In this type of test some numbers and/or alphabetical letters are given. They all form a series and change in a certain order. Series has one or more letters or numbers missing. The candi-dates are required to observe that specific order in which the number or letters would suit for the blank space if they continue to change in the same order.
It will be clarified from the following exam-ples.
Example 1. Which of the alternative figures would correctly fill in the blank space in the following series of numbers ?
6, 13, 27, 55, 111, —
(A) 225 (B) 224
(C) 223 (D) 231
(E) 230
Answer with Explanation—(C) 13 is grea-ter than the double of 6 by 1. Similarly 27 is greater than the double of 13 by 1. 55 is greater than the double of 27 by 1. 111 is greater than the double of 55 by 1. Thus, in blank space there be
2 × 111 + 1 i.e. 223
Hence the correct answer is (C).
Reasoning V. | 9 Example 2. Which one of the letter groups
given below would replace the question mark (?) in the letter series ?
YCL, MQZ, AEN, ?
(A) OSB (B) PUE
(C) MPX (D) OTC
(E) PVF
Answer with Explanation—(A) Last letter of the first group is L and the first letter of second group is M. Here, M is the next letter of L in alphabet. Similarly the last letter of second group is Z and the first letter of the third group is A.
Here A is the next letter of Z in alphabet. There-fore, the first letter of blank space should be the next letter of N, which is O. Besides, there is a gap of three letters between the first and second letters of each group. Therefore, second letter of blank space should be fourth letter after O i.e. it should be S. In given alternatives only (A) is such alternative that has first letter as O and second as S. Hence (A) is the correct answer.
Example 3. Some letters are missing in the following letter series. The missing letters are given in the proper sequence as one of the alter-natives among the five given below. Find the correct alternative.
a — b — c — a — b
(A) aabc (B) cbcb
(C) acba (D) cabc
(E) abca
Answer with Explanation—(D) If the letters of the alternatives (D) are filled in the blank spaces of the series, then the series acbacbacb is formed in which acb is repeated thrice. Any other laternative answer does not form any particular series. Hence, the correct answer is (D).
Exercise
Directions—(Q. 1–12) Find out the number that would replace the question mark (?) in each of the following questions—
1. 20, 32, 45, 59, 74, ?
(A) 95 (B) 90
(C) 85 (D) 79
(E) 74
2. 210, 195, 175, 150, 120, ?
(A) 75 (B) 80
(C) 85 (D) 90
(E) 95
3. 3, 5, 10, 12, 24, 26, ?
(A) 52 (B) 30
(C) 28 (D) 48
(E) 26
4. 3, 6, 5, 20, 7, 42, 9, ?
(A) 60 (B) 54
(C) 72 (D) 66
(E) 46
5. 2, 3, 5, 6, 7, 9, 10, 11, 13, ?
(A) 12 (B) 15
(C) 14 (D) 16
(E) 19
6. 3, 8, 11, 19, 30, 49, ?
(A) 87 (B) 79
(C) 77 (D) 73
(E) 78
7. 5, 4, 15, 7, 23, 11, 29, 16, 33, ?
(A) 22 (B) 29
(C) 34 (D) 15
(E) 28
8. 10, 12, 18, 22, 34, 42, 66, 82, ?
(A) 148 (B) 138
(C) 130 (D) 126
(E) 127
9. 9, 17, 32, 61, 118, 231, ?
(A) 456 (B) 236
(C) 224 (D) 218
(E) 356
10. 5, 9, 16, 29, 54, 103, ?
(A) 102 (B) 94
(C) 103 (D) 200
(E) 92
11. 4, 9, 20, 43, 90, ?
(A) 180 (B) 182
(C) 179 (D) 185
(E) 172 12. 6, 12, 21, 33, ?
(A) 38 (B) 40
(C) 45 (D) 48
(E) 51
10 | Reasoning V.
Directions—(Q. 13–18) Find out the missing term in each of the following questions—
13. EDBA, KJHG, QPNM, ?
(A) KIGH (B) QOMK
(C) WVTS (D) ZXVU
(E) LMQR
14. ced, ihg, lkm, ……, uts
(A) npo (B) orq
(C) oqp (D) qro
(E) roq
15. ACE, GIK, ?, SUW, YAC
(A) MOQ (B) MNP
(C) MOP (D) MPQ
(E) QMP
16. AZBY, ?, EVFU, GTHS
(A) BYCZ (B) CYDR
(C) CXDW (D) EXDZ
(E) HTSG
17. ……, zxv, fdb, ljh, rpn
(A) ywv (B) ayw
(C) lxu (D) wxu
(E) pnr
18. prt, ……, bdf, hjl, npr
(A) vya (B) xza
(C) vxz (D) uyb
(E) avy
Directions—(Q. 19–20) Complete the follo-wing series from the given alternatives—
19. DKY, FJW, HIU, JHS, ?
(A) KGR (B) LFQ
(C) KFR (D) LGQ
(E) MAC 20. afo, zgl, bhi, yif, ?
(A) cjd (B) ckc
(C) xjc (D) cjc
(E) jcj
Directions—(Q. 21–25) In each of the following questions which number will complete the series if filled in the blank spaces—
21. 4, 8, 16, ……, 44
(A) 24 (B) 28
(C) 32 (D) 40
(E) 42
22. 1, 5, ……, 30, 55
(A) 9 (B) 10
(C) 13 (D) 14
(E) 15
23. 18, 14, 12, ……, 14, 18
(A) 10 (B) 12
(C) 14 (D) 16
(E) 18
24. 1, 3, 6, 10, 15, ……, 28, 36
(A) 20 (B) 21
(C) 23 (D) 24
(E) 25
25. 1, 5, 21, 57, 121, ……
(A) 150 (B) 176
(C) 200 (D) 221
(E) 201
Directions—(Q. 26–30) Some letters are missing in the following letter-series. The missing letters are given in the proper sequence as one of the alternatives among the five given below. Find out the correct alternative.
26. a—bbc—aab—cca—bbcc
(A) bacb (B) acba
(C) abba (D) caba
(E) bcba
27. ab—aa—bbb—aaa—bbba
(A) abba (B) baab
(C) aaab (D) abab
(E) abbb
28. bc—b—c—b—ccb
(A) cbcb (B) bbcb
(C) cbbc (D) bcbc
(E) bbcc
29. abb—baa—a—bab—aba
(A) abba (B) abab
(C) ccac (D) aabb
(E) bbaa
30. abca—bcaab—aa—caa—c
(A) ccaa (B) acbb
(C) abac (D) abba
(E) aaba
Reasoning V. | 11
Answers with Explanations
1. (B) The differences of two consecutive num-bers are 12, 13, 14, 15 and 16 respecti-vely.
2. (C) The differences of two consecutive num-bers are 15, 20, 25, 30 and 35 respec-tively.
3. (A) On adding 2 in the first number, second number is obtained and on doubling the second number, third number is obtai-ned.
4. (C) In the series second term is double of the first term, fourth term is four times of third term, sixth term is six times of fifth term and thus eight term will eighth times of the seventh term.
5. (C) There are three series in the original series—
2, 6, 10, …; 3, 7, 11, … and 5, 9, 13, … In each series the difference of two con-secutive terms is 4.
6. (B) Third term is the sum of first and second terms. Fourth term is the sum of second and third terms. The same order is repea-ted.
7. (A) Two series are formed in this—
5,15,23,29,33,…and4, 7,11,16,22,…
8. (C) Third terms is two less than the double of first term and fifth term is also two less than the double of third term. The same order is repeated. Fourth term is two less than the double of second term and sixth term is two less than the double of fourth term. The same order is repeated.
9. (A) Second term is 1 less than the double of first term. Third term is 2 less than the double of second term. The same order is repeated.
10. (D) The numbers are as follows—
5,5×2–1=9,9×2 –2=16,16×2–3
= 29, 29 × 2 – 4 = 54, 54 × 2 – 5 = 103, 103 × 2 – 6 = 200
11. (D) The numbers are as follows—
4,4×2+1=9,9×2+2 = 20, 20 × 2 + 3
= 43, 43 × 2 + 4 = 90, 90 × 2 + 5 = 185 12. (D) The difference of two consecutive
num-bers are 6, 9, 12 and 15.
13. (C) In each term first and second letters are in reverse order of alphabet. Similarly the third and fourth letters are. Besides, there is a gap of one letter between the second and third letters.
14. (C) By interchanging the second and third letters of first term, the letters are arran-ged in alphabetical order. Similarly by interchanging the first and third letters of second term, the letters are arranged in alphabetical order. The same order is repeated. Besides, after arranging the letters in alphabetic order, there is a gap of one letter between the last letter of first term and first letter of second term.
15. (A) In each term one letter is missing bet-ween two consecutive letters.
16. (C) In each term the first and third letters are in alphabetical order while the second and fourth letters are in reverse order.
17. (B) In each term between the two conse-qutive letters one letter is missing in reverse direction of alphabet.
18. (C) In each term between the two consecu-tive letters one letter is missing. Besides, the first letter of each term stands two places ahead from the last letter of its previous term.
19. (D) The first letters of each term are in alphabetical order and one letter is miss-ing between them. The second letters of each term are in reverse order of alphabet. Third letters of each are also reverse order of alphabet and one letter is missing between them.
20. (D) First letters of first and third terms are in alphabetical order while the first letters of second and fourth terms are in reverse order. Second letter of each term is in alphabetical order while third letter of each term is in reverse order and two letters are missing between third letters of two consecutive terms.
21. (B) The differences of two consecutive num-bers are 4, 8, 12 and 16 i.e. they are mul-tiple of 4.
22. (D) On keeping 14 in blank space the diffe-rences between two consecutive numbers are 22, 32, 42, and 52.
23. (B) The series is completed on reversing the first three terms in reverse order.
12 | Reasoning V.
24. (B) The differences between two consecutive numbers are 2, 3, 4, 5, 6, 7 and 8 res-pectively.
25. (D) The differences between two consecutive numbers are 22, 42, 62, 82 and 102. 26. (B) aabbcc is repeated thrice.
27. (B) The series formed is—
abbaaabbbaaaabbbb.
28. (A) bccb is repeated thrice.
29. (A) abbabaab is repeated twice.
30. (B) abca is repeated four times.