MATHEMATICAL LOGIC NOTES
REASONING (INCLUDING MATHEMATICS)
Reasoning is of two types, namely, verbal and non-verbal. Verbal reasoning is
basically about words rather than things. Verbal reasoning tests use words, letters, and
numbers and require logical reasoning and a reasonable knowledge of English. It is also
necessary to be familiar with simple, basic mathematical operations such as addition,
subtraction, division, and multiplication. Non-verbal is basically about figures.
As far as UGC NET Exam pattern is concerned, mathematical reasoning is covering
mainly verbal and basic mathematical skills such as series completion, coding and decoding,
classification (odd man out, and so on), and analogical relationship. Questions on direction
sense and seating arrangement also appear regularly in the exam.
Some topics such as Direction Sense and Venn Diagrams combine both verbal and
non-verbal skills.
Series Completion
A series may be a number series or letter series. There are several kinds of series such
as finding the missing numbers, replacing the wrong numbers, finding the missing letters,
finding the wrong group of numbers or letters, etc.
NUMBER SERIES
Prime Number Series
Example-1
2, 3, 5, 7, 11, 13, …
a) 18 (b) 19 (c) 15 (d) 17
Solution: This series is a prime number series. So the next number in series is (d) 17.
Example-2
2, 5, 11, 17, 23, 31, 37, ….
a) 29 (b) 31 (c) 43 (d) 39
Solution: The prime numbers are written alternately. (c) 43
Difference Series
Example-3
2, 5, 8, 11, 14, 17, ….., 23, 26
a) 19 (b) 21 (c) 20 (d) 18
Solution: The difference between the numbers is (c) 2. (17+3=20)
Multiplication Series
Example-4
2, 6, 18, 54, ….., 486, 1458
a) 152 (b) 182 (c) 162 (d) 108
Solution: The numbers are multiplied by 3 to get the next number. (54 x 3 = 162) (c)
Example-5
3, 12, 48, ……, 768, 3072
a) 192 (b) 216 (c) 512 (d) 72
Solution: The numbers are multiplied by 4 to get the next number. (48 x 4 = 192) (a)
Division Series
Example-6
32, 48, 72, …., 162, 243
a) 84 (b) 96 (c) 108 (d) 132
Solution: Each number is being multiplied by 3/2 to get the next number. (c)
N
2 Series
Example-7
1, 4, 9, 16, 25, 36, …., 64
a) 42 (b) 44 (c) 45 (d) 49
Solution: The series is squares of 1, 2, 3, 4, and so on. (d)
Example-8
0, 4, 16, 36, 64, ….., 144
a) 100 (b) 84 (c) 96 (d) 120
Solution: The series is squares of even number such as 2, 4, 6, 8, 10 and 12. So, the answer is
102
= 100. (a)
N
2
– 1 Series
Example-9
0, 3, 8, 15, 24, 35, 48, 63, ….
a) 80 (b) 82 (c) 83 (d) None of these
Solution: The series is 12
– 1, 22
– 1, 32
– 1, and so on. The next number is 92
– 1 = 80. (a)
Alternative Solution: The differences between the numbers across the series are 3, 5, 7, 9, 11,
13, 15, and 17. The next number is 63 + 17 = 80.
N
2 + 1 Series
Example-10
2, 5, 10, 17, 26, 37, ……, 65
a) 50 (b) 48 (c) 49 (d) 51
Solution: The series is 12
+ 1, 22
+ 1, 32
+ 1, and so on. The next number is 72
+ 1 = 50. (a)
N
2 + N Series and N2
– N Series
Example-11
0, 2, 6, 12, 20, 30, …..., 56
a) 36 (b) 40 (c) 42 (d) None of these
Solution: The series is 0 (square) +0, 1 (square) + 1, 2 (square) + 2, 3 (square) + 3 and so on.
The missing number is 6 (square) + = 42. The next number is 62
+ 6 = 42. (c)
First Alternative Solution: The series is 0 x 1, 1 x 2, ….. 1 x 2, 2 x 3, 3 x 4, 4 x 5 and 5 x 6 =
30. The next number is 6 x 7 = 42.
Second Alternative Solution: The series is 12
– 1, 22
– 2, 32
– 3, 42
– 4, 52
– 5, 62
– 6, 72
– 7,
8
2
– 8, and so on.
N
3 Series
Example-12
1, 8, 27, 64, 125, 216, ….
a) 256 (b) 343 (c) 365 (d) 400
Solution: The series is 13
, 23
, 33
, etc. The missing number is 73
= 343. (b)
N
3 + 1 Series
Example-13
2, 9, 28, 65, 126, 217, 344, ….
a) 512 (b) 362 (c) 369 (d) 361
Solution: The series is 13
+1, 23
+1, 33
+1, and so on. Thus, the missing number is 83
+1 = 513. (a)
Reasoning is of two types, namely, verbal and non-verbal. Verbal reasoning is
basically about words rather than things. Verbal reasoning tests use words, letters, and
numbers and require logical reasoning and a reasonable knowledge of English. It is also
necessary to be familiar with simple, basic mathematical operations such as addition,
subtraction, division, and multiplication. Non-verbal is basically about figures.
As far as UGC NET Exam pattern is concerned, mathematical reasoning is covering
mainly verbal and basic mathematical skills such as series completion, coding and decoding,
classification (odd man out, and so on), and analogical relationship. Questions on direction
sense and seating arrangement also appear regularly in the exam.
Some topics such as Direction Sense and Venn Diagrams combine both verbal and
non-verbal skills.
Series Completion
A series may be a number series or letter series. There are several kinds of series such
as finding the missing numbers, replacing the wrong numbers, finding the missing letters,
finding the wrong group of numbers or letters, etc.
NUMBER SERIES
Prime Number Series
Example-1
2, 3, 5, 7, 11, 13, …
a) 18 (b) 19 (c) 15 (d) 17
Solution: This series is a prime number series. So the next number in series is (d) 17.
Example-2
2, 5, 11, 17, 23, 31, 37, ….
a) 29 (b) 31 (c) 43 (d) 39
Solution: The prime numbers are written alternately. (c) 43
Difference Series
Example-3
2, 5, 8, 11, 14, 17, ….., 23, 26
a) 19 (b) 21 (c) 20 (d) 18
Solution: The difference between the numbers is (c) 2. (17+3=20)
Multiplication Series
Example-4
2, 6, 18, 54, ….., 486, 1458
a) 152 (b) 182 (c) 162 (d) 108
Solution: The numbers are multiplied by 3 to get the next number. (54 x 3 = 162) (c)
Example-5
3, 12, 48, ……, 768, 3072
a) 192 (b) 216 (c) 512 (d) 72
Solution: The numbers are multiplied by 4 to get the next number. (48 x 4 = 192) (a)
Division Series
Example-6
32, 48, 72, …., 162, 243
a) 84 (b) 96 (c) 108 (d) 132
Solution: Each number is being multiplied by 3/2 to get the next number. (c)
N
2 Series
Example-7
1, 4, 9, 16, 25, 36, …., 64
a) 42 (b) 44 (c) 45 (d) 49
Solution: The series is squares of 1, 2, 3, 4, and so on. (d)
Example-8
0, 4, 16, 36, 64, ….., 144
a) 100 (b) 84 (c) 96 (d) 120
Solution: The series is squares of even number such as 2, 4, 6, 8, 10 and 12. So, the answer is
102
= 100. (a)
N
2
– 1 Series
Example-9
0, 3, 8, 15, 24, 35, 48, 63, ….
a) 80 (b) 82 (c) 83 (d) None of these
Solution: The series is 12
– 1, 22
– 1, 32
– 1, and so on. The next number is 92
– 1 = 80. (a)
Alternative Solution: The differences between the numbers across the series are 3, 5, 7, 9, 11,
13, 15, and 17. The next number is 63 + 17 = 80.
N
2 + 1 Series
Example-10
2, 5, 10, 17, 26, 37, ……, 65
a) 50 (b) 48 (c) 49 (d) 51
Solution: The series is 12
+ 1, 22
+ 1, 32
+ 1, and so on. The next number is 72
+ 1 = 50. (a)
N
2 + N Series and N2
– N Series
Example-11
0, 2, 6, 12, 20, 30, …..., 56
a) 36 (b) 40 (c) 42 (d) None of these
Solution: The series is 0 (square) +0, 1 (square) + 1, 2 (square) + 2, 3 (square) + 3 and so on.
The missing number is 6 (square) + = 42. The next number is 62
+ 6 = 42. (c)
First Alternative Solution: The series is 0 x 1, 1 x 2, ….. 1 x 2, 2 x 3, 3 x 4, 4 x 5 and 5 x 6 =
30. The next number is 6 x 7 = 42.
Second Alternative Solution: The series is 12
– 1, 22
– 2, 32
– 3, 42
– 4, 52
– 5, 62
– 6, 72
– 7,
8
2
– 8, and so on.
N
3 Series
Example-12
1, 8, 27, 64, 125, 216, ….
a) 256 (b) 343 (c) 365 (d) 400
Solution: The series is 13
, 23
, 33
, etc. The missing number is 73
= 343. (b)
N
3 + 1 Series
Example-13
2, 9, 28, 65, 126, 217, 344, ….
a) 512 (b) 362 (c) 369 (d) 361
Solution: The series is 13
+1, 23
+1, 33
+1, and so on. Thus, the missing number is 83
+1 = 513. (a)
