Collection of number series exercizes
Number series questions are an integral part of almost all numerical reasoning tests. Many companies deal with processing and analysing numerical data in daily work.
Employers and organizations are interested in evaluating candidates' skills in solving because they will need them in a in a realistic workplace context.
111. What number comes next?
3, 10, 24, x, 108, 220
Scroll down to see the answer
Correct answer is 52
3, 10, 24, x, 108, 220
We can solve it in 2 ways.
Α way
Calculate the differences between
those that are next to each other.
10-3=7
24-10=14
108-52=56
220-108=112
The number series of the differences is:
7,14, x, 56, 112
Notice that every term is multiple by 2
7X2=14 56X2=114
The number series is GP with common ratio 2
So the number series of differences is:
7, 14, 28, 56, 112
Therefore the missing number is:
24+28=52
B way
The rule is as follows:
add 2 to the previous number then multiply times 2.
(3+2)x2=10
(10+2)x2=24
(24+2)x2=52
(52+2)x2=108
(108+2)x2=220
Correct answer is:
52
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Example questions
with answers and detailed explanations.
Select the number that can replace the question mark (?)
in the following series.
3, 3, 9, 45, 315, ?
A) 945 B) 1050 C) 2835 D) 2205
Corect answer is C
EXPLANATION
3X1=3
3X3=9
9X5=45
45X7=315
We observe that the numbers by which they are multiplied are
1,3,5,7
It is an arithmetic progression with difference 2
The next term is 7+2=9
So the missing number in the given series is:
315 x 9=2835
Correct answer is C
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Different types of number series Εxamples with detailed explanations methodologies tips and tricks.
Squares: When numbers are a series of perfect squares.
For example: 81, 100, 121, 144, 169...
81=9^2 100=10^2 121=11^2 144=12^2 169=13^2
The numbers of series are perfect squares of 9, 10, 11, 12,....
Cubes: When the numbers are a series of perfect cubes.
For example: 512, 729, 1000...
512=8^3 729=9^3 1000=10^3
The numbers of series are perfect cubes of 8, 9, 10,...
Examples
Example 1
9, 25, 49, 81, ?
9=3² 25=5² 49=7² 81=9²
Theese are the perfect squares of number series
3, 5, 7, 9, 11,...
The next term is 11² = 121
Example 2
In the sequence one of the term is wrong
3600, 8100, 14200, 22500
Select the option that has his number.
A. 22.500 B. 14200 C.8100 D.3600
3600= 60^2
8100=90^2
22500=150^2
14200 it is not a square of any nunber
S0 correct answer is B
*The correct number is 14400
All the terms of series are perfect squares of series
60, 90, 120, 150
Example 3
In the sequence one of the term is wrong
8000, 27000, 54000, 125000
Select the option that has his number.
A. 27.000 B. 54000 C 8000 D 125000.
The first digit in each term is a cube of some number .
27=3³
8=2³
125=5³
54 its't the cube of any number
So correct answer is B.
Number series questions are intimidating for candidates and have varying levels of difficulty
Students find number sequencing questions difficult, but in reality they are not, it is a matter of proper preparation.
Practice with selective questions that cover the full range of number series problems in competitive exams.
Questions number series squares-cubes-two stage type series
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One type of number series that often appears in competitive exams is the alternating series.
What is Alternating number series
This type of series may consists of two series combined into a single series. The alternating terms of this series may form an independent series in itself
The alternating series are quite difficult. You need to make many examples to get acquainted and get into their spirit and be able to deal with them in the exams. Many exercises-practice will give you the confidence to succeed in the competitive exams.
Examples
Question1: Look carefully at the following series.What pair comes next?
46, 43, 40, 38, 35, 32, 30,...?,,,,,?
This is an alternating subtraction series in which 3 is subtracted twice, then 2 is subtracted once, then 3 is subtracted twice, and so on. So the next terms in the following series will be 27, 24
Question2: Look carefully at the following series.What pair comes next?
18, 8, 18, 10, 18, 12, 18, ...
In this alternating repetition series, the random number 18 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 8.
12+2=14
18 is interpolated every other number
Answer is 14, 18
Question3: Look carefully at the following series.What pair comes next?
9,18,10,20,12,24,...
This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.
9X2=18 18-8=10 10X2=20 20-8=12 12X2=24
So 24-8=16 16x2=32
Answer is 16, 32
Practice with selective questions
Alternating number series test
Detailed solutions
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By Panos Kalliantasis
An arithmetic progression or arithmetic sequence
is a sequence in which the difference between
any two consecutive terms is constant.
The difference between the consecutive terms
is known as the common difference
and is denoted by d.
If the first term is a A(rithmetc) P(rogression) is
a, a+d, a+2d, a+3d, a+4d
Examples
3,5,7,9,11 is an AP
3, 3+2, 3+2+2, 3+2+2+2
Common difference is d=2
If the initial term of an arithmetic progression is
and the common difference of successive members is ,
then the -th term of the sequence () is given by:
The best questions "Number Series"
Band-SSC Exams
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By Panos kalliantasis
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Number series questions are central
to all bank exams.
Practice with selective questions
that cover the full range of number series
problems in Bank exams.
1.Notice, if the order of number given is ascending
( smaller to larger number) or
descending ( larger to smaller number).
if the numbers increase or decrease a little
then we have the addition or subtraction
If the numbers increase or decrease a lot
then we have multiplication or division.
2.Calculate the differences between
those that are next to each other.
3. Find the pattern that applies
Find the pattern that applies
to get from one number to
the next number in the sequence.
Questions examples
Example Question#1
Find the missing number in the following set:
3, 10, 24, x, 108, 220
We can solve it in 2 ways.
Α way
Calculate the differences between
those that are next to each other.
10-3=7
24-10=14
108-52=56
220-108=112
The number series of the differences is:
7,14, x, 56, 112
Notice that every term is multiple by 2
7X2=14 56X2=114
The number series is GP with common ratio 2
So the number series of differences is:
7, 14, 28, 56, 112
Therefore the missing number is:
24+28=52
B way
The rule is as follows:
add 2 to the previous number then multiply times 2.
(3+2)x2=10
(10+2)x2=24
(24+2)x2=52
(52+2)x2=108
(108+2)x2=220
Correct answer is:
52
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Example Question#2
Find the missing number in the following set:
5 ,17 ,29, x, 53, 65
Calculate the differences between
those that are next to each other.
17-5=12
29-17=12
65-53=12
To each number we add 12 and find the next number.
Therefore:
29+12=41
Correct answer:
41
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Example Question#3
ee
Find the missing number in the following set:
8, 16, x, 64, 128, 256
Calculate the differences between
those that are next to each other.
16-8=8
128-64=64
256-128=128
We observe that to find the next number
in the series we multiply by 2.
8Χ2=16
64Χ2=128
128Χ2=256
Therefore the missing number is:
16X2=32
Answer is:
32
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Example Question#4
Select the number that can replace the question mark (?)
in the following series.
3, 3, 9, 45, 315, ?
A) 945 B) 1050 C) 2835 D) 2205
3X1=3
3X3=9
9X5=45
45X7=315
We observe that the numbers by which they are multiplied are
1,3,5,7
It is an arithmetic progression with difference 2
The next term is 7+2=9
So the missing number in the given series is:
315 x 9=2835
Correct answer is C
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Example Question#5
Study the given pattern carefully and select the number
that can replace the question mark (?) in it.
(7, 21, 3) (8,72, 9) (12,84, ?)
A)10 B) 9 C) 7 D)6
First 7x3=21
Second 8x9=72
Third 12 x ?=84
Therefore 12x7=84
Correct is C=7
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Example Question#6
8, 4, 4, 8, 32, ?
A) 8 B) 64 C)256 D) 16 E) 128
The pattern is:
8x1/2=4
4x(2x1/2)=4x1=4
4x2=8
8x4=32
The numbers with which we multiply are a Geometric progression
First term is 1/2 and common ratio is 2
1/2, 1, 2, 4, 8
Therefore the next term is 32X8=256
Write answer is C 256
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Example Question#7
What will come in place of question mark (?)
4, 5, 12, 39, 160, ?
(A) 324 (B) 434
(C) 685 (D) 715
(E) 805
4*1+1 = 5
5*2+2 = 12
12*3+3 = 39
39*4+4 = 160
160*5+5 = 805
Answer is option E
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Example Question#8
What will come in place of question mark (?)
8, 7, 12, 44, ?
Solution
The pattern is:
8X1-1=7
7X2-2=12
12X4-4=44
44X8-8=344
Answer is 344
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Example Question#9
What will come in place of question mark (?)
2, 9, 28,? , 126, 217
The pattern is:
1^3 +1=2
2^3+1=9
3^3+1=28
4^3+1=65
5^3+1=126
6^3+1=217
Correct answer is 65
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Example Question#10
What will come in place of question mark (?)
8, 9, 24, 125, ?
The pattern is:
8X1+1=9
9X3-3=24
24X5+5=125
125X7-7=868
The missing number is:
868
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