PPT: Number and Letter Series | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

 Page 1


Number and Letter 
Series
Page 2


Number and Letter 
Series
What is a Number 
Series?
Definition
A sequence of numbers following a specific 
pattern or rule.
Objective
Identify the pattern to find missing terms or 
detect wrong numbers.
Importance
4-5 marks in 2-3 minutes in Quantitative 
aptitude section.
Page 3


Number and Letter 
Series
What is a Number 
Series?
Definition
A sequence of numbers following a specific 
pattern or rule.
Objective
Identify the pattern to find missing terms or 
detect wrong numbers.
Importance
4-5 marks in 2-3 minutes in Quantitative 
aptitude section.
Common Types of Number Series
Addition/Subtraction 
or 
Multiplication/Divisio
n
P a tte r n: T erms change by 
adding/subtracting or 
multiplying/dividing.
Tip: Check differences for 
addition; ratios for 
multiplication.
E xa mp le: 19, 23, 39, 75, ?, 
239
Differences: +4, +16, 
+36, +64, +100 
(squares: 2², 4², 6², 8², 
10²)
Missing term: 
75 + 64 = 139
Perfect Square or 
Perfect Cube
P a tte r n: T erms are 
squares (n²) or cubes (n³) 
of integers.
E xa mp le: 4, 18, 48, 100, 
180, ?
Form: n³ - n² (n = 2, 3, 4, 
5, 6, ...)
Missing term: 
7³ - 7² = 343 - 49 = 294
Factorisation/Prime 
Factorisation
P a tte r n: T erms are 
products of prime 
numbers.
E xa mp le: 6, 15, 35, 77, 
143, ?
Products: 2×3, 3×5, 
5×7, 7×11, 11×13, 
13×17
Missing term: 
13×17 = 221
Fibonacci Series
P a tte r n: Each term is the sum of the two previous terms.
E xa mp le: 1, 4, 5, 9, 14, 23, ?
1 + 4 = 5, 4 + 5 = 9, ..., 14 + 23 = 37
Missing term: 37
Page 4


Number and Letter 
Series
What is a Number 
Series?
Definition
A sequence of numbers following a specific 
pattern or rule.
Objective
Identify the pattern to find missing terms or 
detect wrong numbers.
Importance
4-5 marks in 2-3 minutes in Quantitative 
aptitude section.
Common Types of Number Series
Addition/Subtraction 
or 
Multiplication/Divisio
n
P a tte r n: T erms change by 
adding/subtracting or 
multiplying/dividing.
Tip: Check differences for 
addition; ratios for 
multiplication.
E xa mp le: 19, 23, 39, 75, ?, 
239
Differences: +4, +16, 
+36, +64, +100 
(squares: 2², 4², 6², 8², 
10²)
Missing term: 
75 + 64 = 139
Perfect Square or 
Perfect Cube
P a tte r n: T erms are 
squares (n²) or cubes (n³) 
of integers.
E xa mp le: 4, 18, 48, 100, 
180, ?
Form: n³ - n² (n = 2, 3, 4, 
5, 6, ...)
Missing term: 
7³ - 7² = 343 - 49 = 294
Factorisation/Prime 
Factorisation
P a tte r n: T erms are 
products of prime 
numbers.
E xa mp le: 6, 15, 35, 77, 
143, ?
Products: 2×3, 3×5, 
5×7, 7×11, 11×13, 
13×17
Missing term: 
13×17 = 221
Fibonacci Series
P a tte r n: Each term is the sum of the two previous terms.
E xa mp le: 1, 4, 5, 9, 14, 23, ?
1 + 4 = 5, 4 + 5 = 9, ..., 14 + 23 = 37
Missing term: 37
Advanced Number Series Types
Alternate Pattern Series
P a tte r n: Two patterns alternate between 
terms.
E xa mp le: 2, 7, 4, 9, 6, 11, ?
Series 1: 2, 4, 6, ... (+2); Series 2: 7, 9, 11, ... 
(+2)
Missing term: 8
Decimal Pattern Series
P a tte r n: Involves decimals with consistent 
increments.
E xa mp le: 0.1, 0.2, 0.3, 0.4, ?
+0.1 each term
Missing term: 0.5
Bracket Pattern Series
P a tte r n: Combines operations within brackets.
E xa mp le: 3, 28, 180, ?, 3676
(3+1)×7 = 28, (28+2)×6 = 180, (180+3)×5 
= 915
Missing term: 915
Dual Pattern Series
P a tte r n: Two interrelated series.
E xa mp le: 15, 9, 8, 12, 36, 170 and 19, a, b, ?, d, 
e
Pattern: (n-6)×1, (n-5)×2, ...; for 19: (19-
6)×1 = 13, ..., (16-4)×3 = 36
Missing term: 36
Factorial Based Series
P a tte r n: T erms involve factorials (n!).
E xa mp le: 1, 2, 6, 24, 120, ?
1!, 2!, 3!, 4!, 5!, 6!
Missing term: 6! = 720
Page 5


Number and Letter 
Series
What is a Number 
Series?
Definition
A sequence of numbers following a specific 
pattern or rule.
Objective
Identify the pattern to find missing terms or 
detect wrong numbers.
Importance
4-5 marks in 2-3 minutes in Quantitative 
aptitude section.
Common Types of Number Series
Addition/Subtraction 
or 
Multiplication/Divisio
n
P a tte r n: T erms change by 
adding/subtracting or 
multiplying/dividing.
Tip: Check differences for 
addition; ratios for 
multiplication.
E xa mp le: 19, 23, 39, 75, ?, 
239
Differences: +4, +16, 
+36, +64, +100 
(squares: 2², 4², 6², 8², 
10²)
Missing term: 
75 + 64 = 139
Perfect Square or 
Perfect Cube
P a tte r n: T erms are 
squares (n²) or cubes (n³) 
of integers.
E xa mp le: 4, 18, 48, 100, 
180, ?
Form: n³ - n² (n = 2, 3, 4, 
5, 6, ...)
Missing term: 
7³ - 7² = 343 - 49 = 294
Factorisation/Prime 
Factorisation
P a tte r n: T erms are 
products of prime 
numbers.
E xa mp le: 6, 15, 35, 77, 
143, ?
Products: 2×3, 3×5, 
5×7, 7×11, 11×13, 
13×17
Missing term: 
13×17 = 221
Fibonacci Series
P a tte r n: Each term is the sum of the two previous terms.
E xa mp le: 1, 4, 5, 9, 14, 23, ?
1 + 4 = 5, 4 + 5 = 9, ..., 14 + 23 = 37
Missing term: 37
Advanced Number Series Types
Alternate Pattern Series
P a tte r n: Two patterns alternate between 
terms.
E xa mp le: 2, 7, 4, 9, 6, 11, ?
Series 1: 2, 4, 6, ... (+2); Series 2: 7, 9, 11, ... 
(+2)
Missing term: 8
Decimal Pattern Series
P a tte r n: Involves decimals with consistent 
increments.
E xa mp le: 0.1, 0.2, 0.3, 0.4, ?
+0.1 each term
Missing term: 0.5
Bracket Pattern Series
P a tte r n: Combines operations within brackets.
E xa mp le: 3, 28, 180, ?, 3676
(3+1)×7 = 28, (28+2)×6 = 180, (180+3)×5 
= 915
Missing term: 915
Dual Pattern Series
P a tte r n: Two interrelated series.
E xa mp le: 15, 9, 8, 12, 36, 170 and 19, a, b, ?, d, 
e
Pattern: (n-6)×1, (n-5)×2, ...; for 19: (19-
6)×1 = 13, ..., (16-4)×3 = 36
Missing term: 36
Factorial Based Series
P a tte r n: T erms involve factorials (n!).
E xa mp le: 1, 2, 6, 24, 120, ?
1!, 2!, 3!, 4!, 5!, 6!
Missing term: 6! = 720
Arithmetic and Geometric Series
Arithmetic Series
D e f in itio n: Constant difference (d) between terms.
F o r mu la s:
a = first term
n = no. of terms
l = last term
E xa mp le: 7, 12, 17, 22, 27, ?
d = 5; 27 + 5 = 32
Geometric Series
D e f in itio n: Constant ratio (r) between terms.
F o r mu la s:
nth term: 
Sum: 
E xa mp le: 3, 12, 48, 192, ?
r = 4; 192 × 4 = 768
Mixed Series
P a tte r n: Combines multiple operations.
E xa mp le: 2, 8, 26, 80, 242, ?
×3 + 2 each term
Missing term: 242 × 3 + 2 = 728
Arithmetic-Geometric Series
P a tte r n: Alternates arithmetic and geometric operations.
E xa mp le: 3, 5, 10, 12, 24, 26, ?
+2, ×2, +2, ×2, ...
Missing term: 26 × 2 = 52
Prime Number Series
P a tte r n: T erms are prime numbers or follow prime-based rules.
E xa mp le: 3, 5, 7, 11, 13, ?
Next prime: 17