options: A. 44
B. 45 C. 46 D. 47
6. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
3, 9, 27, 81,
Options: A. 324
B. 243 C. 210 D. 162
7. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
1, 9, 17, 33, 49, 73,
Options: A. 97
B. 98 C. 99
D. 100
Hint: The pattern is + 8, + 8, + 16, +16, + 24,....
.'. Missing number = 73 + 24 = 97
8. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
2, 5, 9, ? , 20, 27
Options: A. 14
B. 16 C. 18 D. 24
Hint: The pattern is + 3, + 4, +5, +6, +7....
.Missing number = 9 + 5 = 14.
9. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
5, 9, 17, 29, 45,
Options: A. 60
B. 65 C. 68 D. 70
Hint: The pattern is + 4, + 8, + 12, + 16, ...
.'. Missing number = 45 + 20 = 65.
10. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
3, 7, 15, 31, 63,
Options: A. 92
B. 115 C. 127 D. 131
Hint: The difference between Successive numbers are:
+4,+8,+16,+32,+64
63+64 = 127
11. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
1, 6, 15, ? , 45, 66,
91
Options: A. 25
B. 26 C. 27 D. 28
Hint: The pattern is + 5, + 9, +13, +17, + 21, + 25….
.'. Missing number = 15 + 13 = 28.
12. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
1, 2, 3, 5, 8,
Options:
A. 9 B. 11 C. 13 D. 15
Hint: Each term in the series is the sum of the preceding
two terms.
Thus, 1 + 2 = 3,
2 + 3 = 5,
3 + 5 = 8 and so on.
.'. Missing number = 5 + 8 = 13.
13. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
121, 225, 361,…
Options: A. 441
B. 484 C. 529 D. 729
Hint: The numbers are 112, 152, 192,... i.e. 112, (11 + 4 *
1)2, (11 + 4 * 2)2,....
.'. Missing number =(11 + 4 * 3)2 = (23)2 = 529.
14. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
0, 2, 8, 14, ? , 34
Options: A. 24
B. 22 C. 20 D. 18
Hint: The number are 12 - 1,
22 - 2, 32 - 1, 42 - 2,....
.'. Missing number = 52 - 1 = 24.
15. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
19, 2, 38, 3, 114, 4,….
Options: A. 228
B. 256 C. 352 D. 456
Hint The sequence is a combination of two series :
I. 19, 38, 114,
(....) and II.
2, 3, 4
The pattern followed in I is
x2, x3, x4...
.'. Missing number = 114 x 4 = 456.
20. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
1, 2, 3, 6, 9, 18, ?, 54
Options: A. 18
B. 27 C. 36 D. 81
The numbers are alternately multiplied by 2 and 1.5.
Thus, 1 x 2 = 2,
2 x1.5 = 3,
3 x 2 = 6,
6 x1.5 = 9 and 9x2 =18
and so on.
.'. Missing number = 18 x1.5
= 27.
21. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
4, 5, 9, 18, 34, (…..)
Options:
A. 43 B. 49 C. 50 D. 59
Hint: The pattern is + 1, + 4, + 9, + 16,... i.e., + 12, +
22, + 32,+ 42,...
.'. Missing number = 34 + 52 = 34 + 25 = 59.
22. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
3, 6, 18, 72,
Options: A. 144
B. 216 C. 288 D. 360
Hint: The pattern is x
2, x3, x4,...
.'. Missing number = 72 x5 = 360.
23. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
66, 36, 18,
Options: A. 3 B.
6 C. 8 D. 9
Hint: Each number is the series is the product of the digit
of the preceding number.
Thus, 6 x6 = 36,
3 x 6 = 18 and so on.
.'. Missing number = 1 x8 = 8.
24. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
1, 2, 6, 24,
Options:
A. 60 B. 95 C. 120 D. 150
The pattern is x 2,
x3, x4,....
.'. Missing number = 24 * 5 = 120.
25. In following question, a number series is given with one
term missing. Choose the correct alternative that will same pattern and fill in
the blank spaces.
95, 115.5, 138, , 189
Options: A. 154.5
B. 162.5 C. 164.5 D. 166.5
Hint: The pattern is + 20.5, + 22.5,....
.'. Missing term = 138 + 24.5 = 162.5.
