## Sunday, November 18, 2012

### MTS / POSTMAN / GDS TO PA / POSTAL ASSISTANT MATERIAL

This material prepared and compiled by Akula. Praveen Kumar, SPM, Papannapet Sub Office-502 303,MedakDivision,AndhraPradesh,9849636361,        8019549939

Disclaimer:- All Material/Questions/Information provided in this post are Compiled by A. Praveen Kumar for in good faith of Departmental Employees. The types of questions, number of questions and standard of questions may be vary in actual examination. This is my predictions only. Author of blog does not accepts any responsibility in relation to the accuracy, completeness, usefulness or otherwise, of the content

3. SERIES COMPLETION

This chapter consists of questions in which series of numbers or alphabetical letters or combinations of both are given,which are generally called the terms of series. These terms follow a certain pattern throughout the series.The candidate is required to study the given series,identify the pattern followed in the series and either complete the given series with the most suitable alternative or find the wrong term in the series.

Number Series

Prime Number Series:

Example 1. 4, 9, 25, 49, 121, 169,…
(a) 324      (b) 289     (c) 225          (d) 196

Solution. (b) The given series is a consecutive square of prime number series. The next prime number is 289.

Example 2. 5, 7, 13, 23, …
(a) 25        (b) 27       (c) 29            (d) 41

Solution. (d) The difference between prime numbers is increasing. 7 is next prime to 5; 13 is second to next prime to 7; 23 is third to next to 13. Hence, next should be fourth to next prime to 23. Hence, required number is 41.

Multiplication Series:

Example 3. 4, 8, 16, 32, 64… 256
(a) 96      (b) 98       (c) 86             (d) 106

Solution. (a) The numbers are multiplied by 2 to get the next number.
64 × 2 = 128

Example 4. 5, 20, 80, 320, … 1280
(a) 5120     (b) 5220     (c) 4860      (d) 3642
Solution. (a) The numbers are multiplied by 4 to get the next number.
1280 × 4 = 5120

Difference Series:

Example 5. 3,6,9,12,15,…. 21
(a) 16        (b) 17        (c) 20           (d) 18

Solution. (d) The difference between the numbers is 3.
15 + 3 = 18

Example 6. 55, 50, 45, 40,….30
(a) 33       (b) 34         (c) 35             d) 36

Solution. (c) The difference between the numbers is -5.
40 – 5 = 35

Division Series:

Example 7. 5040, 720, 120, 24, ….2,1
(a) 8           (b) 7         (c) 6             (d) 5
Solution. (c)

Example 8. 16, 24, 36,… 81
(a) 52        (b) 54     (c) 56      (d) 58

Solution. (b) Previous number × = Next number

n2 Series

Example 9. 4, 16, 36, 64, …. 144
(a) 112       (b) 78    (c) 100       (d) 81

Solution. (c) The series is square of consecutive even numbers. 22, 42,62, 82
Next number is 102 = 100

Example 10. 1, 4, 9, 16, 25, 36, 49, … 81
(a) 100       (b) 121         (c) 64    (d) 144

Solution. (c) The series is 12, 22, 32, 42, 52,62, 72,….
The next number is 82 = 64

(n2 + 1) Series

Example 11. 17, 26, 37, 50, 65,….101
(a) 82     (b) 75     (c) 78       (d) 90

Solution. (a) The series is 42 + 1, 52 +1, 62 + 1, 72 + 1, 82 + 1.
The next number is 92 + 1 = 82

Example 12. 101, 401, 901, 1601, 2501, …. 4901
(a) 2201      (b) 3301    (c) 4401     (d) 3601

Solution. (d) The series is 102 + 1, 202 +1, 302 + 1, 402 + 1, 502 + 1, etc.
The next number is 602 + 1 = 3601

(n2 -1) Series

Example 13. 3, 8, 15, 24,…48
(a) 32     (b) 33     (c) 34       (d) 35

Solution. (d) The series is 22 – 1, 32 –1, 42 – 1,52 – 1. etc.
The next number is 62 – 1 =35

Example 14. 99, 80, 63,….35
(a) 48      (b) 84     (c) 46      (d) 64

Solution. (a) The series is 102 -1, 92 -1, 82 -1, etc.
The next number is 72 – 1 = 48

(n2 + n) Series

Example 15. 2, 6, 12, 20, 30,…. 56
(a) 32        (b) 34       (c) 42       (d) 24
Solution. (c) The series is 12 + 1, 22 + 2, 32 + 3, 42 + 4, 52 + 5, etc.
The next number is 62 + 6 = 42

Example 16. 110, 132, 156, 182,….
(a) 212       (b) 201     (c) 211      (d) 210

Solution. (d) The series is 102 + 10, 112 + 11, 122 + 12, etc.
The next number is 142 + 14 = 210

(n2 – n) Series

Example 17. 0, 2, 6, 12, 20,….42
(a) 25       (b) 30      (c) 32         (d) 40

Solution. (b) The series is 12 – 1 = 0, 22 – 2 = 2, 32 – 3 = 6, etc.
The next number is 62 – 6 = 30

Example 18. 90, 380, 870, 1560,…..
(a) 2405         (b) 2450         (a) 2400      (d) 2455

Solution. (b) The series is 102 – 10, 202 – 20, 302 – 30, etc.
The next number is 502 – 50 = 2450

n3 Series

Example 19. 1, 8, 27, 64,…. 216
(a) 125        (b) 512        (c) 215         (d) 122

Solution. (a) The series is 13, 23, 33 , 43, etc.
The next number is 53 = 125

Example 20. 1000, 8000, 27000, 64000,….
(a) 21600         (b) 125000       (c) 152000     (d) 261000

Solution. (b) The series is 103 , 203, 303, 403, etc.
The next number is 503 = 125000

(n3 + 1) Series

Example 21. 2, 9, 28, 65,…217
(a) 123      (b) 124           (c) 125         (d) 126
Solution. (d) The series is 13 +1, 23 + 1, 33 + 1, etc.
The next number is 53 + 1 = 126

Example 22. 1001, 8001, 27001, 64001, 125001,….
(a) 261001        (b) 216001           (c) 200116      (d) 210016

Solution. (b) The series is 103 + 1, 203 + 1, 303 + 1, etc.
The next number is 603 + 1 = 216001

(n3 -1) Series

Example 23. 0, 7, 26, 63, 124,…
(a) 251        (b) 125      (c) 215         (d) 512

Solution. (c) The series is 13 – 1, 23 – 1, 33 – 1, etc.
The next number is 63 – 1 = 215

Example 24. 999, 7999, 26999, 63999,….
(a) 199924         (b) 124999        (c) 129994        (d) 999124

Solution. (b) The series is 103 – 1, 203 – 1, 303 – 1, etc.
The next number is 503 – 1 = 124999

(n3 + n) Series

Example 25. 2, 10, 30, 68,….222
(a) 130          (b) 120        (c) 110            d) 100

Solution. (a) The series is 13 + 1, 23 + 2, 33 + 3, etc.
The next number is 53 + 5 = 130

Example 26. 1010, 8020, 27030, 64040,….
(a) 125500          (b) 125050           (c) 100255       (d) 120055

Solution. (b) The series is 103 + 10 = 1010, 203 + 20 = 8020, etc.
The next number is 503 + 50 = 125050

(n3 – n) Series

Example 27. 0, 6, 24, 60,…. 210
(a) 012         (b) 210       (c) 201         (d) 120
Solution. (d) The series is 13 – 1 = 0, 23 – 2 = 6, 33 – 3 = 24, etc.
The next number is 53 – 5 = 120

Example 28. 990, 7980, 26970, 63960,….
(a) 124500         (b) 124005          (c) 120045     (d) 124950

Solution. (d) The series is 103 – 10, 203 – 20, 303 – 30 etc.
The next number is 503 – 50 = 124950

Case 1 :  Completing the given series by finding the missing terms.
Directions :  Find the missing terms in each of the following series.

Ex. 1.  1,6,15,?,45,66,91
(a)25     (b) 26    (c) 27          (d) 28
Soln.  Clearly, the given sequence follows the pattern :
+5,+9,+13,+17,+21,+25,……
Thus, 1+5=6,6+9=15,…..
So, missing terms=15+13=28.

Ex. 2. 2,5,9,19,37,?
(a)   73           (b) 75                (c) 76                  (d) 78

Soln.  Clearly, we have : 2x2+1=5,5x2-1=9,9x2+1=19,19x2-
1=37,.
So, missing terms=37x2+1=75.
Ex. 3. 4,8,28,80,244,?
(a)   278      (b) 428             (c) 628                 (d) 728

Soln. The terms of the given series are : 31+1,32-2,33+1,34-
1,35+1
So,missing terms=36-1=729-1=728
Ex. 4.  10000,11000,9900,10890,9801,?.
(a)   10241   (b) 10423      (c) 10781          (d) 10929

Soln. Clearly,alternately we add and subtract 10% of a term to
obtain the next term of the series .
Thus, 10000+(10% of 10000)=11000;
11000-(10% of 11000)=9900
9900+(10%  of 9900)=10890;
10890-(10% of 10890)=9801;
So,missing term=9801+(10% of 9801)=9801+980=10781.

Ex.5.  0,6,24,60,120,210,?
(a)   240           (b) 290            (c) 336             (d) 504

Soln.  Clearly,the given series is  : 13-1,23-2,33-3,43-4,53-5,63-6
So, Missing term =73-7=343-7=336

Ex.6.   1,4,27,16,?,36,343
(a)   25             (b) 87             (c) 120             (d) 125

Soln.   Clearly,the given series consists of cubes of odd number
and square of even number. i.e. 13,22,33,42,…..
So, missing term=53=125

Ex.7.   4,6,12,14,28,30,?
(a)   32           (b) 60             (c) 62                (d) 64

Soln.   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 two above series is : +8, +16, +32,…….
So, missing no =(28+32)=60.

Ex.8. 1,3,3,6,7,9,?,12,21
(a)   10             (b) 11             (c) 12             (d) 13

Soln . 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 in
II is +3,.
So,  missing no is =7+6=13.
Hence , the answer is (d).

Ex.9. which fraction comes next in the sequence
1/2,3/4,5/8,7/16,?
(a)   9/32        (b)10/17         (c) 11/34         (d) 12/35

Soln. 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 terms.
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+2) i.e. 9
and the denominator will be 25
Thus, the next term is 9/32.
Hence , the answer is (a).

CASE II: Finding the Wrong term in the Given Series.

Ex1.Find the wrong number in the series :
7, 28, 63, 124, 215, 342, 511
(a) 7            (b)28               (c)124              (d)215            (e)342

Sol. Clearly, the correct sequence is :
23-1,33-1,43-1,53-1,63-1,73-1,83-1
So, 28 is wrong and should be replaced by 33-1.

Ex2. Find the wrong number in the series :
3, 8, 15, 24, 34, 48, 63
(a) 15           (b)24             (c)34             (d)48             (e)63

Sol. The difference between consecutive terms of the given
series are respectively 5, 7, 9,11,13 and 15.
Clearly, 34 is a wrong number and must be replaced by
(24+11) i.e. 35.

Ex3. Identity the wrong number in the series :
69, 55, 26, 13, 5
(a)5      (b)13      (c)26       (d)55

Sol. Clearly in the given series, each term is one more than the
product of the digits of the preceding term. Thus,
(6x9)+1=55, (5x5)+1=26, (2x6)+1=13.
So, 5 is wrong and must be replaced by (1x3)+1 i.e.4.

EXERCISE -1
Directions  : In each of the following questions, a number series is given with one term missing.Chosse the correct alternative that will continue the same pattern and replace the questions mark in the given series.
1.      1,9,25,49,?,121.
(a)   64               (b) 81                   (c) 91                   (d) 100

Ans B,   Series consists of square of ODD numbers.

--> 1^2, 3^2, 5^2, 7^2, 9^2, 11^2
--> 1 , 9 , 25 , 49 , 81 , 121

1, 9, 25, 49, 81, 121

2.      4,7,12,19,28,?.
(a)   30               (b) 36                   (c) 39                   (d) 49

Ans : C,  The sequence in n^2 + 3

1+3, 4+3, 9+3, 16+3, 25+3, Hence 36+3 = 39

3.      11,13,17,19,23,25,?
(a)   26               (b) 27                   (c) 29                   (d) 37

Ans: C  ,  The pattern is + 2, + 4, + 2, + 4, .....
So, missing term = 25 + 4 = 29.

4.      6,12,21,?,48.
(a)   33               (b) 38                   (c) 40                   (d) 45
Ans A,   Pattern is +6, +9, +12, +15...

6 +6=12, 12+9=21
Missing term : 21 +12=33

5.      2,5,9,?,20,27
(a)   14               (b) 16                   (c) 18                   (d) 24

Ans. A, it is increased in the order of no.+3,no.+4,no.+5,no.+6.
i.e=> 2+3=5 , 5+4=9 , 9+5=14 , 14+6=20 , 20+7=27.

6.      6,11,21,36,56,?
(a)   42               (b) 51                   (c) 81                   (d) 91
Ans: C,  The pattern is + 5, + 10, + 15, + 20,....
So, missing term = 56 + 25 = 81.

7.      10,18,28,40,54,70,?
(a)   85              (b) 86                    (c) 87                   (d) 88
Ans: D, the pattern is + 8, + 10, + 12, + 14, .....
So, missing term = 70 + 18 = 88.

8.      120,99,80,63,48,?
(a)   35              (b) 38                    (c) 39                   (d) 40
Ans: A,  The pattern is - 21, - 19, - 17, - 15,.....
So, missing term = 48 - 13 = 35.

9.      22,24,28,?,52,84.
(a)   36             (b) 38                     (c) 42                   (d) 46
Ans: A
The difference of each successive term is 4,8,16,32
Hence 28+8 = 36 or 52-16= 36

10.  4832,5840,6848,?
(a)   7815         (b) 7846                (c) 7856               (d) 7887
Ans:C
The pattern is + 1008. So, missing term - 6848 + 1008 = 7856

11.  10,100,200,310,?
(a)   400           (b) 410                  (c) 420                 (d) 430
Ans: D
This pattern is  +90, +100, +110, +120
Hence 310+120 =430

12.  0,2,8,14,?,34
(a)   20             (b) 23                    (c) 24                   (d) 25
Ans : C,     0+2=2,  2+(2+4)=8, 8+(2+4)=14, 14+(2+4+4)=24, 24+(2+4+4)=34

13.  28,33,31,36,?,39.
(a)   32             (b) 34                    (c) 38                   (d) 40
Ans:B. ,  Series like +5,-2,+5,-2.......
28 +5=33,  33 -2=31, 31 +5=36, 36 -2=34

14.  125,80,45,20,?.
(a)   5               (b) 8                      (c) 10                   (d) 12
Ans: A, Series decreased by 5 *9,5 *7,5 *5,5 *3(i.e, 45,35,25,15)

125-45 =80, 80 -35 =45, 45 -25 =20, 20 -15 =5
Final sequence = 125,80,45,20,5

15.  1,5,13,25,41,?
(a)   51             (b) 57                   (c) 61                    (d) 63

Ans: C 1+4 = 5, 5+8 = 13, 13+12 = 25, 25+16 = 41,41+20 = 61
nth term is, 2n(n-1) + 1
16.  2,15,41,80,?
(a)   111          (b) 120                  (c) 121                  (d) 132
Ans: D, The pattern is like = + 13, + 26, + 39,...
Missing number = 80 + 52 = 132.

17.  6,17,39,72,?
(a)   83          (b) 94             (c) 116                    (d) 127
Ans: C.,  17-6=11, 39-17=22,   72-39=33,  116-72=44.
they are increased by 11.

18.  325,259,204,160,127,105,?.
(a)   94          (b) 96             (c) 98                      (d) 100
Ans : A

19.  1,4,10,22,46,?
(a)   64          (b) 86            (c) 94                       (d) 122
Ans: C ,   4*2+2=10, 10*2+2=22, 22*2+2=46, 46*2+2=94, 94*2+2=190, 190*2+2=382

20.  0.5,0.55,0.65,0.8,?
(a)   0.9        (b) 0.82          (c) 1                         (d) 0.95
Ans: C, The pattern is + 0.05, 0.10, + 0.15,....
Missing number = 0.8 + 0.20 = 1.

21.  5,6,9,15,?,40
(a)   21         (b) 25             (c) 27                       (d) 33
Ans: B
5 6 9 15 25 40,  1 3 6 10 15,   2 3 4 5

22.  2,3,5,7,11,?,17
(a)   12         (b) 13            (c) 14                        (d)  15
Ans: B.,It is series contains consecutive prime numbers.
Final = 2,3,5,7,11,13,17

23.  4,9,25,?,121,169,289,361
(a)   49         (b) 64            (c) 81                        (d) 87
Ans: A, because each consecutive prime number is squared.

24.  1,9,25,49,81,?
(a)   100              (b) 112            (c) 121              (d) 144
Ans: C.
the series is +8,+16,+32,+40.....
therefore 81+40=121
25.  1,1,4,8,9,27,16,?
(a)   32                (b) 64              (c) 81                 (d) 256
Ans: B.
The sequence is (1^2)(1^3)(2^2)(2^3)(3^2)(3^3)(4^2)(4^3)

26.  4,12,36,108,?
(a)   144             (b) 216            (c) 30                 (d) 324
Ans: D  The Pattern is

4X3=12, 12x3=36, 36x3=108, 108x3= 324

27.  1,1,2,6,24,?,720.
(a)   100             (b) 104            (c) 108                (d) 120

Ans:D    20/6=120, 120/5=24, 24/4=6
6/3=2, 2/2=1, 1/1=1

28.  240,?,120,40,10,20
(a)   180             (b) 240           (c) 420                 (d) 480
Ans: B.,  From the back, series is like

2 *5 = 10,   10 *4 = 40,  40 *3 = 120, 120*2 = 240, 240*1 = 240
So, missing term is 240

29.  4,6,9,13.1/2,?
(a)   17.1/2        (b) 19             (c) 20.1/4             (d) 22.3/4

30.  5760,960,?,48,16,8.
(a)   120            (b) 160           (c) 192                   (d) 240
Ans:C., The pattern is 6, 5, 4, 3, 2.

So, missing term = 960 - 5 = 192.

31.  1,2,6,7,21,22,66,67,?
(a)   70              (b) 134           (c) 201                   (d) 301
Ans: C, The pattern is + 1, x 3, + 1, x 3, + 1, x 3, + 1,.....
So, missing term = 67 x 3 = 201.
32.  48,24,96,48,192,?
(a)   76              (b) 90             (c) 96                     (d) 98
Ans: C  The Pattern is

48/2= 24, 96/2=48, 192/2=96

33.  1,2,3,6,9,18,?,54.
(a)   18              (b) 27             (c) 36                     (d) 81
Ans: B  The pattern is x 2, x 3/2, x 2, x 3/2, x 2,.....
So, missing term = 18 x 3/2 = 27.

34.  165,195,255,285,345,?.
(a)   375           (b) 390           (c) 420                   (d) 435
Ans:  D  , 15*11=165, 15*13=195, 15*17=255, 15*19=285, 15*23=345, 15*29=435

35.  9,27,31,155,161,1127,?
(a)   316           (b) 1135         (c) 1288                 (d) 2254
Ans: B  , (9*3)27..(27+4)31..(31*5)155..(155+6)161..(161*7)1127..(1127+8 )1135

36.  2,3,3,5,10,13,?,43,172,177
(a)   23             (b) 38             (c) 39                     (d) 40
Ans: C,  43*4= 172,
so series becomes
2, 3, 3, 5, 10, 13, 39, 43,172,177

37.  3,15,?,63,99,143
(a)   27             (b) 35             (c) 45                     (d) 56
Ans: B
The difference between ,  3,15 - 12
15,x - Unknown 1
x,63 - - Unknown 2
63,99 - 36
99,143 - 44
143,195 - 52
The difference between them increases by 8
So the *unknown difference* are 20,28.

15 + 20 = 35 (or) 63 - 28 = 35

38.  7,26,63,124,215,342,?.
(a)   391          (b) 421           (c) 481                    (d) 511
Ans: D
The sequence is:
U[n] = (n + 1)³ - 1 = n³ + 3n² + 3n = n (n² + 3n + 3)

39.  3,7,15,?,63,127.
(a)   30            (b) 31             (c) 47                      (d) 52
Ans: B
3x2=6+1=7, 7x2=14+1=15, 15x2=30+1=31, 631x2=62+1=63 so on

40.  4,10,?,82,244,730
(a)   24            (b) 28             (c) 77                      (d) 218
Ans: B, the difference is tripled, each term.

41.  6,13,25,51,101,?.
(a)   201          (b) 202          (c) 203                     (d) 205

42.  8,28,116,584,?.
(a)   1752        (b) 3502        (c) 3504                   (d) 3508

Ans: D 8*3+4=28, 28 *4 +4 =116, 116 * 5 +4 =584, 584*6+4=3508

43.  6,13,28,59,?.
(a)   111          (b) 113           (c) 114                    (d) 122
Ans: D., The pattern is x 2 + 1, x 2 + 2, x 2 + 3,.....

So, missing term = 59 x 2 + 4 = 122.

44.  3,7,23,95,?
(a)   62            (b) 128           (c) 479                    (d) 575
Ans: C   3 * 2 +1 = 7
7 * 3 +2 =23
23 *4 +3 =95
95 *5+4 = 479
see the number you multiply it goes up by one, as does the number you add

45.  2,3,8,27,112,?
(a)   226          (b) 339           (c) 452                     (d) 565
Ans is D
ie is 2*1+1=3,  3*2+2=8, 8*3+3=27, 27*4+4=112, 112*5+5=565

46.  1,5,14,30,55,91,?.
(a)   130          (b) 140           (c) 150                    (d) 160
Ans: B, Series is increasing +2^2, +3^2, +4^2, +5^2, +6^2, +7^2,

1 +(2^2) = 5, 5 +(3^2) = 14, 14+(4^2) = 30, 30+(5^2) = 55, 55+(6^2) = 91
91+(7^2) = 140

47.  198,194,185,169,?.
(a)   92             (b) 112          (c) 136                    (d) 144
Ans: D

48.  2,2,5,13,28,?.
(a)   49             (b) 50            (c) 51                      (d) 52
Ans: D, There difference b/w series is 0,3,8,15,24,...(2-2,5-2,..)
ie,
2*0=0, 3*1=3, 4*2=8, 5*3=15 so then
6*4=24.

49.  2,7,27,107,427,?
(a)   1262        (b) 1707        (c) 4027                   (d) 4207
Ans: B
1707------ 2,7,27,107,427,1707------difference between them is 5,20,80,320----and differrence btwn dis is all multiplication to 4 each ... So the result comes nxt is = 1707

50.  24,60,120,210,?
(a)   300          (b) 336           (c) 420                     (d) 525
Ans  B , The pattern is+ 36, + 60, + 90, ....
i.e., + [ 6 * (6 + 0) ], + [ 6 * (6 + 4) ], + [ 6 * (6 + 9) ],.....
.'. Missng number = 210 + [ 6 * (6 + 15)]  = 210 + 126 = 336.

EXERCISE-2
Directions : In the following questions, one term in the number series is wrong. Find out the wrong term.

1. Find out the incorrect number 121, 143, 165, 186, 209

A. 143       B. 165       C. 186       D. 209
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.

2.  Find out the incorrect number 1, 2, 4, 8, 16, 32, 64, 96
A. 4       B. 32       C. 64       D. 96
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.

3. Find out the incorrect number  13, 21, 32, 47, 63, 83
A. 13       B. 21       C. 32       D. 47
The sequence is + 5, + 8, + 11,...
.'. 47 is wrong and must be replaced by (32 + 14)  i.e. 46.

4. Find out the incorrect number 380, 188, 92, 48, 20, 8, 2
A. 188       B. 92       C. 48       D. 20
Each term in the series is four more than two  times the next term.
So, 48 is wrong and must be replaced by (20 * 2 + 4) i.e. 44.

5. Find out the incorrect number 1, 3, 7, 15, 27, 63, 127
A. 7       B. 15       C. 27       D. 63
Ans: C, Go on multiplying the number by 2 and adding 1 to it to get the next number.
So, 27 is wrong.

6. Find out the incorrect number 5, 10, 17, 24, 37
A. 10       B. 17       C. 24       D. 37
Answer:      C , The sequence is + 5, + 7,.....
So, 24 is wrong and should be replaced by (17 + 9) i.e.  26.

7. Find out the incorrect number 1, 3, 10, 21, 64, 129, 256, 778
A. 10       B. 21       C. 129       D. 256
Answer:      D, The sequence is * 2 + 1, * 3 + 1, * 2 + 1, * 3 + 1,....
So, 256 is wrong and must be replaced by (129 * 2 + 1)  i.e.  259.

8. Find out the incorrect number 15, 16, 22, 29, 45, 70
A. 16       B. 22       C. 45       D. 70
Answer:      B , The pattern is + 1, + 4, + 9, + 16, + 25,....  i.e. + 12, + 22, + 32, + 42, + 52,...
So, 22 is wrong and must be replaced by (16 + 4) i.e. 20.

9. Find out the incorrect number 6, 14, 30, 64, 126
A. 6       B. 14       C. 64       D. 126
Answer:      C , Each term is multiplied by 2 and then increased by 2 to obtain the next term. So, 64 is wrong and must be replaced by (30 * 2 + 2)  i.e. 62.

10. Find out the incorrect number 10, 26, 74, 218, 654, 1946, 5834
A. 26       B. 74       C. 218       D. 654
Answer:      D , Each term is 4 less than thrice the preceding number.
So, 654 is wrong and must be replaced by (218 * 3 - 4) = 650.

11. Find out the incorrect number 3, 7, 15, 39, 63, 127, 255, 511
A. 15       B. 39       C. 63       D. 127
Answer:      B, Each number in the series is multiplied by 2 and the result increased by 1 to obtain the next number.
So, 39 is wrong and should be replaced bu (15 * 2 + 1)   i.e. 31.

12. Find out the incorrect number 445, 221, 109, 46, 25, 11, 4
A. 25       B. 46       C. 109       D. 221
Answer:      B, 3 is subtracted from each number and the result is divided by 2 to obtain the next number of the series.
So , 46 is wrong and must be replaced by 109 - 3 / 2   i.e. 53.

13. Find out the incorrect number 1236, 2346, 3456, 4566, 5686
A. 1236       B. 3456       C. 4566       D. 5686
Answer:      D ,The first digits of the numbers from the series 1, 2, 3, 4, 5;
the second digits from the series 2, 3, 4, 5,6;
the third digits from the series 3, 4, 5, 6;
while the last digit in each of the numbers is 6.
So, 5686 is wrong and must be replaced by 5676.

14. Find out the incorrect number 5, 10, 40, 80, 320, 550, 2560
A. 80       B. 320       C. 550       D. 2560
Answer:      C , The  sequence is * 2, * 4, * 2, * 4,....
So, 550 is wrong and must be replaced by (320 * 2)  i.e. 640.

15. Find out the incorrect number 3, 2, 8, 9, 13, 22, 18, 32, 23, 42
A. 8       B. 9       C. 13       D. 22
Answer:      B , The given sequence is a combination of two series :
I.   3, 8, 13, 18, 23  and
II   2, 9, 22, 32,42
The pattern in I is + 5 and the pattern in II is + 10.
So, in II, 9 is wrong and must be replaced by (2 + 10)  i.e. 12

16. Find out the incorrect number 8, 27, 125, 343, 1331
A. 8       B. 343       C. 1331       D. None of these
Answer:      D The numbers are cubes of prime numbers  i.e. 23, 33, 53, 73, 113.
Clearly, none is wrong.

17. Find out the incorrect number 8, 27, 125, 343, 1331
A. 8       B. 343       C. 1331       D. None of these
Answer:      D ,The numbers are cubes of prime numbers  i.e. 23, 33, 53, 73, 113.
Clearly, none is wrong.

18. Find out the incorrect number 10, 14, 28, 32, 64, 68, 132
A. 28       B. 32       C. 64       D. 132
Answer:      D , Alternately, the numbers are increased by four and doubled to get the next number>Thus, 10 + 4 = 14; 14 * 2 = 28; 28 + 4 = 32; 32 * 2 =64  and so on.
So, 132 is wrong and must be replaced by (68 * 2)  i.e.  136.

19. Find out the incorrect number 1, 5, 5, 9, 7, 11, 11, 15, 12, 17
A. 11       B. 12       C. 17       D. 15
Answer:      B , The given sequence is a combination of two series :
I.    1, 5, 7, 11, 12   and
II.   5, 9, 11, 15, 17
The pattern in both I and II is + 4, + 2, + 4, + 2.
So, 12 is wrong and must be replaced by (11 + 2)  i.e. 13.

20. Find out the incorrect number 11, 2, 21, 3, 32, 4, 41, 5, 51, 6
A. 21       B. 11       C. 32       D. 51
Answer:      C ,  The given sequence is a combination of two series :
I.   11, 21, 32, 41, 51   and
II.   2, 3, 4, 5, 6.
Clearly, the pattern in I is + 10.
So, 32 is wrong and should be replaced by (21 + 10)  i.e. 31

21. Find out the incorrect number 11, 5, 20, 12, 40, 26, 74, 54
A. 5       B. 20       C. 40       D. 26
Answer:      C , The given sequence is a combination of two series :
I.   11, 20, 40, 74   and
II.   5, 12, 26, 54, The pattern in I becomes + 9, + 18, + 36, ... if 40 is replaced by 38.
So, 40 is wrong.

22. Find out the incorrect number 56, 72, 90, 110, 132, 150
A. 72       B. 90       C. 110       D. 150
Answer:      D , The numbers are 7 * 8, 8 * 9, 9 * 10, 10 *11, 11 * 12, 12 * 13.
So, 150 is wrong and must be replaced by (12 * 13)  i.e. 156.

23. Find out the incorrect number 8, 13, 21, 32, 47, 63, 83
A. 13       B. 32       C. 47       D. 63
Answer:      C , The sequence is + 5, + 8, + 11,....
So, 47 is wrong and must be replaced by (32 + 14)  i.e. 46.

24. Find out the incorrect number 89, 78, 86, 80, 85, 82, 83
A. 83       B. 82       C. 86       D. 78
Answer:      C , The sequence is - 11, + 9, - 7, + 5, - 3, + 1.
So, 86 is wrong and should be replaced by (78 + 9)  i.e. 87.

25. Find out the incorrect number 25, 36, 49, 81, 121, 169, 225
A. 36       B. 49       C. 169       D. 225
Answer:      A , The correct sequence is 52, 72, 92, 112, 132, 152.
So, 36 is wrong.

26. Find out the incorrect number 2, 5, 10, 17, 26, 37, 50, 64
A. 17       B. 26       C. 37       D. 64
Answer:      D, The numbers are 12 + 1, 22 + 1, 32 + 1 and so on.
So, 64 is wrong. The correct term is (82 + 1)  i.e. 65.

27. Find out the incorrect number 1, 5, 9, 16, 25, 37, 49
A. 9       B. 15       C. 25       D. 37
Answer:      B The given sequence is a combination of two series :
I.   1, 9, 25, 49   and
II.   5, 15, 37, The pattern in I is + 8, + 16, + 24.
The sequence in II is 22 + 1, 42 + 1, 62 + 1.
So, 16 is wrong and must be replaced by (42 + 1)  i.e. 17.

28. Find out the incorrect number 2, 5, 10, 50, 500, 5000
A. 5       B. 10       C. 50       D. 5000
Answer:      D , Each term of the series is the product of the preceding two terms.
So, 5000 is wrong and must br replaced by (50 * 500)  i.e 25000.

29. Find out the incorrect number 46080, 3840, 384, 48, 24, 2, 1
A. 384       B. 48       C. 24       D. 2
Answer:      C , The terms are successfully divided by 12, 10, 8, 6,....
So, 24 is wrong and must be replaced by (48 / 6)  i.e. 8.

30. Find out the incorrect number 105, 85, 60, 30, 0, -45, -90
A. 105       B. 60       C. 0       D. -45
Answer:      C , The sequence is - 20, - 25, - 30,....
So, 0 is wrong and must be replaced by (30 - 35)  i.e. -5

31. Find out the incorrect number 325, 259, 202, 160, 127, 105, 94
A. 94       B. 127       C. 202       D. 259
Answer:      C , The sequence is - 66, - 55, - 44, - 33, - 22, -11.
So, 202 is wrong.
The correct term is (259 - 55)  i.e 204.

32. Find out the incorrect number 125, 126, 124, 127, 123, 129
A. 126       B. 124       C. 123       D. 129
Answer:      D , The sequence is + 1, - 2, + 3, - 4, + 5.
So, 129 is wrong and and must be replaced by (123 + 5)  i.e. 128.

33. Find out the incorrect number 3, 4, 10, 32, 136, 685, 4116
A. 10       B. 32       C. 685       D. 4116
Answer:      B ,The sequence is as follows :
2nd term = (1st term + 1) * 1
3rd term = (2nd term + 1) * 2
4th term = (3rd term + 1) * 3 and so on.
So, 32 is wrong and must be replaced by (10 + 1) * 3  i.e. 33.

34. Find out the incorrect number 3, 10, 27, 4, 16, 64, 5, 25, 125
A. 3       B. 4       C. 10       D. 27
Answer:      C, The correct sequence is 3, 32, 33, 4, 42, 43, 5, 52, 53.
So ,10 is wrong and should be replaced by 32  i.e. 9.

35. Find out the incorrect number 5, 27, 61, 122, 213, 340, 509
A. 27       B. 61       C. 122       D. 509
Answer:      A ,The correct sequence is 23 - 3, 33 - 3, 43 - 3, 53 - 3, 63 - 3, 73 - 3, 83 - 3.
So, 27 is wrong and should be replaced by 33 - 3  i.e. 24.

ALPHABET SERIES

In this type of questions, a series of single , pairs or group of letters of combination of letters and numeral is given .The terms of the series form a certain pattern as regards the position  of the letter in the English alphabet. The candidate is required to decipher this pattern and accordingly find the missing term or the wrong term in the given series.

ILLUSTRATIVE EXAMPLES.

Ex. 1. Find the next two terms in the series : A,C,F,J,?,?,
(a) L,P          (b) M,O            (c) O,U               (d) R,V

Sol. Clearly,the 1st,2nd,3rd,…..letters of the series are respectively    moved 2,3,4 steps forward to obtain the successive terms of the series.
Thus, the 5th term in the series must be a letter which is 5 steps ahead of J i.e. O, while the 6th term must be a letter six  steps a head  of O i.e. U.
Thus,we have the following pattern:
+2       +3       +4       +5       +6
A---àC---àF----àJ----àO----àU
So, the missing term are O and U.

Ex.2. Which term comes next I the sequence :AC,FH,KM,PR,?
(a) UW     (b) VW      (c) UX       (d) TV

Soln : Clearly, the first and the second letters of each term are moved five steps forward to obtain the corresponding letters of the next term.
Thus,the first letter of the missing term must be five steps ahead of P i.e. while the second letter must be five steps ahead of R i.e. W.
So, the missing term is UW.

Ex.3. Find the next term in the series : BMO,EOQ,HQS,?
(a) KSU(b) LMN(c) SOV(d) SOW

Soln : Clearly,we observe the following pattern :
+3       +3            +3
The 1st letter follows the pattern  +3 i.e  B----àE-----àH----àK
+2        +2         +2
The 2nd  letter follows the pattern  +2 i.e  M----àO-----àQ----àS
+2        +2          +2
The 3rd  letter follows the pattern  +2i.e  O----àQ-----àS--àU
Thus,the missing term is KSU.

Ex.4. Which term comes next in the series : YEB,WFD,UHG,SKI,?
(a) QOL      (b) QGL     (c) TOL          (d) QNL

Sol.     Clearly,we observe the following pattern :
-2         -2          -2        -2
1st letter : Y----àW-----àU----àS--àQ
+1      +2        +3         +4
2nd letter: E---àF----àH-----àK----àO
+2         +3          +2      +3
3rd letter : B----àD-----àG----àI---àL
Thus the missing term is QOL.

Ex.5. Which term will replace the ? in the series:
ABD,DGK,HMS,MTB,SBL,?
(a) ZKU       (b) ZKW     (c) ZAB       (d) XKW

Soln. : Clearly,we observe the following pattern :
+3        +4           +5        +6         +7
1st letter : A----àD-----àH----àM---àS---àZ
+5         +6           +7       +8          +9
2nd letter: B----àG-----àM----àT-----àB----àK
+7         +8        +9       +10         +11
3rd letter : D----àK-----àS----àB-----àL------àW
Thus,the missing term is ZKW.

EXERCISE-3
Directions: In each of the following questions ,various terms of an alphabet series are given with one or more terms missing  as shown by (?). Choose the missing terms out of the given alternatives.

1. U, O, I, ?, A
A. E       B. C       C. S       D. G
Answer:      A, The series consists of vowles A, E, I, O, U written in a reverse order.

2. Y, W, U, S, Q, ?, ?
A. N, J       B. M, L       C. J, R       D. L, M       E. O, M
The series consits of alternate letters in reverse order.

3. A, B, D, G, ?
A. M       B. L       C. K       D. H
The first, second, third,.... letters of the series are respectively moved one, two, three,... steps forward to obtain the successive terms.

4. Z, U, Q, ?, L
A. I       B. K       C. M       D. N
The first, second, third,... letters of the series are respectively moved one, two, three,... steps forward to obtain the successive terms.

5. A, C, F, H, ?, M
A. L       B. K       C. J       D. I
The letters are alternately moved two and three steps forward to obtain the successive terms.

6. A, Z, X, B, V, T, C, R, ?, ?
A. P, D       B. E, O       C. Q, E       D. O, Q       E. Q, O
The first, fourth and seventh letters are in alphabetical order.So, tenth letter would be the letter after C  i.e. D.Also, the second and third letters are alternate and in reverse order and so are the fifth and sixth letters and the eighth and ninth letters.

7. R, M, ?, F, D, ?
A. C, B       B. J, H       C. B, H       D. H, C       E. I, C
Letter are in reverse order in which from the last 0, 1, 2, 3 and 4 letters are missing between two consecutive letters.

8. R, M, ?, F, D, ?
A. C, B       B. J, H       C. B, H       D. H, C       E. I, C
Letter are in reverse order in which from the last 0, 1, 2, 3 and 4 letters are missing between two consecutive letters.

9. Z, L, X, J, V, H, T, F, ?, ?
A. R, D       B. R, E       C. S, E       D. Q, D
They given sequence consists of two series -- Z, X, V, T, ? and L, J, H, F, ?, both consisting of alternate letters in a reverse order.

10. Z, S, W, O, T, K, Q, G, ?
A. N, C       B. N, D       C. O, C       D. O, D
The given sequence consists of two series :
I.    Z, W, T, V, Q, ? in which each letter is moved three steps backward to obtain the next term.
II.   S, O, K, G in which each letter is moved four steps backward to obtain the next term.

11. W, V, T, S, Q, P, N, M, ?, ?
A. I, J       B. J, I       C. J, K       D. K, J
The letters are alternately moved one and two steps backward to obtain the successive terms.

12. Z, Y, X, U, T, S, P, O, N, K, ?, ?
A. H, G       B. H, I       C. I, H       D. J, I
The given series consists of three consecutive letters from the end, then two letters skipped, then again three consecutive letters from the end so on.

13. b, e, d, f, ?, h, j, ?, l
A. i, m       B. m, i       C. i, n       D. j, m
The series may be divided into groups as shown :
b  e  d  /  f  i  h  /  j  m  l
In each group, first letter is moved two steps forward to obtain the third letter
while the third letter is moved one step forward to obtain the second letter.

14. AZ, BY, CX, ?
A. EF       B. GH       C. IJ       D. DE       E. DW
The first letter of each term is moved one steps forward and the second letter is moved one steps backward to obtain the corresponding letters of the next term.

15. AZ, CX, FU, ?
A. IR       B. IV       C. JQ       D. KP
The first letter of the first, second, third, .... terms are respectively moved two, three, four, ... steps forward to obtain the first letter of the successive term.The second letter of the first, second, third.... terms are respectively moved two, three, four, ... steps ackward to obtain the second letter of the successive terms.

16. AZ, GT, MN, ?, YB
A. KF       B. RX       C. SH       D. TS
The first letter of each term is moved six steps forward while the second letter is moved six steps backward to obtain the corresponding letter of the next term.

17. BF, CH, ?, HO, LT
A. DN       B. EL       C. EK       D. EM       E. FJ
The first letter of the first, second, third, .... terms are respectively moved one, two, three,... steps forward while the second letter are respectively moved two, three, four,... steps forward to  obtain the corresponding letters of the successive terms.

18. CE, GI, KM, OQ, ?
A. TW       B. TV       C. SU       D. RT       E. UW
The letters of each term are alternate and also the last letter of each term and the first letter of the next term are alternate.

19. BD, GI, LN, QS, ?
A. TV       B. UW       C. WX       D. WY       E. VX
Each term of the series consists of two alternate letters and there is a gap of two letters between the last letter of each term and the first letter of  the next term.

20. AD, EH, IL, ?, QT
A. LM       B. MN       C. MP       D. OM
The first and second letter of each term are moved four steps forward to obtain the corresponding letters of the next term.

21. JE, LH, OL, SQ, ?
A. WV       B. WX       C. VW       D. VX       E. XW
The first letter of the first, second, third,... terms are respectively moved two, three, four,... steps forwardwhile the second letters of three terms are respectively moved three, four, five,... steps forward to obtain the corresponding letters of the successive terms.

22. DF, GJ, KM, NQ, RT, ?
A. UW       B. YZ       C. XZ       D. UX       E. YA
There is a gap of one letter between both the letters of first term, a gap of two letters between both the letters of second term and again a gap of one and two letters between the letters of third and fourth terms respectively.Beside, the last letter of each term and the first letter of next term are in alphabetical order.

23. cx, fu, ir, ?, ol, ri
A. lo       B. mn       C. no       D. op       E. or
The first letter of each term is moved three steps forward andthe second letter is moved three steps backward to obtain the corresponding letters of the next term.

24. OTE, PUF, QVG, RWH, ?
A. SYJ       B. TCI       C. SXJ       D. SXI       E. TYJ
The first letters of the terms are in alphabetical order,and so are the second and third letters.

25. eac, gce, ieg, ?
A. jhi       B. jgi       C. kgi       D. khi       E. kij
The first letters of the terms are alternate and so are the second and third letters.

26. ejo, tyd, ins, xch, ?
A. nrw       B. mrw       C. msx       D. nsx       E. nsw
There is a gap of four letters between the first and second, the second and third letters of each term,and also between the last letter of a term and the first letter of the next term.

27. CAT, FDW, IGZ, ?
A. KJA       B. KTC       C. LHD       D. LJC
All the letters of each term are moved three steps forward to obtain the corresponding letters of the next term.

28. BEH, KNQ, TWZ, ?
A. IJL       B. CFI       C. BDF       D. ADG
All the letters of each term are moved nine steps forward to obtain the corresponding letters of the next term.

29. deb, ijg, nol, ?, xyv
A. rsp       B. stp       C. rsq       D. stq       E. sto
All the letters of each term are moved five steps forward to obtain the corresponding letters of the next term.

30. ?, siy, oeu, kaq, qwm, cri
A. wnc       B. wnb       C. vnc       D. vmc       E. wmc
The letters in each term are moved four steps backward to obtain the corresponding letters of the next term.

31. QPO, SRQ, UTS, WVU, ?

A. XVZ       B. ZYA       C. YXW       D. VWX       E. AZY
Each term in the series consists of three consecutive letters in reverse order.
The first letter of each term and the last letter of the next term are the same.

32. ?, ayw, gec, mki, sqo
A. zxw       B. bzw       C. usq       D. may       E. xyv
Each term in the series consists of alternate letters in reverse order.The first letter of each term and the last letter of the next term arealso alternate.

33. dfe, jih, mln, ?, vut
A. oqp       B. psr       C. prq       D. rsp       E. oqr
There is a gap of three letters between the first letter of each term and the last letter of the next term.

34. DEF, HIJ, MNO, ?
A. STU       B. RST       C. RTV       D. SRQ       E. TUV
The letters in each term are consecutive. There is a gap of one letter between the last letter of the first term and the first letter of the second term and a gap of two letters between the last letter of the second term and the first letter of third term. So, there would be a gap of three letters between the last letter of the third term and the first letter of the fourth term

35. FLP, INS, LPV, ?
A. ORY       B. UXZ       C. VXY       D. SVW
The first and third letters of each term are moved three steps forward and the second letters is moved two steps forward to obtain the corresponding letters of the next term.

36. shg, rif, qje, pkd, ?
A. ole       B. olc       C. nmc       D. nlb
The first and third letters of each term are moved one step backward andthe second letter is moved one step forward to obtain the corresponding letters of the next term.

37. LXF, MTJ, NPN, OLR, ?
A. PHV       B. PIU       C. PJW       D. PKX       E. PRV
The first letter of each term is moved one step forward, the second letter is moved four steps backward andthe third letter is moved four steps forward to obtain the corresponding letters of the next term.

38. MHZ, NIW, OKT, PNQ, ?
A. RRN       B. QRN       C. QRM       D. QQN
The first letters of the terms are consecutive letters. The third letter of eac h term is moved three steps backward to obtain the third letter of the successive term. The middle letters of the first, second, third and fourth terms are moved one, two, three and four steps forward respectively to obtain the middle letter of the successive terms.

39. AYD, BVF, DRH, ?, KGL
A. FMI       B. GMJ       C. HLK       D. GLJ
The first letters of the first, second, third and fourth are moved one, two, three and four steps forward respectively to obtain the first letter of the successive terms.The second letters of the first, second, third and fourth terms are moved three, four, five and six steps backward respectively to obtain the second letters of the successive terms.The last letters of the terms are alternate

40. AB, BA, ABC, CBA, ABCD, ?
A. ACBD       B. BACD       C. CABD       D. DBAC       E. DCBA
The first group of letters is reversed to obtain the second group. The second group is reversed and the next consecutive letter is added to it to obtain the subsequent group.

CONTINUOUS PATTERN SERIES

This type of questions consists of a series of small letters which follow a certain pattern. However, some letters are missing from the series . These missing letters are then given in a proper sequence as one of the alternatives. The candidate is requires to choose this alternative as answer.

Example : aab_aaa_bba_
(a)   Baa       (b) abb       (c) bab       (d) aab          (e) bbb

Solution : we Proceed step by step as shown below :
1.      The first blank space should be filled in by ‘b’ so that we have two a’s followed by  two  b’s .
2.      The second blank space should be filled in either by ‘a’ so that we have four a’s followed by two b’s , or ‘b’ so that we have three  a’s followed by three ‘b’.
3.      The last space must be filled in by ‘a’.
4.      Thus, we have two possible answer: ‘baa’ and ‘bba’. But, only ‘baa’ appear in the alternative. So, the answer is (a).
5.      In case, we had both the possible answer in the alternatives, we would have chosen the one that forms a more prominent pattern, which is aabb/aaabbb/aa.Thus,our answer, would have been ‘bba.’

CORRESPONDENCE SERIES

This type of series consists of three sequence with three different elements(usually capital letters, digits  and small latters).on th basis of the similarity in positions in the three sequence, a capital letter  is found to correspond with a unique digit and a unique small letter, whenever it occurs. The candidate is  requires to trace out this correspondence and accordingly choose the elements to be filled in at the desired places.

Consider the following example:

Ex. In the following series, choose the alternative which   contains the numeral to be filled in the marked places,in the correct order :
B_ _ D _ _ C A B D A C B
- - 4 1 3 2 - - - ? ? ? ?
a _ a _ b c _ c _ _ _ _ _
(a)   1,2,3,4      (b) 2,3,1,4       (c) 1,2,4,3           (d) 2,1,4,3

Soln. Clearly, in the second series,1 occures at the same  positions as D occurs in the first
Series.So, 1 corresponds to D.Thus, the first questions marks below D is to be replaced by   1. Now, in the third series, c at the 8th place  corresponds to A in the  first series, while c at  the 6th place corresponds to 2 in the second series . so, 2 corresponds to A. Thus, the       second questions marks below   A is to be replaced by 2.   In the third series, a at the first  place corresponds to B in   the first series and a at the third  place corresponds to 4 in the  Second series. so, 4 corresponds to B.Thus, the questions mark below B is to be replaced by   4.Now, only 3 remains. So, 3 correspond to C. Thus, the questions mark below C is to be replaced by 3.Thus, DACB corresponds to 1,2,3,4.

EXERCISE-4

Directions: In each of the following letter series, some of the letters are missing which are given in that order as one of the alternatives below it. Choose the correct alternative

1. _ _ aba _ _ ba _ ab
A. abbba       B. abbab       C. baabb       D. bbaba
Answer:      B , The series is ab / ab / ab / ab / ab / ab.
Thus, the pattern ab is repeated.

2. ab _ _ _ b_ bbaa _
A. abaab       B. abbab       C. baaab       D. babba
Answer:      C , The series is abb / aab / abb / aab.
Thus, the pattern abb, aab is repeated.

3. _ baa _ aab _ a _ a
A. aabb       B. aaba       C. abab       D. baab
Answer:      C , The series is aba / aba / aba / aba.
Thus, the pattern aba is repeated.

4. _ _ babbba _ a _ _
A. ababb       B. baaab       C. bbaba       D. babbb
Answer:      D ,The series is bababb / bababb.
Thus, the pattern bababb is repeated.

5. aa _ ab _ _ aaa _ a
A. aaab       B. aabb       C. abab       D. baaa
Answer:      A , The series is aaaaba / aaaaba.
Thus, the pattern aaaaba is repeated.

6. a _ bbc _ aab _ cca _ bbcc
A. bacb       B. acba       C. abba       D. caba
Answer:      B , The series is aabbcc / aabbcc / aabbcc.
Thus, the pattern aabbcc is repeated.

7. ab _ aa _ bbb _ aaa _ bbba
A. abba       B. baab       C. aaab       D. abab
Answer:      B , The series is abb / aaabbb / aaaabbbb / a.
Thus, the letters are repeated twice, then thrice, then four times and so on.

8. bc _ b _ c_ b _ ccb
A. cbcb       B. bbcb       C. cbbc       D. bcbc
Answer:      A , The series is bccb / bccb / bccb.
Thus, the pattern bccb is repeated.

9. abb _ baa _ a _ bab _ aba
A. abba       B. abab       C. ccac       D. aabb
Answer:      A , The series is abba / baab / abba / baab / a.
Thus, the pattern abba, baab is repeated.

10. abca _ bcaab _ ca _ bbc _ a
A. ccaa       B. bbaa       C. abac       D. abba
Answer:      C , The series is abc / aabc / aabbc / aabbcc / a.

11. _ bbca _ bcca _ ac _ a _ cb
A. abcba       B. acbab       C. bacab       D. bcaab
Answer:      B ,The series is abbc / ac / bcca / bc / caab / cb.

12. _ bcc _ ac _ aabb _ ab _ cc
A. aabca       B. abaca       C. bacab       D. bcaca
Answer:      C , The series is bbccaa / ccaabb / aabbcc.
The letter pairs move in a cycle order.

13. a _ bccb _ ca _ cca _ baab _ c
A. ababc       B. abcaa       C. accab       D. bacaa
Answer:      A ,The series is aabcc / bbcaa / ccabb / aabcc.
The letters move in a cyclic order and in each group, the first and third letters occur twice.

14. ab _ aa _ caab _ c _ abb _ c
A. bbcaa       B. bcbca       C. cabac       D. cbbac
Answer:      D ,The series is abc / aabc / aabbc / aabbcc.
First all the letters occur once, then a occurs twice, then both a and b occur twice and finally all the three letters appear twice.

15. c _ baa _ aca _ cacab _ acac _ bca
A. acbaa       B. bbcaa       C. bccab       D. cbaac
Answer:      A , The series is cab / aa / cacab / cacab / aa / cacab / ca.
Thus, the pattern cacab, cacab, aa is repeated.

16. _ aba _ cabc _ dcba _ bab _ a
A. abdca       B. bcadc       C. abcdd       D. cbdaa
Answer:      A .The series  is aababcabcddcbacbabaa.
Thus, the letters equidistant from the beginning and the end of series are the same.

17. a _ cdaab _ cc _ daa _ bbb _ ccddd
A. bdbda       B. bddca       C. dbbca       D. bbdac
Answer:      D , The series is abca / aabbccdd / aaabbbcccddd.
Thus, each letter of first sequence is repeated two times in the second sequence and three times in the third sequence.

18. a _ abbb _ ccccd _ ddccc _ bb _ ba
A. abcda       B. abdbc       C. abdcb       D. abcad
Answer:      C The series is aaa / bbbb / cccc / dddd / cccc / bbbb / a.

19. _ bcdbc _ dcabd _ bcdbc _ dc _ bd
A. aaaaa       B. ccccc       C. bbbbb       D. ddddd
Answer:      A , The series is abcd / bcad / cabd / abcd / bcad / cabd.
Thus, the pattern abcd / bcad / cabd is repeated twice.

20. adb _ ac _ da _ cddcb _ dbc _ cbda
A. bccba       B. cbbaa       C. ccbba       D. bbcad
Answer:      B ,  The series is adbc acbd abcd dcba dbca cbda.
Thus, the letters equidistant from the beginning and the end of series are the same.

21. c _ bbb _ _ abbbb _ abbb _
A. aabcb       B. abccb       C. abacb       D. bacbb
Answer:      B ,The series is cabbbb / cabbbb / cabbbb.
Thus, the pattern cabbbb is repeated.

22. b _ abbc _ bbca _ bcabb _ ab
A. acaa       B. acba       C. cabc       D. cacc
Answer:      C , The series is bcab / bcab / bcab / bcab / bcab.
Thus, the pattern bcab is repeated.

23. ac _ cab _ baca _ aba _ acac
A. aacb       B. acbc       C. babb       D. bcbb
Answer:      A , The series  is acac / abab / acac / abab / acac.
Thus, the pattern acac, abab is repeated.

24. _ acca _ ccca _ acccc _ aaa
A. acca       B. caaa       C. ccaa       D. caac
Answer:      B , The series is ca / ccaa / cccaaa / ccccaaaa.

25._  bc _ _ bb _ aabc
A. acac       B. babc       C. abab       D. aacc
Answer:      A ,The series is abc / cab / bca / abc.

26. aa _ aaa _ aaaa _ aaaa _ b
A. baaa       B. bbaa       C. bbbb       D. bbba
Answer:      D , The series is aab / aaab / aaaab / aaaaab.
Thus, the number of a`s is increasing by one in the successive sequence.

27. aba _ baca _ ba _ bacaabac _ aca
A. cacb       B. ccab       C. cabc       D. abcc
Answer:      A , The series is abac / baca / abac / baca / abac / baca.
Thus, the pattern abac, baca is repeated.

28. ab _ bc _ c _ ba _ c
A. baac       B. aabb       C. caab       D. aaab
Answer:      C ,The series is abc / bca / cab / abc.
Thus, the letters are written in a cyclic order.

29. a _ ca _ bc _ bcc _ bca
A. bbaa       B. bbab       C. aabb       D. baba
Answer:      A , The series is abcab / bcabc / cabca.

30. ab _ bcbca _ _ c _ bab
A. acbc       B. baaa       C. abcc       D. ccaa
Answer:      D ,The series is abcbc / bcaca / cabab.
Thus, the series consists of three sequences.
The first sequence begins with a, the second with b and the third with c.
Each sequence consists of a letter followed by other two letters repeated twice.

31. a _ cacbc _ baca _ _ b
A. baba       B. babc       C. abac       D. cacb
Answer:      B , The series is abcac / bcaba / cabcb.
Thus, the series consits of three sequence.
The first three letters of each sequence are in a cyclic order and the last two letters of each sequence are the same as the first and third letters of the sequence.

32. _ aaba _ bba _ bba _ abaa _ b
A. aabab       B. ababa       C. baaba       D. bbaba
Answer:      A , The series is aaab / aabb / abbb / aaab / aabb.

33. ab _ bbc _ c _ ab _ ab _ b
A. ccaac       B. cbabc       C. cacac       D. bccab
Answer:      C , The series is abc / b / bca / c / cab / a / abc / b.

34. _ bca _ cca _ ca _ b _ c
A. aaaaa       B. bbbab       C. aabaa       D. bbabb
Answer:      B , The series is bbca / bcca / bcaa / bcaa / bbc.

35. b _ ac _ cc _ cb _ ab _ ac
A. cbaba       B. bbaac       C. abbbc       D. aabba
Answer:      D ,The series is baac / accb / cbba / baac.

36. c _ ac _ aa _ aa _ bc _ bcc
A. cabba       B. ccbbb       C. bbbbb       D. cbacb
Answer:      B ,The series is ccacc / aabaa / bbcbb / cc.

37. abc _ d _ bc _d _ b _ cda
A. bacde       B. cdabe       C. dacab       D. decdb
Answer:      C , The series is abcdd / abccd / abbcd / a.

38. ba _ b _ aab _ a _ b
A. abaa       B. abba       C. baab       D. babb
Answer:      B , The series is baab / baab / baab.
Thus, the pattern baab is repeated.

39. gfe _ ig _ eii _ fei _ gf _ ii
A. eifgi       B. figie       C. ifgie       D. ifige
Answer:      C , The series is gfeii / gfeii / gfeii / gfeii.
Thus, the pattern gfeii is repeated.

40.  mnonopqopqrs _ _ _ _ _
A. mnopq       B. oqrst       C. pqrst       D. qrstu
Answer:      C , The series is mno / nopq / opqrs / pqrst.