Aptitude Material Numbers and Alphabet series

CHAPTER-4

NUMBERS & ALPHABETICAL SERIES TEST

Type 1 : NUMBER TEST.

Directions: In this type of questions, a long series of numbers is given. The candidate is required to find out how many times a number satisfying the given conditions.

Examples

Example 1. How many 3’s are there in the following sequence which are neither preceded by 6 nor immediately followed by 9?

9 3 6 6 3 9 5 9 3 7 8 9 1 6 3 9 6 3 9

(a) one

(b) two

(c) three

(d) four.

Solution. Two. The numbers satisfying the given conditions, can be shown as follows:

9 3 6 6 3 9 5 9 3 7 8 9 1 6 3 9 6 3 9.

Example 2. How many even numbers are there in the following sequence of numbers which are immediately followed by an odd number as well as immediately preceded by an even number?

8 6 7 6 8 9 3 2 7 5 3 4 2 2 3 5 5 2 2 8 1 1 9

(a) one

(b) three

(c) six

(d) four

Solution. Four. The numbers satisfying the given conditions, can be shown as follows:

8 6 7 6 8 9 3 2 7 5 3 4 2 2 3 5 5 2 2 8 1 1 9.

EXERCISE (A)

1. In the series. 6 4 1 2 2 8 7 4 2 1 5 3 8 6 2 1 7 1 4 1 3 2 8 6 how many pairs of successive numbers have a difference of 2 each?

a. 4

b. 5

c. 6

d. 7

2. Count each 7 which is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 7’s are there?

5 7 2 6 5 7 3 8 3 7 3 2 5 7 2 7 3 4 8 2 6 7 8

a. 2

b. 3

c. 4

d. 5

3. How many 5’s are there in the following sequence which are immediately followed by 3 but not immediately preceded by 7?

8 9 5 3 2 5 3 8 5 5 6 8 7 3 3 5 7 7 5 3 6 5 3 3 5 7 3 8

a. 1

b. 2

c. 3

d. 4

4. How many 6’s are there in the following series of numbers which are preceded by 7 but not immediately followed by 9?

6 7 9 5 6 9 7 6 8 7 6 7 8 6 9 4 6 7 7 6 9 5 7 6 3

a. 4

b. 3

c. 2

d. 1

5. How many 6’s are there in the following number sequence which are immediately preceded by 9 but not immediately followed by 4?

5 6 4 3 2 9 6 3 1 6 4 9 6 4 2 1 5 9 6 7 2 1 4 7 4 4 9 6 4 2

a. 1

b. 2

c. 3

d. 4

6. If the numbers from 1 to 45 which are exactly divisible by 3 are arranged in ascending order, minimum number being on the top, which would come at the ninth place from the top?

a. 24

b. 15

c. 27

d. 30

Directions (Qs. 7-9): Study the following number sequence and answer the question given below it:

5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6

7. How many odd numbers are there in the sequence which are immediately followed by an odd number?

a. 1

b. 5

c. 3

d. 4

8. How many even numbers are there in the sequence which are immediately preceded by an odd number but immediately followed by an even number?

a. 2

b. 3

c. 1

d. 4

9. How many odd numbers are there in the sequence which are immediately preceded and also immediately followed by an even number?

a. 1

b. 2

c. 3

d. 4

Directions (Qs. 10-12) : Study the following numbers sequence and answer the question given below it:

5 6 8 6 7 6 5 6 5 6 8 5 9 6 5 6 9 6 8 6 5 5 6 8 6 5 9 5 6 9 5 6 8

10. How many 6’s in the series are preceded by 5 but not followed by 9?

a. 4

b. 6

c. 7

d. 5

11. Which number has the second least frequency?

a. 6

b. 7

c. 8

d. 9

12. If the first three numbers were named group first. The next three group second, the next three group third and thus process continued till the end with group 11^th and the numbers in each group were added together, which group will have the highest score?

a. 4^th

b. 6^th

c. 9^th

d. 5^th

Directions (Qs. 13-14) : Study the number series given below and answer the questions that follow:

7 8 9 7 6 5 3 4 2 8 9 7 2 4 5 9 2 9 7 6 4 7

13. How many 7’s are preceded by 9 and followed by 6?

a. 3

b. 2

c. 5

d. 4

14. Which number have equal frequency?

a. 865

b. 245

c. 253

d. 375

15. In the following series of numerals, how many 2’s are followed by 1’s but not preceded by 4?

4 2 1 2 1 4 2 1 1 2 4 4 4 1 2 2 1 2 1 4 4 2 1 4 2 1 2 1 2 4 1 4 2 1 2 4 1 4 6

a. 5

b. 4

c. 3

d. 2

16. In the series 6 4 1 2 2 8 7 4 2 1 5 3 8 6 2 1 7 1 4 1 3 2 8 6 how many alternative pairs of numbers have a difference of 2?

a. 4

b. 3

c. 2

d. 1

17. How many numbers amongst the numbers 9 to 54 are there which are exactly divisible by 9 but not by 3?

a. 5

b. 6

c. 8

d. Nil

18. How many 7’s are there in the following series which are not immediately followed by 3 but immediately preceded by 8?

8 9 8 7 6 2 2 6 3 2 7 9 7 3 2 8 7 2 7 7 8 7 3 7 7 9 4

a. 2

b. 3

c. 10

d. 0

Type 2: ALPHABETICAL ORDER OF WORDS.

Directions : Arrange the given words in alphabetical order and choose the one that given in question.

Example 1. In a telephone directory, which of the following names will appear in the middle?

(a) sajewat

(b) segvan

(c) sajevar

(d) sajewet

(e) salwar

Solution. Sajewat. The correct alphabetical order of the given words is shown below:

Sajevar, sajewat, sajewet, salwar and segvan.

Example 2. Arrange the given words in alphabetical order and choose the one that comes first.

(a) Dictum

(b) Dictionary

(c) Didactic

(d) Dictate

(e) Diastole.

Solution. Diastole. The correct alphabetical order of the given words is:

Diastole, Dictate, Dictionary, Dictum, Didactic.

Example 3. Arrange the given words in alphabetical order and select one that comes in the middle.

(a) Hilt

(b) History

(c) Hillock

(d) Heaven

(e) Hawker

Solution. Hillock. The correct alphabetical order of the given words is:

Hawker, Heaven, Hillock, Hilt, History.

Example 4. Arrange the given words in alphabetic order and select one that comes at the second place.

(a) converse

(b) curator

(c) cushion

(d) current

(e) cutaneous

Solution. Curator. The correct alphabetical order of the given words is:

Converse, Curator, Current, Cushion, Cutaneous.

Example 5. Arrange the given words in alphabetical order and select the correct sequence.

1. credential 2. creed 3. crease 4. cremate 5. credible

(a) 1, 5, 3, 4, 2

(b) 5, 1, 2, 3, 4

(c) 1, 2, 3, 4, 5

(d) 3, 1, 5, 2, 4

Solution. 3, 1, 5, 2, 4. The correct alphabetical order the given words is:

crease, credential, credible, creed, cremate.

Example 6. Arrange the given words in the order which they occur in a telephone directory and select of that comes in the middle.

(a) Jenson

(b) Jaina

(c) Jaisons

(d) Jetley

(e) Jainson

Solution. Jaisons. The correct alphabetical order Jaina, Jainson, Jaisons, Jenson, Jetley.

EXERCISE 4 (B)

Directions : Arrange the given words in alphabetical order and select one that comes first.

1. a. Sport b. Squash c. Spouse d. Sporadic e. Sprout

2. a. Cloud b. Grunt c. Middle d. Chain e. Mob

3. a. Science b. Script c. Scripture d. Scruting e. Scramble

4. a. Narrate b. Naughty c. Nascent d. Native e. Nature

5. a. Charge b. Certify c. Homage d. Filter e. Chastise

6. a. Grand b. Gradient c. Granary d. Granule e. Grammar

7. a. Heavy b. Heredity c. Hedge d. Herald e. Hesitate

8. a. Blast b. Bondage c. Bonafide d. Bottle e. Boisterous

9. a. Prank b. Practise c. Prayer d. Praise e. Practical

10. a. Probe b. Proceed c. Proclaim d. Probate e. Problem.

Directions: Arrange the given words in alphabetical order and select one that comes in the middle.

11. a. Revive b. Rumour c. Remove d. Rigour e. Retrospect

12. a. Shocks b. Shock c. Snooker d. Sharp e. Sound

13. a. Bicycle b. Bitter c. Brink d. Bishop e. Bifocal

14. a. Devise b. Dew c. Devour d. Deduce e. Dexterity

15.a. Passion b. Partition c. Parlour d. Particle e. Participate.

16. a. Entry b. Entreat c. Every d. Ensure e. Ettlorescent

17. a. finish b. Fissure c. First d. Fiscal e. Firmament

18. a. Antigen b. Antique c. Antipathy d. Branch e. Apology.

19. a. Pepsin b. People c. Penitent d. Penalty e. Penury

20. a. Radar b. Radius c. Racket d. Radiate e. Radical

Directions: Arrange the given words in alphabetical order and select one that comes at the second place.

21. a. Achieve b. Appreciate c. Afforest d. Alive e. Anticipate.

22. a. Vibrate b. Verrigate c. Trench d. Wavering e. Vindictive

23. a. Murder b. Mink c. Multitude d. Music e. Multiple

24. A. genuine b. Gentle c. Generous d. Gesture e. Gourd

25. a. Shudder b. Shroud c. Shuffle d. Shuttle e. Shroud

26. a. Never b. Nemiss c. Ninth d. Narcotic e. Niger

27. a. Yearn b. Yield c. Zygote d. Wrong e. Wrought

28. a. Tempest b. Tennis c. Tendor d. Tender e. Terminal

29. a. Invent b. Intestive c. Interlude d. Interview e. Interface.

30. a. Eager b. Ecstasy c. Emergency d. Explosion e. Entaemotogy

31. a. Collect b. Cover c. Caught d. Career e. Callous

32. a. Hesitate b. Hamper c. Hectic d. Hollow e. Hunter

33. a. Institution b. Examination c. Derive d. Inference e. Pillow

34. a. Actuate b. Acquit c. Accumulate d. Abandon e. Achieve

35. a. Hobby b. Hoarse c. Holiday d. Hobble e. Hollow

Directions: Arrange the given words in the alphabetical order and select the correct sequence.

36. 1. Seldom 2. Send 3. Select 4. Seller 5. Selfish

a. 2,1,5,4,3

b. 1,3,5,4,2

c. 2,5,4,1,3.

d. 2,1,4,5,3

37. 1. Long 2. Late 3. Liver 4. Letter 5. Luminous 6. Load

a. 2,4,3,6,1,5

b. 3,1,6,2,4,5

c. 2,4,5,3,6,1

d. 1,6,3,2,5,4

38. 1. Pestle 2. Pestilence 3. Pester 4. Pest 5. Pessimist

a. 4,3,1,5,2

b. 3,4,2,5,1

c. 5,4,3,2,1

d. 4,5,1,2,3

EXERCISE 4 (C)

Type 3 : LETTER – WORD PROBLEMS.

Example 1. If any two letters in the word ‘PRISON’ have as many letters between them in the word as there are in the English alphabet, they form an alpha-pair. How many such alpha-pairs are there in the word ‘PRISON’?

(a) 1

(b) 2

(c) 3

(d) Nil

(e) More than 3

Solution. More than 3.

Letters in the word P R I S R I S O R I S O N O N

Letters in the alphabet P Q R S R Q P O R Q P O N O N

Example 2. How many pairs of letters are there in the word ‘ADEQUATELY’ which have as many letters between them in the word as in the alphabet?

(a) 1

(b) 2

(c) 3

(d) 4

Solution. 3.

Letters in the word D E Q U A T Q U A T E L

Letters in the alphabet D E Q R S T Q P O N M L

1. How many pairs of letter are there in the word ‘BUCKET’ which has many letters between them in the word as in the alphabet?

a. 4

b. 3

c. 2

d. 1

e. More than four

2. How many pairs of letters are there in the word ‘SEQUENTIAL’ which have as many letters between them as are in the alphabet?

a. 1

b. 2

c. 3

d. 4

e. Nil

3. How many pairs of Letters are there in the word ‘CARROT’ which have as many letters between them in the word as in the alphabet?

a. 2

b. 1

c. 3

d. 4

e. More than 4.

4. How many pairs of letters are there in the word ‘PENCIL’ which have as many letters between them in the word as in the alphabet?

a. 1

b. 2

c. 3

d. Nil

e. None of those.

5. How many pairs of letters are there in the word ‘DONATE’ which have as many letters between them as there are in the alphabet?

a. 1

b. 2

c. 3

d. Nil

e. None of those.

6. How many pairs of letters are there in the word ‘CHAIRS’ which have as many letters between them as there are in the alphabet?

a. 1

b. 2

c. 3

d. 4

e. None

7. How many pairs of letters are there in the word ‘CLANGOUR’ which have as many letters between them in the word as in the alphabet?

a. 1

b. 2

c. 3

d. 4

e. 5

8. How many pairs of letters in the word ‘DABBLE’ have as many letters between them in the word as in the alphabet?

a. 1

b. 2

c. 3

d. Nil

e. More than three

9. How many letters are there in the word ‘CREATIVE’ which has many letters between them in the word as in the alphabet?

a. 1

b. 2

c. 3

d. 4

e. None

Type 4 A: ALPHABETICAL SERIES (MISSING TERM)

EXERCISE 4 (D)

Directions: Find out the missing term out of the given options.

Example 1. R, M, …….., F, …….

(a) C, B

(b) J, H

(c) B, H

(d) I, D

Solution. I, D. Letters are given in reverse order and 4, 3, 2 and 1 letters are missing between two consecutive letters.

Example 2. BEN, KNQ, TWZ, ……..

(a) ILL

(b) CFI

(c) BDF

(d) ADG

Solution. CFI. All the letters of each term are moved nine steps forward to get the corresponding letters of the next term.

Example 3. b, e, d, f, ………, h, j, ………., l.

(a) i, m

(b) m, i

(c) i, n

(d) j, m

Solution. i, m. This series can be divided into three groups.

I. b e d

II. f i h

III. j m l

In each group, first letter is moved two steps forward to get second letter and the second letter is moved one step backward to get the third letter.

Example 4. A, B, D, G, ……

(a) M

(b) L

(c) K

(d) H

Solution. K. The first, second, third …….. letters are moved one, two, three, ……. Steps forward respectively to get the next term.

1. Z, U, Q, ….., L.

a. I

b. K

c. M

d. N

2. A, C, F, H, ….., M

a. J

b. K

c. L

d. I

3. CAT, FDW, IGZ,…..

a. KTC

b. LJC

c. KJA

d. LHD

4. ex fu ir….ol ri

a. no

b. lo

c. mn

d. op

5. AB, BA, ABC, CBA, ABCD,…..

a. DCBA

b. DBAC

c. BACD

d. ACBD

6. U, O, I, ….., A

a. S

b. C

c. E

d. G

7. BDF, CFI, DHL,….

a. EJO

b. EMI

c. EIM

d. CJM

8. YEB, WFD, UHG, SKI,….

a. QGL

b. QNL

c. TOL

d. QOL

9. Z, L, X, J, V, H, T, F…..

a. S, E

b. Q, D

c. R, E

d. R, D

10. AZ, CX, FU,……

a. IR

b. IV

c. KP

d. JQ

11. MHZ, NIW, OKT, PNQ,…..

a. RRN

b. QRM

c. QQN

d. QRN

12. FLP, INS, LPV,…..

a. ORY

b. VXY

c. SVW

d. UXZ

13. sng rif qje pkd….

a. ole

b. nlb

c. ole

d. nme

14. AZ, GT, MN,….., YB

a. KF

b. RX

c. SH

d. TS

15. BF, CH,….., HO, LT.

a. EL

b. EM

c. EK

d. DN

16. 3F, 6G, 11I, 18L,….

a. 27P

b. 27Q

c. 21O

d. 25N

17. C4X, F9U, I16R,…..

a. L27P

b. L25O

c. L25P

d. K25P

18. KM5, IP8, GS11, EV14,….

a. BX17

b. BY17

c. CY18

d. CY17

19. 2Z5, 7Y7, 14X9, 23W11, 34V13,…

a. 27U24

b. 47U15

c. 45U15

d. 47V14

20. JEZ, K4X, 17V,….H16R, M22P

a. I11T

b. L11T

c. L12T

d. L11S

Type 4 B: INCOMPLETE SERIES

Directions: In this type of alphabetical series, some letters are missing. The candidate is required to find out the sequence of letters and choose the correct one of the given options.

Examples

Example 1. bac …babacc … … ccbabaccb … bac.

(a) abac

(b) cbba

(c) bbaa

(d) cbaa

Solution. cbaa. The pattern of the series is baccbabaccbabaccbabaccbabac

Example 2. baca …b … cabba … abbacabb … ca

(a) abcb

(b) baca

(c) bcca

(d) caca

Solution. baca. The pattern of the series is bacabbacabbacabbacabbaca.

Example 3. ac … bcac … be … cbbc … cbbcac.

(a) abba

(b) bcac

(c) bbaa

(d) cbaa

Solution. bbaa. The pattern of the series is acbbcacbbcacbbcacbbcac

Example 4. cbaa … be … acc … aa bcaa … cba

(a) babc

(b) cabc

(c) bacc

(d) abcb

Solution. cabc. The pattern of the series is cbaacbcaaccbaacbcaaccba.

Example 5. a … caabc … bba … caab … abbab

(a) abca

(b) aabc

(c) babc

(d) bacc

Solution. babc. The pattern of the series is abcaabcabbabcaabcabbab.

EXERCISE 4 (E)

Directions : In this type of alphabetical series, some letters are missing. Choose the correct one of the given alternatives.

1. c….bba…cab…ac…ab…ac

a. abcbc

b. acbcb

c. babcc

d. bcacb

2. …cb…ca…bacb…ca…bac…d

a. bddddb

b. bbbbdd

c. addddb

d. addbbb

3. aab…ab…cabcca…bcab…c.

a. bbbc

b. bbab

c. cabc

d. cbab

4. cccbb…aa…cc…bbbaa…c.

a. acbc

b. baba

c. acba

d. baca

5. abca…bcaab…aa…caa…c.

a. bbac

b. bbaa

c. acac

d. acbb

6. b…b…bb…,…bbb…bb…b

a. bbbbba

b. bbaaab

c. ababab

d. aabaab

7. …aba…cabc…deba…bab…a.

a. abdca

b. cbadc

c. abcdd

d. cbdaa

8. a…cdaab…cc…daa…bbb…ccddd.

a. bdbda

b. bddca

c. bbcad

d. bbdac

9. a…abbb…ccccd…ddccc…bb…ba

a. abcda

b. abdbc

c. abdcb

d. abcad

10. …bcdbc…deabd…bcdbc…dc…bd

a. aaaaa

b. ccccc

c. bbbbb

d. ddddd

11. b…b…cab…baca…cba…a…

a. cacbbb

b. cacbcb

c. cabcbc

d. aaccbc

12. adb…ac…da…cddcb…..dbc…cbda.

a. bccba

b. cbbaa

c. ccbba

d. bbcad

13. a…bbc…aab…cca…bbcc

a. bacb

b. acba

c. abba

d. caba

14. ab…aa…bbb…aaa…bbba

a. abba

b. baab

c. aaab

d. abab

15. bc…b…c…b…ccb

a. cbcb

b. bbcb

c. cbbc

d. bcbc

16. abb…baa…a…bab…aba.

a. abba

b. abab

c. ccac

d. aabb

17. abca…bcaab…ca…bbe…a

a. ccaa

b. bbaa

c. abac

d. abba

18. a…bbaa…baa…b

a. aba

b. aab

c. abb

d. bab

19. b…aab…aabb…a

a. aba

b. bab

c. aab

d. bba

20. …bbb…a…bb…

a. abbb

b. baaa

c. baba

d. aabb

21. bb…ab…ba…bb…bb…a

a. aaaab

b. babab

c. bbbab

d. baaba

22. aba…aba…aba…aba…

a. bbbb

b. abab

c. bbba

d. abba

23. aa…baa…baa……

a. abab

b. aaab

c. abaa

d. baab

24. a…bb…a…bb…

a. bbba

b. abab

c. baba

d. abaa

25. a…ab…a…a…a

a. bbaa

b. aaab

c. aabb

d. bbba

26. c…bbb…….abbbb…abbb…

a. aabcb

b. abccb

c. abacb

d. bacbb

27. b…abbc…bbca…bcabb…ab.

a. acaa

b. acba

c. cabc

d. cacc

28. ac…cab…baca…aba…acac

a. aacb

b. acbc

c. babb

d. bcbb

29. ….acca…ccca…acccc…aaa

a. aacb

b. acbc

c. babb

d. caaa

30. …bc……bb…aabc

a. acac

b. babc

c. abab

d. aacc