TRIVENI NTSE PROGRAM Number Series 1
1 1
Mental ability is the ability to distinguish
between right and wrong, to judge the minutest
difference and to adapt to the ever changing
environment, the wit to master the situation, the
capacity to learn and to put past experience to the
most advantageous use in future and the ability to
distinguish between important, less important and
more important.
v EXAMPLES v
Completing the Given Series
Ex.1 Which number would replace question mark
in the series 7, 12, 19, ?, 39.
(A) 29 (B) 28
(C) 26 (D) 24
Sol. Clearly, the given sequence follows the
pattern:
+5, +7, +9 ... i.e., 7 + 5 = 12, 12 + 7 = 19, ...
Missing number = 19 + 9 = 28
Hence, the answer is (B).
Ex.2 Which is the number that comes next in the
sequence : 0, 6, 24, 60, 120, 210 ?
(A) 240 (B) 290 (C) 336 (D) 504
Sol. Clearly, the given series is
13 – 1, 23 – 2, 33 – 3, 43 – 4, 53 – 5, 63 – 6.
Next number = 73 – 7 = 343 – 7 = 336
Hence, the answer is (C).
Ex.3 Which is the number that comes next in the
following sequence ?
4, 6, 12, 14, 28, 30,(...)
(A) 32 (B) 60 (C) 62 (D) 64
Sol. The given sequence is a combination of two
series :
I. 4, 12, 28 (...) and II. 6, 14, 30.
Now, the pattern followed in each of the
above two series is : +8, +16, +32 ....
So, missing number = (28 + 32) = 60
Hence, the answer is (B).
Ex.4 Find out the missing number in the following
sequence : 1, 3, 3, 6, 7, 9, ?, 12, 21.
(A) 10 (B) 11 (C) 12 (D) 13
Sol. Clearly, the given sequence is a combination
of two series :
I. 1, 3, 7, ?, 21 and II. 3, 6, 9, 12
The pattern followed in I is + 2, + 4, ...; and
the pattern followed in II is +3. Thus, missing
number = 7 + 6 = 13.
Hence, the answer is (D).
Ex.5 Which fraction comes next in the sequence
, , , , ?
(A) (B) (C) (D)
1
CHAPTER
CONTENTS
Definition
Completing the series
Arithmetic Series
Series of Cubes, Squares
Mixed Series
Two-Tier Arithemetic series
Three-Tier Arithemetic series
Twin-Series
Two line number series
Wrong Number series
2
1
4
3
8
5
16
7
32
9
17
10
34
11
35
12
TRIVENI IIT IMPACT
NTSE - MAT MATERIAL
CHAPTER : NUMBER SERIES
TRIVENI NTSE PROGRAM Number Series 2
2 2
Sol. Clearly, the numerators of the fractions in the
given sequence form the series 1, 3, 5, 7, in
which each term is obtained by adding 2 to
the previous term. The denominators of the
fractions form the series 2, 4, 8, 16,
i.e. 21, 22, 23, 24.
So, the numerator of the next fraction will be
(7 + 12) i.e., 9 and the denominator will be 25
i.e. 32.
The next term is
Hence, the answer is (A).
Elementary Idea of Progressions
(I) Arithmetic Progression (A.P.)
The progression of the form a, a + d, a + 2d,
a + 3d, ... is known as an A.P. with first term
= a and common difference = d.
Ex. 3, 6, 9, 12, .... is an A.P. with a = 3 and
d = 6 – 3 = 3.
In an A.P., we have nth term = a + (n – 1)d.
(II) Geometric Progression (G.P.)
The progression of the form a, ar, ar2, ar3, ...
is known as a G.P. with first term = a and
common ratio = r.
Ex. 1, 5, 25, 125, ... is a G.P. with a = 1 and
r = = = ... = 5.
In a G.P. we have nth term = arn–1.
v EXAMPLES v
Ex.6 In the series 357, 363, 369, ..., what will be
the 10th term ?
(A) 405 (B) 411 (C) 413 (D) 417
Sol. The given series is an A.P. in which a = 357
and d = 6.
10th term = a + (10 – 1) d = a + 9d.
= (357 + 9 × 6) = (357 + 54)
= 411
Hence, the answer is (B).
Ex.7 How many terms are there in the series 201,
208, 215, .... 369 ?
(A) 23 (B) 24 (C) 25 (D) 26
Sol. The given series in an A.P. in which a = 201
and d = 7.
Let the number of terms be n.
Then, 369 = 201 + (n – 1) × 7 or n = 25.
Hence, the answer is (C).
Ex.8 In the series 7, 14, 28, ..., what will be the
10th term ?
(A) 1792 (B) 2456 (C) 3584 (D) 4096
Sol. Clearly, 7 × 2 = 14, 14 × 2 = 28, ... and so on.
So, the given series is a G.P. in which
a = 7 and r = 2.
10th term = ar(10–1) = ar9 = 7 × 29
= 7 × 512 = 3584
Hence, the answer is (C).
Ex.9 1, 4, 9, 16, 25, (...)
(A) 35 (B) 36 (C) 48 (D) 49
Sol. The numbers are 12, 22, 32, 42, 52
Missing number = 62 = 36
Ex.10 20, 19, 17, (...), 10, 5
(A) 12 (B) 13 (C) 14 (D) 15
Sol. The pattern is –1, –2, ...
Missing number = 17 – 3 = 14
Ex.11 2, 3, 5, 7, 11, (...), 17
(A) 12 (B) 13 (C) 14 (D) 15
Sol. Clearly, the given series consists of prime
numbers starting from 2. The prime number
after 11 is 13. So, 13 is the missing number.
Ex.12 6, 11, 21, 36, 56, (...)
(A) 42 (B) 51 (C) 81 (D) 91
Sol. The pattern is +5, +10, +15, + 20, ...
Missing number = 56 + 25 = 81
Ex.13 1, 6, 13, 22, 33, (...)
(A) 44 (B) 45 (C) 46 (D) 47
Sol. The pattern is + 5, + 7, + 9, + 11, ...
Missing number = 33 + 13 = 46
Ex.14 3, 9, 27, 81, (...)
(A) 324 (B) 243 (C) 210 (D) 162
Sol. Each term of the given series is obtained by
multiplying its preceding term by 3.
Missing number = 81 × 3 = 243
32
9
1
5
5
25
TRIVENI NTSE PROGRAM Number Series 3
3 3
Ex.15 1, 9, 17, 33, 49, 73, (...)
(A) 97 (B) 98 (C) 99 (D) 100
Sol. The pattern is +8, +8, +16, +16, +24, ...
Missing number = 73 + 24 = 97
Ex.16 2, 5, 9, (...), 20, 27
(A) 14 (B) 16 (C) 18 (D) 24
Sol. The pattern is +3, +4, ...
Missing number = 9 + 5 = 14
Ex.17 5, 9, 17, 29, 45, (...)
(A) 60 (B) 65 (C) 68 (D) 70
Sol. The pattern is +4, +8, +12, +16, ...
Missing number = 45 + 20 = 65
Ex.18 3, 7, 15, 31, 63, (...)
(A) 92 (B) 115 (C) 127 (D) 131
Sol. Each number in the series is the preceding
number multiplied by 2 and then increased by
1.
Thus, (3 × 2) + 1 = 7, (7 × 2) + 1 = 15,
(15 × 2) + 1 = 31 and so on.
Missing number = (63 × 2) + 1 = 127
Ex.19 1, 6, 15, (...), 45, 66, 91
(A) 25 (B) 26 (C) 27 (D) 28
Sol. The pattern is +5, +9, ..., +21, +25
Missing number = 15 + 13 = 28
Ex.20 1, 2, 3, 5, 8, (...)
(A) 9 (B) 11 (C) 13 (D) 15
Sol. 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
Series
Series is a sequence of numbers obtained by
some particular predefined rule and applying
that predefined rule it is possible to find out
the next term of the series.
A series can be created in many ways. Some
of these are discussed below :
(i) Arithmetic Series.
For example,
Ø 3, 5, 7, 9, 11,......
Ø 10, 8, 6, 4, 2,......
Ø 13, 22, 31, 40, 49,.....
Ø 31, 27, 23, 19, 15,.....etc.
are arithmetic series because in each of them
the next number can be obtained by adding or
subtracting a fixed number. For example in 3,
5, 7, 9, 11,..... every successive number is
obtained by adding 2 to the previous number.
(ii) Geometric Series.
For example,
Ø 4, 8, 16, 32, 64,....
Ø 15, –30, 60, –120, 240,....
Ø 1024, 512, 256, 128, 64,....
Ø 3125, –625, 125, –25, 5,.....
are geometric series because, in each of them,
the next number can be obtained by
multiplying (or dividing) the previous number
by a fixed number. (For example, in : 3125–
625, 125, –25, 5... every successive number is
obtained by dividing the previous number by
–5.)
(iii) Series of squares, cubes :
These series can be formed by squaring or
cubing every successive number.
For example,
Ø 2, 4, 16, 256,.....
Ø 3, 9, 81, 6561,....
Ø 2, 8, 512,.... etc.
are such series. (In the first and second, every
number is squared to get the next number
while in the third it is cubed).
(iv) Mixed Series :
By a mixed series, we mean a series which is
created according to any non-conventional
(but logical) rule. Because there is no
limitation to people's imagination, there are
infinite ways in which a series can be created
and naturally it is not possible to club
together all of them.
Classification
(I) Two-tier Arithmetic Series :
In an arithmetic series the difference of any
two successive numbers is fixed. A Two-tier
Arithmetic Series shall be the one in which
the differences of successive numbers
themselves form an arithmetic series.
TRIVENI NTSE PROGRAM Number Series 4
4 4
For example,
(a) 1, 2, 5, 10, 17, 26, 37,.....
(b) 3, 5, 9, 15, 23, 33, .....etc.
are examples of such series. In 1, 2, 5, 10, 17,
26, 37, ......; for example, the differences of
successive numbers are 1, 3, 5, 7, 9, 11,
....which is an arithmetic series.
Note :
Two-tier arithmetic series can be denoted as a
quadratic function. For example, the above
series
(a) is 02 + 1, 12 + 1, 22 + 1, 32 + 1,.... which can
be denoted as f(x) = x2 + 1, where x = 0, 1,
2,.... similarly example (b) can be denoted as
f(x) = x2 + x + 3, x = 0, 1, 2, 3,.....
(II)Three-tier Arithmetic Series :
This, as the name suggests, is a series in
which the differences of successive numbers
form a two-tier arithmetic series; whose
successive term's differences, in turn, form an
arithmetic series.
For example
(a) 336, 210, 120, 60, 24, 6, 0,...
is an example of three-tier arithmetic series.
[The differences of successive terms are 126,
90, 60, 36, 18, 6,.....
The differences of successive terms of this
new series are 36, 30, 24, 18, 12,.....
which is an arithmetic series.]
Note :
Three-tier arithmetic series can be denoted as
a cubic function. For example, the above
series is (from right end) 13 –1, 23 –2, 33 –3,
43 –4, .... which can also be denoted as f(x) =
x3 –x; x = 1, 2,....
(III) Important Results
Ø In an arithmetic series we add (or deduct) a
fixed number to find the next number, and
Ø In a geometric series we multiply (or divide) a
fixed number to find the next number.
We can combine these two ideas into one to
from
(a) Arithmetico-geometric Series :
This series each successive term should be
found by first adding a fixed number to the
previous term and then multiplying it by
another fixed number.
For example
1, 6, 21, 66, 201,.........
is an arithmetico-geometric series. (Each
successive term is obtained by first adding 1
to the previous term and then multiplying it
by 3).
Note :
The differences of successive numbers should
be in Geometric Progression.
In this case, the successive differences are 5,
15, 45, 135,.... which are in G.P.
(b) Geometrico-Arithmetic Series
A geometrico-arithmetic series should be the
one in which each successive term is found
by first multiplying (or dividing) the previous
term by a fixed number and then adding (or
deducting) another fixed number.
For example
3, 4, 7, 16, 43, 124,....
is a geometrico-arithmetic series. (Each
successive term is obtained by first
multiplying the previous number by 3 and
then subtracting 5 from it.)
Note :
The differences of successive numbers should
be in geometric progression. In this case, the
successive differences are 1, 3, 9, 27, 81,
....which are in G.P.
(IV) Twin Series :
We shall call these twin series, because they
are two series packed in one.
1, 3, 5, 1, 9, –3, 13, –11, 17,.......
is an example of twin series. (The first, third,
fifth etc., terms are 1, 5, 9, 13, 17 which is an
arithmetic series. The second, fourth, sixth
etc. are 3, 1, –3, –11 which is a geometricoarithmetic series in which successive terms
are obtained by multiplying the previous term
by 2 and then subtracting 5.)
TRIVENI NTSE PROGRAM Number Series 5
5 5
(V) Other Series :
Besides, numerous other series are possible
and it is impossible to even think of all of
them.
SUMMARY OF THREE STEPS
[Very Important]
Step I : Do a preliminary screening of the series.
If it is a simple series you will be able to solve it
easily.
Step II : If you fail in preliminary screening then
determine the trend of the series. Determine
whether it is increasing, decreasing or alternating.
Step III (A) : Perform this step only if a series is
increasing or decreasing. Use the following rules :
(a) If the rise of a series is slow or gradual, the
series is likely to have an addition-based increase;
successive numbers are obtained by adding some
numbers.
(b) If the rise of a series is very sharp initially but
slows down later on, the series is likely to be
formed by adding squared or cubed numbers.
(c) If the rise of a series is throughout equally
sharp, the series is likely to be multiplicationbased; successive terms are obtained by
multiplying by some terms (and, maybe, some
addition or subtraction could be there, too).
(d) If the rise of a series is irregular, there may be
two possibilities. Either there may be a mix of two
series or two different kinds of operations may be
going on alternately. (The first is more likely
when the increase is very irregular : the second is
more likely when there is a pattern, even in the
irregularity of the series).
Step (III) (B) : (to be performed when the series
is alternating)
[Same as (iv) of step (iii), Check two possibilities]
Some Solved Examples
Ex. Find the next number of the series
(i) 8, 14, 26, 50, 98, 194
(ii) 8, 8, 9, 9, 11, 10, 14, 11
(iii)325, 259, 204, 160, 127, 105
(iv) 54, 43, 34, 27, 22, 19
(v) 824, 408, 200, 96, 44, 18
(vi) 16, 17, 21, 30, 46, 71
(vii) 3, 3, 6, 18, 72, 360
(viii) 3, 4, 8, 17, 33, 58
(ix) 6, 16, 36, 76, 156, 316
(x) –2, 4, 22, 58, 118, 208
Solution
(i) Sharp increase and terms roughly doubling
every time. On checking with 2 as multiple
the series is:
next term = previous term × 2 –2. Next term =
382.
(ii) Irregular. Very irregular. Likely to be,
therefore, mixed. On checking it is a mix of
two series:
8, 9, 11, 14, (+1, +2, +3 etc.) and 8, 9, 10, 11.
Next term = 14 + 4 + 18.
(iii)Gradual slow decrease. Likely to be
arithmetical decrease. Check the differences
of successive terms. They are 66, 55, 44, 33,
22. Hence, next decrease will be : 11.
Next term = 105 – 11 = 94.
(iv)Gradual slow decrease. Likely to be
arithmetical decrease. Check the differences.
They are 11, 9, 7, 5, 3. Hence, next decrease
will be 1. Next term = 19 – 1 = 18.
(v) Sharp decrease and terms roughly being
halved every time. Checking with 2 as divisor
the series is :
Next term (previous term – 8) ÷ 2.
Next term = 5.
(vi) preliminary screening tells us that each term
is obtained by adding 12, 22, 32, 42, 52......
respectively.
Next term = 71 + 62 = 107
(vii) Sharp increase. The series is : × 1, × 2, ×3,
×4, ×5, ....Next term = 360 × 6 = 2160
(viii) Sharp increase that slows down later no.
(Ratios of successive terms rise sharply from
4 ÷ 3 = 1.3 to 8 ÷ 4 = 2 to 17 ÷ 8 = 2. 125 and
then start falling to 33 ÷ 17 » 1.9 and then to
58 ÷ 33 ÷ 1.8). Hence likely to be addition of
squared or cubed numbers. On checking the
series is:
+ 12 +22, +32, +42, +52, .... Next term =
58 + 62 = 94.
TRIVENI NTSE PROGRAM Number Series 6
6 6
(ix) Sharp increase with terms roughly doubling
each time. Likely to have geometrical nature
with 2 as multiple. On checking the series is:
×2 +4. Next term = 316 × 2 + 4 = 636
(x) Series increases sharply but then its speed of
rise slows down. Likely to be addition of
squared or cubed numbers. On checking, the
series is: 13 – 3, 23 – 4, 33 – 5, 43 – 6.... Next
term = 73 – 9 = 334.
Wrong Number in Series
In examinations, a series is more likely to be
given the format of a complete series in
which an incorrect number is included & it is
required to find out the wrong number. On
studying a given series and applying the
concepts employed so far you should be able
to understand and thus "decode" the
formation of the series. Usually six terms are
given and it means that at least five correct
terms are given.
Some Unique Series
These series may be asked in examinations, so
you must be aware of them.
I. Series of Date or Time
1. Which of the following doesn't fit into the
series?
5–1–96, 27–1–96, 18–2–96, 12–3–96,
Sol. Each successive date differs by 22 days.
Recall that 96 is a leap year, you will find that
12–3–96 should be replaced by 11–3–96.
2. Which of the following doesn't fit into the
series?
5.40, 8.00, 10.20, 12.30, 3.00, 5.20
Sol. Each successive time differs by 2 hrs. 20
minutes. So 12.30 should be replaced
by 12.40.
Note : Keep in mind that the problem of series may
be based on dates or times. Sometimes it
doesn't strike our mind and the question is
solved wrongly.
II. Fractional series
Which of the following doesn't fit into the
series?
1. , , , ,
Sol. Whenever you find that most of the fractions
have the same denominators, change all the
denominators to the same value. For example,
in this question, the series becomes :
, , , ,
Now, it is clear that numerators must decrease
successively by 5. Therefore, should be
replaced by .
2. , , , , ,
Sol. By the above rule if we change all the
fractions with the same denominators, the
series is , , , , , .
We see that numerators decrease by 5, thus
should be replaced by .
Now, we conclude that the above fractions
decrease successively by or .
3 , , , , ,
Sol. We see that all the denominators differ, so we
can't use the above rule. In this case usually,
the numerators and denominators change in a
definite pattern. Here, numerators decrease
successively by 18 whereas denominators
decrease successively by 26. Thus
should be replaced by .
4. , , , , ,
Sol. Numerators increase successively by 3
whereas denominators decrease successively
by 3. Thus should be replaced by .
5
4
15
7
15
1
5
1 - 15
8 -
15
12
15
7
15
1
15
3 - 15
8 -
15
1
15
2
5
4
35
23
35
18
35
12
35
8
35
3
35
28
35
23
35
18
35
12
35
8
35
3
35
12
35
13
35
5
7
1
225
118
199
100
173
82
147
66
121
46
95
28
147
66
147
64
89
12
86
15
82
18
80
21
77
24
74
27
82
18
83
18
TRIVENI NTSE PROGRAM Number Series 7
7 7
III. Some numbers followed by their LCM or
HCF
1. 1, 2, 3, 6, 4, 5, 6, 60, 5, 6, 7,..... (Fill up the
blank)
Sol. The series can be separated in three parts. 1,
2, 3, 6/4, 5, 6, 60/5, 6, 7..... In each part fourth
number is LCM of first three
2. 8, 6, 24, 7, 3, 21, 5, 4, 20,.....,9, 18
(1) 1 (2) 3 (3) 4 (4) 5 (5) 6
Sol. 8, 6, 24/7, 3, 21/5, 4, 20/_, 9, 18
Third number in each part is LCM of first two
numbers. Thus, the answer should be 6.
3. 8, 4, 4, 7, 8, 1, 3, 9, 3, 2, 1,....
(1) 1 (2) 2 (3) 3 (4) 5 (5) N.O.T
Sol. 8, 4, 4/7, 8, 1/3, 9, 3/2, 1...
In each part, third number is HCF of first to
numbers. Thus our answer should be 1.
IV. Some numbers followed by their product
1. 2, 3, 6, 18, 108, 1844
Which of the above numbers does not fit into
the series?
Sol. 1844 is wrong, because
2 × 3 = 6, 3 × 6 = 18, 18 × 6 = 108,
but 108 × 18 = 1944.
V. By use of digit-sum
1. 14, 19, 29, 40, 44, 51, 59, 73
Which of the above numbers doesn't fit into
the series ?
Sol. Next number = Previous number + Digit-sum
of previous number Like,
19 = 14 + (4 + 1)
29 = 19 + (1 + 9)
40 = 29 + (2 + 9)
Thus, we see that 51 should be replaced by
52.
2. Fill up the blanks
14, 5, 18, 9, 22, 4, 26, 8, 30, 3, ....., .....
Sol. 1st, 3rd, 5th, 7th, ... numbers follow the
pattern of +4 (14 + 4 = 18, 18 + 4 = 22,...).
Where as 2nd, 4th, 6th are the digit-sums of
their respective previous number (5 = 1 + 4, 9
= 1 + 8),...) Thus, our answer is 34 and 7.
VI. Odd number out
Sometimes a group of numbers is written out
of which one is different from others.
1. 22, 44, 88, 132, 165, 191, 242. Find the
number which doesn't fit in the above series
(or group).
Sol. 191; Others are divisible by 11 or 191 is the
single prime number.
2. Which one of the following series doesn't fit
into the series ?
29, 31, 37, 43, 47, 51, 53
Sol. 51; All other are prime numbers.
Two-line Number Series
Now a days this type of number series is also
being asked in examinations.
In this type of no. series one complete series
is given while the other is incomplete. Both
the series have the same definite rule.
Applying the very definite rule of the
complete series, you have to determine the
required no. of the incomplete series. For
example:
Ex.21 4 14 36 114 460
2 a b c d e
Find the value of e.
Sol. The first series is ×1 + 10, ×2 +8, ×3 +6, ×4 +
4,.....
a = 2 × 1 + 10 = 12, b = 12 × 2 + 8 = 32,
c = 32 × 3 + 6 = 102, d = 102 × 4 + 4 = 412,
and finally e = 412 × 5 + 2 = 2062
Ex.22 5 6 11 28 71 160
2 3 a b c d e
What is the value of e?
Sol. The differences of two successive terms of the
first series are 1, 5, 17, 43, 89, the sequence
of which is 03 + 12, 13 + 22, 23 + 32, 33 + 42,
43 + 52.
a = 3 + 5 = 8, b = 8 + 17 = 25, c = 25 + 43
= 68, d = 68 + 89 = 157, and finally
e = 157 + (53 + 62
= 125 + 36 =) 161 = 318
TRIVENI NTSE PROGRAM Number Series 8
8 8
Ex.23 1296 864 576 384 256
1080 a b c d e
What should replace c ?
Sol. The first series is ÷ 3 × 2
a = 1080 ÷ 3 × 2 = 720, b = 720 ÷ 3 × 2=480,
and finally c = 480 ÷ 3 × 2 = 320
Ex.24 7 13 78 83 415
3 a b c d e
Find the value of b.
Sol. The first series is +6, ×6, +5, ×5
a = 3 + 6 = 9 and b = 9 × 6 = 54
Ex.25 3240 540 108 27 9
3720 a b c d e
What is the value of d?
Sol. The first series is ÷ 6, ÷ 5, ÷ 4, ÷ 3
a = 3720 ÷ 6 = 620, b = 620 ÷ 5 = 124, c =
124 ÷ 4 = 31, and finally d = 31 ÷ 3 = 10.33
Ex.26 27 44 71 108 155
34 a b c d e
What is the should replace e?
Sol. The differences of two successive terms of
the series are 17, 27, 37, 47.
a = 34 + 17 = 51, b = 51 + 27 = 78,
c = 78 + 37 = 115, d = 115 + 47 = 162, and
finally e = 162 + 57 = 219
Ex.27. 108 52 24 10 3
64 a b c d e
What is the value of c ?
Sol. The series is –4 ÷ 2
a = (64 – 4) ÷ 2 = 30, b =(30 – 4) ÷ 2 = 13,
c = (13 – 4) ÷ 2 = 4.5
Ex.28 –4 –2 –1 8 31
–1 a b c d e
Find the value of b.
Sol. The series is repeated as ×2 + 6 and
× 3 + 7 alternately.
a = –1 × 2 + 6 = 4 and b = 4 × 3 + 7 = 19
Ex.29 5 8 41 33 57 42 61
3 4 a b c d e
Find the value of d.
Sol. This is an alternate number series having two
series :
S1 = 5 41 57 61.
The differences between two successive terms
are 36 (= 62), 16 (= 42), 4( = 22) and
S2 = 8 33 42
The differences between two successive terms
are 25 (= 52), 9 (= 32)
b = 4 + 25 = 29 and d = 29 + 9 = 38.
Ex.30 Find the wrong number in the series :
7, 28, 63, 124, 215, 342, 511
(A) 7 (B) 28 (C) 124 (D) 215
Sol. Clearly, the correct sequence is
23 – 1, 33 – 1, 43 – 1, 53 – 1, 63 – 1, 73 – 1,
83–1
28 is wrong and should be replaced by
(33 – 1) i.e. 26.
Hence, the answer is (B).
Ex.31 Find the wrong number in the series :
3, 8, 15, 24, 34, 48, 63
(A) 15 (B) 24 (C) 34 (D) 48
Sol. The difference between consecutive terms of
the given series are respectively 5, 7, 9, 11
and 13.
Clearly, 34 is a wrong number and must be
replaced by (24 + 11) i.e. 35.
Hence, the answer is (C).
Ex.32 24, 27, 31, 33, 36
(A) 24 (B) 27 (C) 31 (D) 33
Sol. Each term in the series is increased by 3 to
obtain the next term.
So, 31 is wrong and must be replaced by
(27 + 3) i.e. 30.
Ex.33 196, 169, 144, 121, 80
(A) 80 (B) 121 (C) 169 (D) 196
Sol. The sequence is (14)2, (13)2, (12)2, (11)2,
(10)2.
So, 80 is wrong and must be replaced by (10)2
i.e. 100.
TRIVENI NTSE PROGRAM Number Series 9
9 9
Ex.34 3, 5, 7, 9, 11, 13
(A) 3 (B) 5 (C) 7 (D) 9
Sol. The series consists of consecutive prime
numbers. So, 9 is wrong.
Ex.35 121, 143, 165, 186, 209
(A) 143 (B) 165 (C) 186 (D) 209
Sol. Each term of the series is increased by 22 to
obtain the next term.
So, 186 is wrong and must be replaced by
(165 + 22) i.e. 187.
Ex.36 1, 2, 4, 8, 16, 32, 64, 96
(A) 4 (B) 32 (C) 64 (D) 96
Sol. Each term of the series is obtained by
multiplying the preceding term by 2
So, 96 is wrong and must be replaced by
(64 × 2) i.e. 128.
Ex.37 8, 14, 26, 48, 98, 194, 386
(A) 14 (B) 48 (C) 98 (D) 194
Sol. Each term in the series is less than twice the
preceding term by 2.
So, 48 is wrong and should be replaced by
(26 × 2 – 2) i.e. 50.
Ex.38 8, 13, 21, 32, 47, 63, 83
(A) 13 (B) 21 (C) 32 (D) 47
Sol. The sequence is + 5, + 8, +11, ...
47 is wrong and must be replaced by
(32 + 14) i.e. 46.
Ex.39 3, 10, 27, 4, 16, 64, 5, 25, 125
(A) 3 (B) 4 (C) 10 (D) 27
Sol. The correct sequence is
3, 32, 33, 4, 42, 43, 5, 52, 53.
So, 10 is wrong and must be replaced by 32
i.e. 9.
TRIVENI NTSE PROGRAM Number Series 10
10 10
EXERCISE
Q.1 3, 15, 35, ...., 99, 143.
(A) 63 (B) 69 (C) 77 (D) 81
Q.2 5, 11, 17, ...., 29, 41.
(A) 19 (B) 21 (C) 23 (D) 25
Q.3 7, 17, 31, 49 ...., 97, 127
(A) 59 (B) 61 (C) 71 (D) 87
Q.4 1, 3, 6, 10, 15 ...., 28, 36.
(A) 20 (B) 21 (C) 23 (D) 24
Q.5 2, 5, 9, ....., 20, 27
(A) 14 (B) 15 (C) 16 (D) 17
Q.6 0, 2, 8, 14, 24, 34, ...., 62.
(A) 40 (B) 42 (C) 48 (D) 52
Q.7 4, 9, 20, 37, 60,....
(A) 88 (B) 89 (C) 90 (D) 91
Q.8 1, 3, 3, 6, 7, 9 ...., 12, 21
(A) 10 (B) 11 (C) 12 (D) 13
Q.9 8, 10, 14, 18, ...., 34, 50, 66
(A) 28 (B) 27 (C) 26 (D) 25
Q.10 19, 2, 38, 3, 114, 4, ....
(A) 228 (B) 256 (C) 352 (D) 456
Q.11 4, 9, 17, 35, ...., 139.
(A) 89 (B) 79 (C) 69 (D) 59
Q.12 7, 15, 32, ...., 138, 281.
(A) 57 (B) 67 (C) 77 (D) 87
Q.13 8, 12, 10, 16, 12, ....
(A) 20 (B) 18 (C) 16 (D) 14
Q.14 10, 2, 20, 3, 30, 4, ....
(A) 40 (B) 50 (C) 60 (D) 70
Q.15 24, 6, 48, 12, 96, 24 .....
(A) 191 (B) 192 (C) 193 (D) 194
Q.16 3, 10, 18, 27, 37, 48, .....
(A) 60 (B) 70 (C) 80 (D) 90
Q.17 1, 3, 9, 27, 81, 243, ........
(A) 729 (B) 730 (C) 731 (D) 732
Q.18 10, 7, 6, 8, 5, 4, ....
(A) 4 (B) 5 (C) 6 (D) 7
Q.19 5, 2, 6, 2, 7, 2, .....
(A) 8 (B) 9 (C) 10 (D) 11
Q.20 4, 8, 16, 32, 64, 128 .....
(A) 256 (B) 257 (C) 258 (D) 259
Q.21 0.5, 1.5, 4.5, 13.5, (.....)
(A) 45.5 (B) 39.5 (C) 30.5 (D) 40.5
Q.22 121, 225, 361, (.....)
(A) 441 (B) 484 (C) 529 (D) 729
Q.23 0, 2, 8, 14, (.....), 34
(A) 24 (B) 22 (C) 20 (D) 18
Q.24 19, 2, 38, 3, 114, 4, (.....)
(A) 228 (B) 256 (C) 352 (D) 456
Q.25 1, 2, 3, 6, 9, 18, (.....), 54
(A) 18 (B) 27 (C) 36 (D) 81
Q.26 4, 5, 9, 18, 34, (.....)
(A) 43 (B) 49 (C) 50 (D) 59
Q.27 3, 6, 18, 72, (.....)
(A) 144 (B) 216 (C) 288 (D) 360
Q.28 66, 36, 18, (.....)
(A) 3 (B) 6 (C) 8 (D) 9
Q.29 21, 25, 33, 49, 81, (.....)
(A) 145 (B) 129 (C) 113 (D) 97
Q.30 12, 32, 72, 152, (.....)
(A) 312 (B) 325 (C) 515 (D) 613
Q.31 3, 6, 5, 20, 7, 42, 9, (.....)
(A) 54 (B) 60 (C) 66 (D) 72
Q.32 1, 3, 4, 8, 15, 27, (.....)
(A) 37 (B) 44 (C) 50 (D) 55
Q.33 2, 15, 41, 80, (.....)
(A) 111 (B) 120 (C) 121 (D) 132
Q.34 8, 10, 14, 18, (.....), 34, 50, 66
(A) 24 (B) 25 (C) 26 (D) 27
Q.35 1, 2, 6, 24, (.....)
(A) 60 (B) 95 (C) 120 (D) 150
Q.36 2, 3, 8, 63, (.....)
(A) 1038 (B) 1998 (C) 3008 (D) 3968
Q.37 95, 115.5, 138, (.....), 189
(A) 154.5 (B) 162.5 (C) 164.5 (D) 166.5
Q.38 4, 10, (.....), 82, 244, 730
(A) 24 (B) 28 (C) 77 (D) 218
Q.39 4, 32, 128, (.....)
(A) 128 (B) 144 (C) 192 (D) 256
Q.40 2, 5, 9, 19, 37, (.....)
(A) 76 (B) 75 (C) 74 (D) 72
Q.41 24, 60, 120, 210, (.....)
(A) 300 (B) 336 (C) 420 (D) 525
Q.42 165, 195, 255, 285, 345, (.....)
(A) 375 (B) 420 (C) 435 (D) 390
TRIVENI NTSE PROGRAM Number Series 11
11 11
Q.43 5, 17, 37, 65, (.....), 145
(A) 95 (B) 97 (C) 99 (D) 101
Q.44 9, 11, 20, 31, (.....), 82
(A) 41 (B) 51 (C) 60 (D) 71
Q.45 5, 16, 49, 104, (.....)
(A) 115 (B) 148 (C) 170 (D) 181
Q.46 34, 18, 10, 6, 4, (.....)
(A) 0 (B) 1 (C) 2 (D) 3
Q.47 462, 420, 380, (.....), 306
(A) 322 (B) 332 (C) 342 (D) 352
Q.48 3, 8, 22, 63, 185, (.....)
(A) 550 (B) 310 (C) 295 (D) 285
Q.49 1, 2, 5, 12, 27, 58, 121, (.....)
(A) 246 (B) 247 (C) 248 (D) 249
Q.50 0.5, 0.55, 0.65, 0.8, (.....)
(A) 0.9 (B) 0.82 (C) 1 (D) 0.95
Directions :
In each of the following questions, one term in the
number series is wrong. Find out the wrong term.
Q.51 380, 188, 92, 48, 20, 8, 2
(A) 188 (B) 92 (C) 48 (D) 20
Q.52 1, 3, 7, 15, 27, 63, 127
(A) 7 (B) 15 (C) 27 (D) 63
Q.53 5, 10, 17, 24, 37
(A) 10 (B) 17 (C) 24 (D) 37
Q.54 1, 3, 10, 21, 64, 129, 256, 778
(A) 10 (B) 21 (C) 129 (D) 256
Q.55 15, 16, 22, 29, 45, 70
(A) 16 (B) 22 (C) 45 (D) 70
Q.56 6, 14, 30, 64, 126
(A) 6 (B) 14 (C) 64 (D) 126
Q.57 10, 26, 74, 218, 654, 1946, 5834
(A) 26 (B) 74 (C) 218 (D) 654
Q.58 3, 7, 15, 39, 63, 127, 255, 511
(A) 15 (B) 39 (C) 63 (D) 127
Q.59 445, 221, 109, 46, 25, 11, 4
(A) 25 (B) 46 (C) 109 (D) 221
Q.60 1236, 2346, 3456, 4566, 5686
(A) 1236 (B) 3456 (C) 4566 (D) 5686
Q.61 5, 10, 40, 80, 320, 550, 2560
(A) 80 (B) 320 (C) 550 (D) 2560
Q.62 3, 2, 8, 9, 13, 22, 18, 32, 23, 42
(A) 8 (B) 9 (C) 13 (D) 22
Q.63 8, 27, 125, 343, 1331
(A) 8 (B) 343 (C) 1331 (D) None
Q.64 10, 14, 28, 32, 64, 68, 132
(A) 28 (B) 32 (C) 64 (D) 132
Q.65 1, 5, 5, 9, 7, 11, 11, 15, 12, 17
(A) 11 (B) 12 (C) 17 (D) 15
Q.66 11, 2, 21, 3, 32, 4, 41, 5, 51, 6
(A) 21 (B) 11 (C) 32 (D) 51
Q.67 11, 5, 20, 12, 40, 26, 74, 54
(A) 5 (B) 20 (C) 40 (D) 26
Q.68 56, 72, 90, 110, 132, 150
(A) 72 (B) 90 (C) 110 (D) 150
Q.69 8, 13, 21, 32, 47, 63, 83
(A) 13 (B) 32 (C) 47 (D) 63
Q.70 89, 78, 86, 80, 85, 82, 83
(A) 83 (B) 82 (C) 86 (D) 78
Q.71 25, 36, 49, 81, 121, 169, 225
(A) 36 (B) 49 (C) 169 (D) 225
Q.72 2, 5, 10, 17, 26, 37, 50, 64
(A) 17 (B) 26 (C) 37 (D) 64
Find the missing number in the following series
Q.73 4, 7, 11, 18, 29, 47, ....., 123, 199
(A) 76 (B) 70 (C) 84 (D) 102
Q.74 2, 6, 12, 20, ........, 42, 56, 72, 90
(A) 20 (B) 21 (C) 30 (D) 12
Q.75 17, 7, 24, 19, 9, 28, ...., 8, 31, 27, 10, 37
(A) 20 (B) 21 (C) 18 (D) 23
Q.76 6, 126,........, 9, 108, 12, 7, 133, 19, 12, 72, 6
(A) 21 (B) 23 (C) 30 (D) 35
Q.77 2, ...........8, 16, 32, 64, 128, 256
(A) 2 (B) 3 (C) 4 (D) 5
Q.78 45, 54, 47,......, 49, 56, 51, 57, 53
(A) 48 (B) 55 (C) 50 (D) 53
Q.79 3, 128, 6, 64, 9, ....., 12, 16, 15, 8
(A) 32 (B) 12 (C) 108 (D) 72
Q.80 5, 7, 11, 19, 35, 67, ...., 259
(A) 64 (B) 131 (C) 135 (D) 32
Q.81 8, 4, 12, 6, 18,......27
(A) 9 (B) 12 (C) 18 (D) 24
Q.82 16, 22, 34, 58, 106, ....., 394
(A) 178 (B) 175 (C) 288 (D) 202
Q.83 2, 3, 5, 9, 17, 33,......
(A) 85 (B) 37 (C) 63 (D) 65
TRIVENI NTSE PROGRAM Number Series 12
12 12
Q.84 2, 9, 23, 3, 8, 25, 4, ......, 27
(A) 7 (B) 29 (C) 23 (D) 14
Q.85 121, 112, ........, 97, 91, 86
(A) 102 (B) 108 (C) 99 (D) 104
Q.86 6, 9, 15, 27,.....,99
(A) 51 (B) 34 (C) 37 (D) 84
Q.87 4, 7, 12,......, 28, 39
(A) 19 (B) 24 (C) 14 (D) 16
Q.88 83, 82, 81, ....., 69, 60, 33
(A) 73 (B) 80 (C) 75 (D) 77
Q.89 77, 78, 77, 81, 73, ...., 55
(A) 69 (B) 71 (C) 82 (D) 89
Q.90 6, 7, 9, 13, 21,......
(A) 25 (B) 29 (C) 37 (D) 32
Q.91 11, 10, ......, 100, 1001, 1000, 10001
(A) 101 (B) 110 (C) 111 (D) None
Q.92 4, 8, 12, 24, 36, 72,......
(A) 108 (B) 98 (C) 92 (D) 96
Q.93 1, 2, 3, 5, 7,.....
(A) 8 (B) 9 (C) 10 (D) 13
Q.94 3, 6, 6, 12, 9,...........12
(A) 15 (B) 18 (C) 11 (D) 13
Directions (95 – 103) :
In each of the following questions, one number is
wrong in the series. Find out the wrong number :
Q.95 3, 5, 12, 39, 154, 772, 4634
(A) 5 (B) 3 (C) 39 (D) 154
(E) none of these
Q.96 376, 188, 88, 40, 16, 4, –2
(A) 4 (B) 16 (C) 40 (D) 188
(E) none of these
Q.97 444, 300, 200, 136, 87, 84, 80
(A) 200 (B) 136 (C) 87 (D) 80
(E) none of these
Q.98 2, 3, 12, 37, 86, 166, 288
(A) 2 (B) 3 (C) 166 (D) 86
(E) 37
Q.99 4, 9, 19, 43, 90, 185, 375
(A) 9 (B) 19 (C)90 (D) 185
(E) none of these
Q.100 572, 284, 140, 72, 32, 14, 5
(A) 14 (B) 32 (C) 72 (D) 5
(E) 140
Q.101 4, 10, 23, 50, 104, 216, 439
(A) 4 (B) 10 (C) 23 (D) 104
(E) 216
Q.102 701, 348, 173, 85, 41, 19, 8
(A) 173 (B) 41 (C) 19 (D) 8
(E) 348
Q.103 2, 3, 9, 27, 112, 565, 3396
(A) 565 (B) 9 (C) 112 (D) 27
(E) 3396
Direction :
In the following number series, one of the numbers
does not fit into the series. Find the wrong number.
Q.104 1788, 892, 444, 220, 112, 52, 24
(A) 52 (B) 112 (C) 220 (D) 444
(E) 892
Q.105 225, 289, 398, 374, 397, 415, 424
(A) 415 (B) 289 (C) 338 (D) 374
(E) 397
Q.106 5, 7.5, 11.25, 17.5, 29.75, 50, 91.25
(A) 7.5 (B) 17.5 (C) 29.75 (D) 91.25
(E) None of these
Q.107 35, 118, 280, 600, 1238, 2504, 5036
(A) 118 (B) 280 (C) 600 (D) 1238
(E) 2504
Q.108 10, 12, 28, 90, 368, 1840, 11112
(A) 1840 (B) 368 (C) 90 (D) 28
(E) 12
Directions :
In each of the following one number is wrong in the
series. Find out the wrong number in each case
Q.109 1, 2, 5, 14, 41, 124
(A) 2 (B) 5 (C) 14 (D) 41
(E) 124
Q.110 100, 97, 90, 86, 76, 71, 62, 55
(A) 55 (B) 62 (C) 76 (D) 86
(E) 97
Q.111 1, 2, 6, 24, 120, 620, 5040
(A) 5040 (B) 620 (C) 120 (D) 24
(E) 6
Q.112 4, 10, 22, 40, 64, 84, 130
(A) 22 (B) 40 (C) 64 (D) 84
(E) 130
Q.113 1, 4, 8, 16, 31, 64, 127, 256
(A) 31 (B) 16 (C) 8 (D) 6
(E) 1
Q.114 49, 56, 64, 71, 81, 90, 100, 110
(A) 56 (B) 64 (C) 71 (D) 81
(E) 90
TRIVENI NTSE PROGRAM Number Series 13
13 13
Directions (115- 119) :
In each questions given below, Four out of the five
given sets of numbers follow the same pattern, while
the fifth one is different. You have to find out the set
that does not match with others.
Q.115 (A) 3 (58) 7 (B) 1 (10) 3
(C) 2 (20) 4 (D) 5 (51) 6
(E) 8(145) 9
Q.116 (A) 4(36)2 (B) 10(102)1
(C) 6 (121)5 (D) 3(49) 4
(E) 7(225) 8
Q.117 (A) 8(39)5 (B) 12(44)10
(C) 7(48) 1 (D) 9(45)6
(E) 5(17)2
Q.118 (A) 5(68)9 (B) 11(8)13
(C) 3(27)6 (D) 7(125)12
(E) 6(64)10
Directions (119- 128) :
In each of the following questions, a number series is
given. After the series , below it in the next line, a
number is given followed by (A), (B), (C), (D) and
(E). You have to complete the series starting with the
number given following sequence of the given series.
Then, answer the questions given below it.
Q.119 535, 366, 245, 164,
817 , (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (e) ?
(A) 648 (B) 507 (C) 387 (D) 372
(E) none of these
Q.120 3, 5, 18, 72,
7 , (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (d) ?
(A) 416 (B) 9 (C) 2100 (D) 96
(E) none of these
Q.121 2, 9, 57, 337,
3, (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (b) ?
(A) 113 (B) 17 (C) 3912 (D) 8065
(E) none of these
Q.122 15, 159, 259, 323,
7, (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (c) ?
(A) 251 (B) 315 (C) 176 (D) 151
(E) none of these
Q.123 288, 140, 66, 29,
488, (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (e) ?
(A) 106 (B) 18.5 (C) 49 (D) 6.25
(E) none of these
Q.124 140, 68, 36, 16, 10 3
284, (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (b) ?
(A) 38 (B) 72 (C) 84 (D) 91
(E) none of these
Q.125 25, 194, 73, 154,
105
14, (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (d) ?
(A) 90 (B) 84 (C) 102 (D) 94
(E) none of these
Q.126 6, 9, 18, 45, 135
20, (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (c) ?
(A) 324 (B) 81 (C) 175 (D) 150
(E) 216
Q.127 2 9 57 337 1681
3 (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (e) ?
(A) 32416 (B) 4231 (C) 13441 (D) 6392
(E) none of these
Q.128 3, 4, 10, 33, 136
7, (a), (b), (c), (d), (e)
Which of the following numbers will come in
place of (e) ?
(A) 1035 (B) 1165 (C) 1039 (D) 891
(E) none of these
Directions (129- 137) :
Each of the following questions consists of a pair of
numbers that have a certain relationship to each other,
followed by four other pairs of numbers given as
alternatives. Select the pair in which the numbers are
similarly related as in the given pair.
Q.129 27 : 9
(A) 64 : 9 (B) 125 : 5
(C) 135 : 15 (D) 729 : 81
TRIVENI NTSE PROGRAM Number Series 14
14 14
Q.130 11 : 1210
(A) 6 : 216 (B) 7 : 1029
(C) 8 : 448 (D) 9 : 729
Q.131 Find a group similar to (3, 7, 11).
(A) 2, 9, 21 (B) 2, 17, 23
(C) 4, 6 , 14 (D) 7, 9, 16
Q.132 Given set : (49, 25, 9)
(A) (36, 16, 4) (B) (36, 25, 16)
(C) (39, 26, 13) (D) (64, 27, 8)
Q.133 Given set : (21, 51, 15)
(A) (21, 30, 51) (B) (21, 35, 41)
(C) (21, 51, 42) (D) (21, 91, 35)
Q.134 Given set : (9, 15, 21)
(A) (10, 14, 16) (B) (7, 21, 28)
(C) (5, 10, 25) (D) (4, 8, 12)
Q.135 11 : 17 : : 19 : ?
(A) 23 (B) 27 (C) 33 (D) 21
Q.136 Which number is the given set of numbers ?
Given set : (3, 17, 31)
(A) 5 (B) 15 (C) 45 (D) 49
Q.137 As 425 is related to 2, in the same way 613 is
related to -
(A) 1 (B) 2 (C) 3 (D) 4
Directions (138- 142) :
Find the missing term of the pair
Q.138 7528 : 5362 : : 4673 : ?
(A) 2367 (B) 2451 (C) 2531 (D) 2617
(E) None of these
Q.139 9 : 9 : : 8 : ?
(A) 14 (B) 64 (C) 25 (D) 27
(E) 20
Q.140 6 : 24 : : 5 : ?
(A) 23 (B) 22 (C) 25 (D) 27
(E) 20
Q.141 25 : 125 : : 36 : ?
(A) 180 (B) 206 (C) 216 (D) 318
(E) 72
Q.142 3 : 7 : : 08 : ?
(A) 10 (B) 13 (C) 17 (D) 14
(E) 16
TRIVENI NTSE PROGRAM Number Series 15
15 15
ANSWER KEY
EXERCISE-1
HINTS & SOLUTIONS
1. 22 – 1, 42 – 1, 62 – 1
2. +6, +6, +6 ...
3. +10, +14, ...
8. Ist series = 1, 3, 7 .... 21
IInd series = 3, 6, 9, 12
The pattern is Ist series is +2, +4, ...
missing number = 7 + 6 = 13
10. Ist series 19, 38, 114, ......
IInd series 2, 3, 4 .....
The pattern followed in Ist is ×2, ×3 ....
missing number = 114 × 4 = 456
11. 4 × 2 + 1, 9 × 2 – 1, ...
14. 10 × 2 = 20, 10 × 3 = 30 ....
21. Each term of the series is obtained by
multiplying the preceding term by 3.
Missing number = 13. 5 × 3 = 40.5.
22. 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.
23. The numbers are
12 – 1, 22 – 2, 32 – 1, 42 – 2....
Missing number = 52 – 1 = 24.
24. The sequence is a combination of two series:
I. 19, 38, 114, (...) and II. 2, 3, 4
The pattern followed in I is ×2, ×3, ...
Missing number = 144 × 4 = 456.
25. The numbers are alternately multiplied by 2
and . Thus, 1 × 2 = 2, 2 × = 3, 3 × 2 = 6,
6 × = 9 and so on.
Missing number = 18 × = 27.
26. The pattern is +1, +4, + 9, + 16,... i.e.,
+ 12, + 22, + 32, 42, ....
Missing number = 34 + 52 = 34 + 25 = 59.
27. The pattern is ×2, ×3, ×4, ...
Missing number = 72 × 5 = 360.
28. Each number in the series is the product of
the digits of the preceding number.
Thus, 6 × 6 = 36, 3 × 6 = 18 and so on.
Missing number = 1 × 8 = 8.
29. The pattern is +4, +8, +16, +32, ... i.e., + 22, +
23, + 24, + 25,...
Missing number = 81 + 26 = 81 + 64=145.
30. The pattern is +20, +40, +80,...
Missing number = 152 + 160 = 312.
Q.No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. A C C B A C B D C D C B A A B A A C A A
Q.No 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. D C A D B D D C A A D C D C C D B B D B
Q.No 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Ans. B C D B D D C A C C C C C D B C D B B D
Q.No 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
Ans. C B D D B C C D C C A D A C D A C B A B
Q.No 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
Ans. A D D A D A A D C C A A C B C D C C B C
Q.No 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
Ans. D E B B E C D A E A B D C C D B E A D A
Q.No 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
Ans. A B D B D D C B D C B A D D C A A B C E
Q.No 141 142
Ans. C C
2
3
2
3
2
3
2
3