LawpreneurzLogical Reasoning
Introduction
ANALYSIS OF NUMERICAL SERIES: A close analysis of the above examples show that the number series can be of the following types.
 Pure Series: In this type the number follow a pattern which can be easily understood. The number itself may be:
 Perfect square
 Perfect cube
 Prime number
 Combination
Difference Series: The difference series in of the first number with the next number makes a series.
Ex: i) 1, 3, 5, 7, 9, 11, ……. The difference between two consecutive numbers is 2. So it makes a series.
Ex: ii) 1, 2, 4, 7, 11, 16……. The difference between the consecutive number is 1, 2, 3, 4, 5 and so on it also makes a perfect series.
COMPLETING THE GIVEN SERIES
Ex.1. Which is the number that comes next in the sequence?
1, 5, 13, 29, __ , 125
 32
 62
 61
 31
Sol. In this case, the series is increasing by +4, +8, +16, +32, +64. So our answer is 61, as by adding the number 32 to 29 we get the required number i.e. 61.
Ex.2. 1, 4, 9, 16, 25, ?
 35
 36
 48
 49
Sol.: The number are 1^{2}, 2^{2}, 3^{3}, 4^{2}, 5^{2},
Hence 6^{2} = 36
Ex.3. Which is the number that comes next in the sequence?
6, 11, 21, 36, 56, __
 42
 51
 81
 91
The answer here is (3) 81 because the series is progressing by factor of 5, 10, 15, 20, 25.
Ex. 4. Which is the number that comes next in the sequence?
0, 6, 24, 60, 120, 210, ?
 240
 290
 336
 504
Sol. Clearly, the given series is : 1^{3}  1, 2^{3}  2, 3^{3}  3, 4^{3}  4, 5^{3}  5, 6^{3}  6.
Next number = 7 ^{3} – 7 = 343 – 7 = 336
Hence the answer is (3)
Ex. 5. Which is the number that comes next in the sequence?
3, 7, 15, 31, 63, ?
 92
 115
 127
 131
Sol. Each number in the series is the preceding number multiplied by 2 and then increased by 1. Thus, (3 x 2) + 1 = 7, (7 x 2) + 1 = 15, (15 x 2) + 1 = 31 and so on
Missing number = (63 x 2) + 1 = 127
Hence the answer is (3)
Ex. 6. 3, 6, 18, 72, ?
 144
 216
 288
 360
Sol. The pattern is x 2, x 3, x 4, ____
Missing number = 72 x 5 = 360, i.e. answer is 360.
Generally, two kinds of series are asked in the examination. One is based on numbers and the other based on alphabets.
In questions based on series, some numbers or alphabets are arranged in a particular sequence. You have to decipher that particular sequence of numbers or alphabets and on the basis of that particular sequence of numbers or alphabets and on the basis of that sequence, find out the next number or alphabet of the series. Although there is no limit of logics which can be used to build a series, here are some important examples given which highlight the type of series asked in the examination.
Examples
1: Where the difference between two consecutive terms involves various arithmetic operation.
 2, 5, 8, 11, ……
The common difference is +3.  33, 25, 17, 9, ……
The common difference is 8.  4, 8, 24, ……
Here, the series in multiple of 4.  52, 26, 13, ……
The series is based on the rule that the every number is divided by 2 to get the next number.
2: Where the difference between the consecutive numbers is in some progression, i.e. A.P. or G.P.
 7, 18, 34, 55, ……
Here, the difference between the terms is +11, +16, +21, which are in A.P.  8, 9, 12, 21, 48, 129, ……
Here, the difference between the terms is +1, +3, +9, +24, +81. Here, these terms are in G.P.
3: Where series terms differ each other by perfect squares and cubes.
 5, 6, 10, 19, 35, ……
The common difference between the number of series is +(1)^{2}, +(2)^{2}, +(3)^{2}, +(4)^{2} ……  7, 8, 16, 43, 107, ……
The common difference between the term of series is 10743, 4316, 168, 87
(4)^{3}, (3)^{3}, (2)^{3}, (1)^{3}.  1, 4, 9, 16, ……
The term of series are (1)^{2}, (2)^{2}, (3)^{2}, (4)^{2}, ……  27, 64, 125, 216, ……
The term of series are (3)^{3}, (4)^{3}, (5)^{3}, (6)^{3}, ……
Exercise
 5, 14, 27, 44, 65, ?
 3, 4, 10, 33, 136, ?
 5, 6, 9, 18, 45, ?
 7, 24, 75, 228, ?
 17, 68, 612, ?
 84, 64, 46, 30,?
 2, 2, 4, 4, 6, 8, 8, ?
 3, 9, 9, 36, 180, ?
 1, 8, 9, 64, 25, 216, ?, ?
 4, 13, 53, 266, 1597, ?
 81, 72, 63, ?, 45
 7, 13, 21, ?, 43, 57
 3, 15, 35, ?, 99, 143
 9, 11, 15, 23, ?
 8, 15, 28, 53, ?
Solutions
 The difference in the successive terms of the series is increasing by 4. That is, 5 + 9 = 14, then 14 + 13 = 27, then 27 + 17 = 44, 65 + 25 = 90.
 From the first term onwards, the series is x 1 +1, x 2 +2, x 3 +3, x 4 +4 and finally it is 136 x 5 + 5 = 685.
 The difference between the consecutive terms goes on becoming 3 times.
Thus, 45 + 27 x 3 = 45 + 18 = 126.  The series is 7 +17 = 24. Then, 24 + 51 (17x3) = 75, 75 + 153 (51x3) = 228.
So, now it is 228 + (153 x 3) = 687. OR 7 x 3 +3 = 24, 24 x 3 + 3 = 75, 75 x 3 + 3 = 228. Hence next is 228 x 3 +3 = 687.  The series is 17 x 1^{2} = 17, 17 x 2^{2} = 68, 68 x 3^{2} = 612. Hence 612 x 4^{2} = 9792.
 The pattern of the series is 84 – 20 = 64, 64 – 18 = 46, 46 16 = 30 and hence, now it is 30 – 14 = 16.
 This is an alternative series arrangement. The odd terms is an even number series. The even terms is a double series, that is 2 x 2 = 4, 4 x 2 = 8, 8 x 2 = 16.
 The pattern of the series is 3 x 3 = 9, 9 x 4 = 36, 36 x 5= 180 and finally 180 x 6 = 1080.
 This is an alternative series arrangement. The odd terms is a series of square 3, 5, 7. The even terms is a series of cubes of numbers 2, 4, 6 and 8. Hence, the answer is 49, 512.
 The series is x 3 + 1, x 4 + 1, X 5 + 1 and so on.
 All the terms differ by the number 9. So, the answer is 54.
 The difference in the terms of the series is starting from the first term is +6, +8, +10, +2 and +14.
 The pattern of the series is 3 + 12 = 15, 15 + 20 = 35, so now it is 35 + 28 = 63, then 63 + 36 = 99. Hence the difference itself differs by +8.
 The pattern of the series is 9 + 2 = 11, 11 + 4 = 15, 15 + 8 = 23 and finally, it is 23 + 16 = 39.

13 = 7 x 2  1, 25 = 13 x 2  1
Hence, the next term is 49 = 25 x 2  1.
Exercise
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 1, 4, 9, 16, 25, (____)
 5
 36
 48
 49
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 20, 19, 17, (____), 10, 5
 12
 13
 14
 15
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 2, 3, 5, 7, 11, (_), 17
 12
 13
 14
 15
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 6, 11, 21, 36, 56, (___)
 42
 51
 81
 91
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 3, 9, 27, 81, (___)
 324
 210
 243
 162
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 2, 5, 9,(___), 20, 27
 16
 14
 18
 24
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 5, 9, 17, 29, 45, (___)
 65
 60
 70
 68
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 1, 6, 15, (___), 45, 66, 91
 25
 26
 27
 28
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 1, 2, 3, 5, 8, (___)
 13
 11
 9
 15
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 0.5, 1.5, 4.5, 13.5, (___)
 30.5
 45.5
 39.5
 40.5
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 121, 225, 361,(___)
 529
 441
 484
 729
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 19, 2, 38, 3, 114, 4, (___)
 228
 456
 256
 352
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 1, 2, 3, 6, 9, 18, (___), 54
 27
 18
 36
 81
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 12, 32, 72, 152, (___)
 312
 325
 515
 613
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 3, 6, 5, 20, 7, 42, 9, (___)
 72
 66
 60
 54
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 1, 3, 4, 8, 15, 27, (___)
 37
 44
 50
 55
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 95,115.5, 138, (___), 189
 162.5
 154.5
 164.5
 166.5
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 24, 60, 120, 210, (___)
 336
 330
 420
 525
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 5, 17, 37, 65, (____), 145
 97
 95
 99
 101
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 34, 18, 10, 6, 4, (___)
 3
 2
 1
 0
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 1, 2, 5, 12, 27, 58, 121, (___)
 246
 247
 248
 249
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 0.5, 0.55, 0.65, 0.8, (___)
 0.9
 0.82
 1
 0.95
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 17, 19, 23, 29, (___), 37
 36
 35
 33
 31
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 3, 12, 27, 48, 75, 108, (___)
 192
 183
 147
 162
Question : In this questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the black spaces.
Q. 563, 647, 479, 815, (___)
 672
 386
 143
 279
Solution
 B
 C
 B
 C
 C
 B
 A
 D
 A
 D
 A
 B
 A
 A
 A
 C
 A
 A
 D
 C
 C
 D
 C
 C
Lawpreneurz Details of lecture
Sr No.  Topics 

Lecture 1  Alphabetical Series 
Lecture 2  Numerical Series 
Lecture 3  Coding Decoding 
Lecture 4  Directions 
Lecture 5  Blood Relations 
Lecture 6  Analytical Reasoning ( Tabular Arrangement, Seating Arrangement) 
Lecture 7  Coded Inequality 
Lecture 8  Facts Inferences and Judgements 
Lecture 9  Arguments 
Lecture 10  Statement and Assumptions 
Lecture 11  Statement and Conclusions 
Lecture 12  Syllogism 
Lecture 13  Logical Consistency 
Lecture 14  Assertion and Reason 
Lecture 15  Course of Action 
Lecture 16  Clock 
Lecture 17  Calendar 
Lecture 18  Logical Connectives 
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