**Campus Recruitment – Logical Reasoning – **Series

**Concepts**

**Number Series**

In number series questions, a series of numbers is given with one term missing. You need to identify the pattern and find the next number or the missing number. Any number series is formed by the combination of operator and operand. Operators are +, x, ÷. Operand is the factor between two numbers in the sequence.

**Example**: 3, 7,11, 15,19, x. Find the value of ‘x’?

**Explanation**: Here, if we observe first two numbers, i.e. 3 and 7. The operator is + (addition) and the operand is 4. If we observe the entire series, we can easily identify the operator and the operand, they are + and 4 respectively. So, ‘x’ will replace with 23.

**Guidelines to identify the pattern:**

Slep-1:Generally the pattern follows mathematical operation from first term to next term and so on.

Step-2: If the given number series is increasing or decreasing in a small amount, then there must be addition or subtraction between the numbers

Step-3: It the given number senes is increasing or decreasing in a large amount, then there must be multiplication or division between the numbers.

Stcp-4: Jf the given number senes is increasing or decreasing with a very large amount, then there must be square /cube or square root/cube root between the numbers.

**Examples:**

Understand the logical sequence of numbers given below and find the value at ‘x’.

1) 7,15, 24, 34, 45, x.

**Explanation:**

If you observe the series, the difference between the given numbers is constantly increasing. So the next number in the series is 57.

2) 289,169, 121, 49, x.

**Explanation:**

If you observe the series, each number is followed by prime squares in the descending order. So the next number in the series is (5²) = 25.

3) 1, 8, 27, 64, 125, x.

**Explanation:**

If you observe the series, each number is followed by cubes of natural numbers. So the next number in the series is 6³ = 216.

4) 1, 2, 6, 30, 210, x.

**Explanation**:

In this series, each number is multiplied by the next prime number starting from 2. So, 210 x 11 = 2310.

5) 2, 3, 5, 8, 13, 21, 34, x.

**Explanation**:

Every number is added to its previous number.

**Alphabet Series (Word Series)**

In this type of series sequence of alphabets are given in a logical order.You have to understand the logic interpreted in the given series and find the missing or the next alphabet/ word.

**Examples:**

Find the missing word in the following series.

1) EGI, JLN, OQS,____

**Explanation:** Every alphabet is moved 5 steps forward.

E + 5 = J ; G + 5 = L; I + 5 = N

Hence, the next term in the series is ‘TVX’.

2) AZ, BY, CX,___ EV, FU.

**Explanation:** The first letter in the series is increased by 1 and second letter is decreased by 1. Hence, the answer is ‘DW’.

**Letter Series**

Letter series type of questions usually 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 required to choose this alternative as the answer.

**Examples:**

1) Find the missing letters in the following series. ab_ _ b_bab_ab_b_

a)aababa b)abaaba c) babcba d) bbaaba e) ababab

**Explanation**: The pattern in the above series is ababb/ ababb/ ababb. Hence, the missing number in the series is ‘ababab’. Hence, option-e is correct choice.

**Exercise**

**Directions to solve:** Understand the pattern given in the following questions and find the value of ‘x’.

1) 81, 80, x, 67, 51, 26.

a) 74 b) 78 c) 79 d) 76 e) None

2) 12, 21, 37, 73, 49, X.

a) 92 b) 94 c) 86 d) 102 e) None

3) 3,6 , 12, x, 33, 48

a) 18 b) 22 c) 27 d) 21 e) None

4) 55, 56, 55, 59, 51, 60, x.

a) 31 b) 33 c) 87 d) 57 e)None of

5) 11,12,13,15,17, X.

a) 18 b) 19 c) 10 d) 20 e) 23

6) 60, 30, 70, 40, 80, 50, x.

a) 70 b) 80 c) 90 d) 60 e) 95

7) 2, 4,12, 60, 420, x

a) 840 b) 1020 c) 3780 d) 4620 e) None of

8) 3768, 6, 733, 4, 9004, 4, 2314,1, 2014, X?

a) 6 b) 4 c)3 d) 5 e) 7

**Find out the odd number in the following series.**

9) 24, 51, 105, 213, 427, 861

a) 105 b) 213 c) 51 d) 427 e) 861

10) 5, 7.5, 15, 37.5, 112

a) 15 b) 7.5 c) 37.5 d) 5 e) 112

11) 90, 72, 56, 44, 30

a) 90 b) 72 c) 56 d) 44 e) 30

**Direction (12 to 21):** Find the value missing word in the following series which follows a logical order.

12) BE, HK, NQ,___ .

a) TV b) TU c) XD d) TW e) WT

13) E-5, G-7, 1-9, K-ll,__,__ .

a) M-13, O -15 b) M-12 O -15 c) N-14, P-16 d) N-15, P-17 e) none of these

14) HS, IR, JQ, KP, .

a) OL b) QR c) LO d) MO e) NO

15) EVIC, DWHB, CXGA,___.

a) BYLO b) BYMQ c) BYNO d) BYFZ e) CYQM

16)____ , ayw, gee, mki, sqo.

a) bwz b) zxw c) usq d) may e) xyv

17) QPO, SRQ, UTS, WVU,____ .

a) AYZ b) ZYA c) YXW d) VWX e) XVZ

18) KST, JTS, IUR, HVQ,____ .

a) GWR b) GWP c) WGR d) WGP e) WGRT

19) HYD, IVF, KRH,____ , RGL.

a) NMJ b) NMI c) MNJ d) MNI e) LMJ

20) J2Z, K4X, I7V, L11T, H16R,___ .

a) LI IS b) CY24 c) MP22 d) MP24 e) M22P

21) LN18, JQ25, HT32, FW39, ___.

a) DY43 b) DZ46 c) DA43 d) DX43 e) CZ46

**Find out the missing letters in the following series and choose the correct alternatives.**

22) a_aab_b_.cc .

a) abbcc b) abccb c) acbba d) ccbba e) aabbcc

23) a_a_bab_ab_baa_.

a) baaab b) bbaab c) bbbab d)aaaba e) aabba

24) _Q_S_PS_P_RS.

a) RPQRQ b) PRQRQ c) PQRRQ

d) PRQPQ e) PSRPQ

25) aba_b_a_abb_.

a) aabb b)aaaa c) abbb d)abab e)aaab

26) RR_QQQ_P_RR_QQ_.

a) RQPRP b) RPPRQ c) RPRPQ

d) RQRPQ e) RPRQP

27) MN_PPO_MM_OP_ON_.

a) OOMNQ b) MNOPQ c) OMNPO

d) ONNPM e) PMNNO

28) XY _Y_ X_ Y_ X___ Y_

a) XYYYYYY b) XYYYXYY c) YXXXYYY

d) YXXXXXX e) XYXYXYY

29) RS_RSS_R_SS_S_SS.

a) RRSSS b) SSSRS c) RRRSS

d) SRSRS e) None of these

30) XXY_YZ,_XY, Y_Z, X_ Y, YY_ .

a) YYZXY b) XZYZY c) YXYXZ

d) XZXZZ e) None

31) X_ YY_Z, XX_YZ_ X_.

a) XYZXY b) XZYYX ‘ c) XZZYY

d) XXZZY e) XZYZX

**Explanations**

12) d; First and second letters are moved 6 letters forward. Hence, the next term in the series is ‘TW’.

13) a; The letters in the series are increased by 2 and indicates their positional values in English alphabets. Hence, the next term in the series is ‘M-13, O -15’.

14) c; Here, first letter of each term is moved one step forward and second letter is moved one step backward. Hence, next term in the series is ‘LO’.

15) d; From first word to second word the corresponding letter are following the pattern like, -1, +1, -1, -1. Hence, next term in the series is ‘BYFZ’.

16) c; From one word to another, the corresponding letters are increased by 6. Hence, the answer is ‘usq’.

17) c; Each term in the series consists of three consecutive letters in reverse order. The first letter of each term and last letter of the next term are same. Hence, the next term in the series is ‘YXW’.

18) b; The first and third letters of each term are moved one step backward and the second letter is moved one step forward to obtain the corresponding letters of the next term. Hence, next term in the series is ‘GWP’.

19) a; The first letters of words are increasing in the order of 0, 1, 2, 3. The second letters are decreasing by 3, 4, 5, 6. The third letters in the series are increasing by 2. Hence, the missing term is ‘NMJ’.

20) e; Here the last letters are decreasing by 2, the numbers are increasing by 2, 3, 4, 5 etc. The first letters of the words at odd positions are decreasing by 1 and that of even positions are increasing by 1. Hence, the word in the given series is ‘M22P’.

21) b; Here, the first letter of each term is moved two steps backward and second letter is moved three steps forward to obtain the corresponding letter of the next term. The number in each term is increased by 7 from its previous term. Hence, next term in the series is DZ46.

22) a; The pattern of this series is aaaa, bbbb, cccc, so on. Hence the correct alternative is ‘abbcc’.

23) a; The pattern of the series is abaab/abaab/abaab so on. Hence, the correct alternative is ‘baaab’.

24) b; The pattern of the series is PQRS/ QPSR/ PQRS/ QPSR so on. Hence, the correct alternative is ’PRQRQ’.

25) d; The pattern of the above series is ab/ aabb/ aaabbb/ aaaabbbb so on. Hence, the correct answer is ‘abab’.

26) b; The pattern is RRR/ QQQ/ PPP/ RRR/…. so on. Hence, the correct alternative is ‘RPPRQ’.

27) d; The pattern is MNOP/ PONM/ MNOP/ PONM and so on. Hence, the correct alternative is ‘ONNPM’.

28) b; XY/ XYY/ XYYY/ XYYYY Hence, the answer is option (b).

29) a; The pattern is RS/ RR/ SSRR/ SSSSSS so on.Hence, the correct choice is ‘RRSSS’.

30) c; The pattern is XXY/ YYZ/ XXY/ YYZ/… so on. Hence, the correct option is ‘YXYXZ’.

31) e; The pattern is XX/ YY/ ZZ/ XX/ YY/ ZZ so on. Hence, the correct alternative is ‘XZYZX’.

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