Series Completion

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In verbal series, words, letters or digits are given in a specific sequence/order and we have to find out next word, letter or digit to complete the given series.

TYPES OF SERIES COMPLETION

TYPE 1: ALPHABET SERIES

In series, given alphabets follows a particular pattern or sequence or order. We have to detect the pattern from the given alphabets and find missing alphabet or the next alphabet to continue the pattem.

* There are no set niles.

* There can be omission of alphabets in an order.

° Alphabets may also be omitted in an increasing/decresing order, which may be direct increase or decrease.

° Insolving these questions pattern of the alphabet series should be noted.

POSITION OF ALPHABETS

SOME SKIPPING PATTERNS

Regular Order : Number of alphabets skipped remains the same.
Ex. A, D, G, J,………… ?
Ans. M
as 2 alphabets are skipped each time. A B C D E F G H I J K L M
Increasing order: Each time the number of alphabets skipped increases in a given pattern.
Ex. A, C, F, J, O ?
Ans: U (A B C D E F G H I J K L M N O P O R S T U ) Each time number of Ietter skipped increases by 1.
Decreasing order: Each time the number of letters skipped decreases ina given pattern.
Ex: A G L P S ?
Ans. U
Here, Number of Letters skipped decreases by one each time i.e. first 5, then 4, then 3, and so on.
Interlinked Series: In this two or more series are attached together. These different scries follows their own rules.
Ex: A D F J I M R?
Ans. V
Here there are two interlinked series.

SOLVED EXAMPLES

1. Which term comes next in the sequence AC, FH, KM, PR ?

(a) UW (b) VW (c) UX (d) TV (¢) None of these

Answer is (a)

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

2. Find next term in the series

BMO, EQQ, HQS, ?

(a) KSU (b) LMN (c) SOV (d) SOW

Solution: Clearly. we observe the follow ing pattern :

The first letter follows the pattern +3 Le. .

B—E——H— (k)

The second letter follows the pattern +2 ie.

M—O—Q -à (S)

The third letter follows the pattern +2 ie.

O—Q—S—(U)

Thus the missing term is KSU, Hence the answer Is (a).

3. Which term comes next in the series YEB, WFD, UHG, SKI, ?

(a) QOL (b) QGL (c) TOL (d) ONL

Solution: We observe the following patterns.

Thus, the missing term ts QOL, Hence the answer is (a).

PRACTICE TEST-I

1. R, U, X,A, D,?

(a) F (b) G (c) H (d) I

2. ab, ba, abc, cba, abcd , ……….

(a) acbd (b) bacd (c) cabd (d) dcba

3. …., SIY, OEU, KAQ, GWM, CSI

(a) VMC (b) WMC (c) VNC (d) WNC

4. YXZ, XWY.,…………, WUW, UTV, TSU

(a) VWT (b) WXV (c) TVX (d) WVX

5. PTVX, AEGI, ……….., WACE, HLNP

(a) KNQT (b) LPRT (c) KPQS (d) HKLO

6. Z, Y, X, U, T, S, P, O, N, K, ?, ?

(a) H,G (b) H, I (c) I,H (d) JI

7. GH, JL, NQ, SW, YD, ?

(a) EJ (b) FJ (c) EL (d) FL

8. ajs, gpy, ?, sbk, yhq

(a) dmv (b) mve (c) oua (d) qz

9. PMT, OOS, NQR, MSQ, ?

(a) LUP (b) LVP (c) LVR (d) LWP

10. BZA, DYC, FXE, ?, JVI |

(a) HUG (b) HWG (c) UHG (d) WHG (e) None of these

11. ABD, DGK, HMS, MTB, SBL, ?

(a) XKW (b) ZAB (c) ZKU (d) ZKW

12. WFB, TGD, QHG, ?

(a) NIJ (b) NIK (c) NJK (d) OIK (e) PIK

13. UPI, ?, ODP, MBQ, IAW .

(a) RHJ (b) SHJ (c) SV (d) THK (e) TH

14. ATTRIBUTION, TTRIBUTIO, RIBUTIO, IBUTI, ?

(a) IBU (b) UT (c) UTI (d) BUT (e) None of these

15. ADVENTURE, DVENTURE, DVENTUR, ?, VENTU

(a) DVENT (b) VENTURE (c) VENTUR (d) DVENTU (e) None of these

TYPE 2: NUMBER SERIES –

In number series. some numbers are arranged in a particular order. All the numbers form a series and change a in certain order, Sometimes, one or more numbers are wrongly put in the number series. We are required to observe the trend in which number change in the series and find out which number/numbers misfit into the series.

SOLVED EXAMPLES

Ex 1: 4, 8, 28, 80, 244, ?

(a) 278 (b) 428 (c) 628 (d) 728

Sol. The terms of given series are 3¹ +1, 3²-1, 3³+ 1, 3⁴-1, 3⁵+ 1, 3⁶ – 1 :

SO, missing term = 3⁶ — 1 = 729 — 1 = 728

Hence, the answer is (d) on we

Ex 2: 0, 6, 24, 60, 120, 210, ?

(a) 240 (b) 290 (c) 336 (d) 504

Sol. The given series is : 1³ – 1, 2³– 2, 3³– 3 , 4³– 4, 5³– 5, 6³– 6

therefore missing term = 7³ — 7 = 343 — 7 = 336 Hence, the answer is (c) .

Ex 3: 1, 3, 3, 6, 7, 9, 2, 12, 12

(a) 10 (b) 11 (c) 12 d) 13

Sol. The given sequence is a combination of two series. a

l. 1, 3.7, 2,21 and Il. 3, 6, 9, 12

The pattern followed in I is +2, +4,….. and pattern followed in IT is +3 so, missing number = 7+6= 13 Hence, the answer is (d)

Type 2 : (a) Triangular Pattern Series

Sometimes, the difference between the consecutive terms of a series, again form a series. The difference between the consecutive terms of the new series so formed, again form a series. This pattern continues till we attain a uniform difference between the consecutive terms of the series.

Ex 5: Find the missing term in the series 3, 20, 63, 144, 275 , ?

Sol.

Series I: 3 20 63 144 275?

Series II: 17 43 81 131?

Series III : 26 38 50?

Series IV: 12 12?

Now pattern in series III is +12.

So, missing term in series III is 50 + 12 = 62;

Missing term in series II is 131 + 62 = 193 ;

Missing term Is series I is 275 + 193 = 468 ;

Thus, the missing term is 468.

Direct Method: Missing term is = 275 + (131 + 50 + 12) = 468

2. (b) Elementary Idea of Progression

I. Arithmetic Progression (A.P.) : The progression of the form a, a+ d, a+ 2d, a+ 3d…….–.. is known as an A.P. with term = a and common difference = d

Ex. 3, 6, 9, 12, ………… iS an A.P. with

a=3 andd=6-3=3.

In an A.P., we have nth term = a + (n-1) d.

II. Geomeric Progression (G-P.): The progression of the form a, ar, ar², ar³, ……… is known as GP. with first term as a and commomn ratio = r

Ex. 1,5, 25, 125, ……….. is a GP. With a = 1

and r = 5/1 = 25/5 = 125/25 =5

In a GP. we have nth term = ar^n-1

PRACTICE TEST-I

Direction (1 to 30) : In each of the following questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

1. 1, 9, 25, 49, ? 121

(a) 64 (b) 81 (c) 91 (d) 100

2. 4, 7, 12, 19, 28, ?

(a) 30 (b) 36 (c) 39 (d) 49

3. 6, 12, 21, ?, 48 :

(a) 33 (b) 38 (c) 40 (d) 45

4. 6, 11, 21, 36, 56 ?

(a) 42 (b) 51 (c) 81 (d) 91

5. 120, 99, 80, 63, 48, ?

(a) 35 (b) 38 (c) 39 (d) 40

6. 22, 24, 28, ? , 52, 84

(a) 36 (b) 38 (c) 42 (d) 46

7. 0, 2, 8, 14, ?, 34

(a) 20 (b) 23 (c) 24 (d) 25

8. 28, 33, 31, 36, ?, 39

(a) 32 (b) 34 (c) 38 (d) 40

9. 6, 17, 39, 72?

(a) 83 (b) 94 (c) 116 (d) 127

10. 1, 4, 10, 22, 46 ?

(a) 64 (b) 86 (c) 94 (d) 122

11. 4, 9, 25, ?, 121, 169, 289, 361

(a) 49 (b) 64 (c) 81 (d) 87

12. 1, 1, 2, 6, 24, ? , 720

(a) 100 (b) 104 (c) 108 (d) 120

13. 4, 6,9, 13 ?

(a) 17 (b) 19 (c) 20 (d) 22

14. 5760, 960, ?, 48, 16, 8

(a) 120 (b) 160 (c) 192 (d) 240

15. 1, 2, 6, 7, 21, 22, 66, 67, ?

(a) 70 (b) 134 (c) 201 (d) 301

16. 48, 24, 96, 48, 192, ?

(a) 76 (b) 90 (c) 96 (d) 98 a

17. 9, 27, 31, 155, 161, 1127, ?

(a) 316 (b) 1135 (c) 1288 (d) 2254

18. 2, 3, 3, 5, 10, 13, ? , 43, 172, 177

(a) 23 (b) 38 (c) 39 (d) 40

19. 8, 28, 116, 584, ?

(a) 1752 (b) 3502 (c) 3504 (d) 3508

20. 3, 7, 23, 95, ?

(a) 62 (b) 128 (c) 479 (d) 575

21. 1, 5, 14, 30, 55, 91, ?

(a) 130 (b) 140 (c) 150 (d) 160

22. 198, 194, 185, 169, ?

(a) 92 (b) 112 (c) 136 (d) 144

23. 24, 60, 120, 210, ?

(a) 300 (b) 336 (c) 420 (d) 525

24. 563, 647, 479, 815, 2 3

(a) 672 (b) 386 (c) 279 (d) 143

25. 45, 54, 47, ?, 49, 56, 51, 57, 53

(a) 48 (b) 50 (c) 55 (d) None of these

PRACTICE TEST-III

TYPE 3: WRONG NUMBER SERIES

Directions (1 to 5) : In the following number series, one of the numbers does not fit into the series. Find the wrong number.

1. 1788, 892, 444, 220, 112, 52, 24

(a) 52 (b) 112 (c) 220 (d) 444 (e) 892

2. 225, 289, 338, 374, 397, 415, 424

(a) 415 (b) 289 (c) 338 (d) 374 (e) 397

3. 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

4. 35, 118, 280, 600, 1238, 2504, 5036

(a) 18 (b) 280 (c) 600 (d) 1238 (e) 2504.

5. 10, 12, 28, 90, 368, 1840, 11112

(a) 1840 (b) 308 (c) 90 (d) 28 (e) 12

Directions (6 to 10) : In cach of the following questions one number is wrong in the series. Find out the wrong number.

6. 1,2,5, 14, 41, 124

(a) 2 (b) 5 (c) 14 (d) 41 (e) 124

7. 100, 97, 90, 86, 76, 71, 62

(a) 62 (b) 71 (c) 76 (d) 86 (e) 97

8. 1, 2, 6, 24, 120, 620, 5040

(a) 5040 (b) 620 (c) 120 (d) 24 (e) 6

9. 4, 10, 22, 40, 84, 94, 130

(a) 22 (b) 40 (c) 64 (d) 84 (e) 130.

10. 1, 4, 8, 16, 31, 64, 127, 256

(a) 31 (b) 16 (c) 8 (d) 6 (e) 1

Directions (11 to 20) : In each of the following questions, one number is wrong in the series. Find out the wrong number:

11. 49, 56, 64, 71, 81, 90, 100, 110

(a) 56 (b) 64 (c) 71 (d) 81 (e) 90

12. 9, 13, 21, 37, 69, 132, 261

(a) 21 (b) 37 (c) 69 (d) 132 (e) 261

13. 9, 15, 24, 34, 51, 69, 90

(a) 15 (b) 24 (c) 51 (d) 69 (e) 34

14. 1, 3, 8, 19, 42, 88, 184

(a) 3 (b) 8 (c) 19 (d) 42 (e) 88

15. 3, 9, 36, 72, 216, 864, 1728, 3468

(a) 3468 (b) 1728 (c) 864 (d) 216 (e) 42

16. 2, 4, 8, 16, 48, 64, 128, 256

(a) 4 (b) 8 (c) 16 (d) 48 (e) 128.

17. 5, 8, 10, 12, 15, 18, 20, 23

(a) 8 (b) 12 (c) 15 (d) 18 (e) 20

18. 2, 5, 11, 23, 48, 95, 191, 383

(a) 5 (b) 11 (c) 23 (d) 48 (e) 95

19. 3, 10, 36, 180, 1080, 7560, 60480

(a) 3 (b) 10 (c) 1080 (d) 7560 (e) 180

20. 93, 309, 434, 498, 521, 533

(a) 309 (b) 434 (c) 498 (d) 521

(e) None of these |

Directions (21 to 25) : In each of the following number series, a wrong number is given. Find out that wrong number.

21. 258, 130, 66, 34, 18, 8, 6

(a) 130 (b) 66 (c) 34 (d) 18 (e) 8

22. 2, 6, 24, 96, 285, 568, 567

(a) 6 (b) 24 (c) 96 (d) 285 (e) 568

23. 4, 5, 14, 39, 103, 169, 290

(a) 5 (b) 14 (c) 39 (d) 103 (e) 169

24. 6072, 1008, 200, 48, 14, 5, 3

(a) 1008 (b) 200 (c) 48 (d) 14 (e)5

25. 2, 3, 6, 15, 42, 125, 366

(a) 3 (b) 6 (c) 15 (d) 125 (e) 366

ANSWERS :

1. (b) 2. (e) 3. (c) 4. (d) 5. (a) 6. (e) 7. (a) 8. (b) 9. (d) 10. (c) 11. (c) 12. (d) 13. (e) 14. (e) 15. (a) 16. (d) 17. (b) 18. (d) 19. (b) 20. (d) 21. (e) 22. (b) 23. (d) 24.(a) 25. (d)

PRACTICE TEST-IV

1. 80 50 130 100 180 150

900 (A) (B) (C) (D) (E)

Which number will come in place of (C) ?

(a) 1050 (b) 920 (c) 1000 (d) 950 (e) None of these

2. 60 121 131 264 284 571

120 (A) (B) (C) (D) (E)

Which number will come in place of (D) ?

(a) 324 (b) 1011 (c) 1010 (d) 514 (e) None of these

3. 2 4 9 20 43 90

31 (A) (B) (C) (D) (E)

Which number will come in place of (D) ?

(a) 7132 (b) 115 (c) 68 (d)117 (e) None of these

4. 14 42. 147 388 2646 13230

8 (A) (B) (C) (D) (E)

Which number will come in place of (E) ?

(a) 28 (b) 1176 (c) 294 (d)216 (e) None of these

5. 140 68 36 16 10 3

284 (A) (B) (C) (D) (E)

Which number will come in place of (C) ?

(a) 50 (b) 34 (c) 64 (d) 57 (e) None of these

6. 25 194 73 154 105 130

14 (A) (B) (C) (D) (E)

Which number will come in place of (E) ?

(a) 120 (b) 116 (c) 119 (d)202 (e) None of these

7. 6 8 20 36 76

20 (A) (B) (C) (D)

Which number will come in place of (C) ?

(a) 148 (b) 130 (c) 136 (d) 140 (e) None of these

8. 2 9 45 247.5 1485

3 (A) (B) (C) (D)

Which number will come in place of (B) ?

(a) 64.5 (b)72 (c) 7 (d)68 (e) 67.5

9. 3 4 10 33 136 685

q (A) (B) (C) (D) (E)

Which number will come in place of (E) ?

(a)1160 (b) 920 (c) 1165 (d) 1840 (e) None of these

10. 200 184 193 157 182 118

150 (A) (B) (C) (D) (E)

Which number will come in place of (C) ?

(a) 132 (b) 115 (c) 68 (d) 117 (e) None of these

Il. 4 7 12 19 28 39

5 (A) (B) (C) (D) (E)

Which number will come in place of (D) ? :

(a) 29 (b) 24 (c) 36 (d) 42 (e) None of these

12. 77 78 77 81 73 82

86 (A) (B) (C) (D) (E)

Which number will come in place of (C)?

(a) 98 (b) 161 (c) 182 (d)90

(e) None of these

13. 2 3 8 27 112 565

5 (A) (B) (C) (D) (E)

Which number will come in place of (E) ?

(a) 680 (b) 670 (c)510 (d)430

(e) None of these

14. 121 250 777 3172 15985

160 (A) ( B) (C) (D)

Which number will come in place of (D) ?

(a) 4166 (b) 4132 (c) 4068 (d) 4128 (e) None of these

15. 50 99 301 1177 6141

80 (A) (B) (C) (D)

Which number will come in place of (C) ?

ANSWERS

I (d) 2 (e) 3 (e) 4 (e) 5 (b) 6 (c) 7 (a) 8 (e) 9(c) 10(e)

IL (a) 12(d) 13 (e) 14 (e) 15 (b)