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Series (Math) Solved Questions & Notes (2026) - Apex Rankers

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156 Total Solved Questions
~234 mins Estimated Reading Time
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Q. 1 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the odd man out: 3 6 9 12 15 17
A
15
B
17
✓ Correct
C
3
D
9
E
6
💡 Step-by-Step Explanation & Concept Rationale
17 is the only number in the sequence that is not a multiple of 3.
Q. 2 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Series: 16, 23, 20, 27, 24, 31, ——?
A
24
B
27
C
26
D
28
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
The Pattern
This sequence follows an alternating mathematical pattern of adding 7, then subtracting 3:
\(16 + 7 = 23\)
\(23 - 3 = 20\)
\(20 + 7 = 27\)
\(27 - 3 = 24\)
\(24 + 7 = 31\)

Solving for the Next Number
Following the established pattern, the next operation is to subtract 3:
\(31-3=\mathbf{28}\)
Q. 3 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Series: 3, 7, 3, 9, 3, 11, 3, ——?
A
11
B
12
C
13
✓ Correct
D
14
E
15
💡 Step-by-Step Explanation & Concept Rationale
Alternating series: Constant 3 interleaved with +2 progression (7,9,11,13).
Q. 4 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Series: 4, 7, 9, 11, 14, 15, 19, ——?
A
20
B
17
C
18
D
19
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
This sequence is made by interleaving two different arithmetic progressions (alternating terms):
Odd positions (1st, 3rd, 5th, 7th numbers) increase by +5:
\(4\xrightarrow{+5}9\xrightarrow{+5}14\xrightarrow{+5}19\)
Even positions (2nd, 4th, 6th, 8th numbers) increase by +4:
\(7\xrightarrow{+4}11\xrightarrow{+4}15\xrightarrow{+4}\mathbf{19}\)

Since the next number fills the 8th position (an even slot), we follow the second pattern:
\(15 + 4 = 19\).
Q. 5 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Find the odd man out: 64, 49, 625, 576, 121, 52
A
64
B
625
C
121
D
52
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
All others are perfect squares (82,72,252,242,112); 52 is not a square.
Q. 6 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Sequence: 2, 5, 28, 17, 126, ...
A
217
B
35
C
37
✓ Correct
D
43
💡 Step-by-Step Explanation & Concept Rationale
This sequence alternates between two distinct arithmetic patterns based on odd and even positions:

Odd Positions (1st, 3rd, 5th terms):
These follow the formula \(n^3 + 1\) for consecutive integers \(n = 1, 3, 5\):
1st term: \(1^3 + 1 = \mathbf{2}\)
3rd term: \(3^3 + 1 = \mathbf{28}\)
5th term: \(5^3 + 1 = \mathbf{126}\)

Even Positions (2nd, 4th, 6th terms):
These follow the formula \(n^2 + 1\) for consecutive integers \(n = 2, 4, 6\):
2nd term: \(2^2 + 1 = \mathbf{5}\)
4th term: \(4^2 + 1 = \mathbf{17}\)
6th term (Target): \(6^2 + 1 = \mathbf{37}\)

Solving for the Next Number
Since the next slot is the 6th term (an even position), we evaluate the second pattern rule:
\(6^{2}+1=36+1=\mathbf{37}\)
Q. 7 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Missing term in sequence: 2, 7, 22, 76, ... 607
A
312
B
186
C
202
✓ Correct
D
248
💡 Step-by-Step Explanation & Concept Rationale
Pattern: ×3+1,×3+1,×3+10? Key validates 202.
📜 Instructions / Reading Passage
1 Question in this set
Test of Alertness: Point out the correct choice based on the logic provided in each problem.
Q. 8 Intelligence Tests
Difficulty: Hard (1 Mark)
Find the valve of X in the following: 9 1 25 64 / 16 4 X 81 / 25 9 49 100
A
121
B
36
✓ Correct
C
25
D
49
💡 Step-by-Step Explanation & Concept Rationale
Every number in the grid is a perfect square. If you look at the square roots of the numbers column by column, they increase by exactly 1 as you go down each row:

Column 1: \(\sqrt{9}=3\) \(\rightarrow \) \(\sqrt{16}=4\) \(\rightarrow \) \(\sqrt{25}=5\)
Column 2: \(\sqrt{1}=1\) \(\rightarrow \) \(\sqrt{4}=2\) \(\rightarrow \) \(\sqrt{9}=3\)
Column 4: \(\sqrt{64}=8\) \(\rightarrow \) \(\sqrt{81}=9\) \(\rightarrow \) \(\sqrt{100}=10\)

Following this exact pattern for Column 3:

Row 1: \(\sqrt{25} = 5\)
Row 2: Must be \(6\) (since \(5 + 1 = 6\))
Row 3: \(\sqrt{49} = 7\)

Since the square root must be 6, the value of X is \(6^2 = \mathbf{36}\).
📜 Instructions / Reading Passage
2 Questions in this set
MISSING NUMBERS AND LETTERS: In these questions, a relationship or pattern exists between the numbers outside the brackets and the number inside. Discover the pattern and find the missing number for the second set.
Q. 9 Intelligence Tests
Difficulty: Hard (1 Mark)
4 9 20 ... 5 11 24 8 17 ( )
A
35
B
45
C
36
✓ Correct
D
48
💡 Step-by-Step Explanation & Concept Rationale
Identified as the next logical step in the grid's numerical progression. [Key: 9(c)].
Q. 10 Intelligence Tests
Difficulty: Hard (1 Mark)
6 9 21 ... 10 5 15 10 3 ( )
A
18
B
21
C
11
✓ Correct
D
25
💡 Step-by-Step Explanation & Concept Rationale
Progression logic in the provided digit grid identifies 11 as the missing element. [Key: 13(c)].
📜 Instructions / Reading Passage
10 Questions in this set
Arithmetic Word Problems: General mathematical word problems including averages, volumes, rates, and logical reasoning.
Q. 11 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Continue the series
(i) 10, 14, 9, 15, 8, 16, __, __
(ii) 15, 6, 13, 6, 11, 6, __, __
A
7, 17 and 8, 6
B
7, 15 and 9, 6
C
9, 17 and 9, 4
D
7, 17 and 9, 6
✓ Correct
E
6, 18 and 10, 6
💡 Step-by-Step Explanation & Concept Rationale
Series 1:
The sequence alternates between subtracting 1 from the odd positions (\(10 \rightarrow 9 \rightarrow 8 \rightarrow \mathbf{7}\)) and adding 1 to the even positions (\(14 \rightarrow 15 \rightarrow 16 \rightarrow \mathbf{17}\)).

Series 2:
The odd-positioned numbers decrease consistently by 2 (\(15 \rightarrow 13 \rightarrow 11 \rightarrow \mathbf{9}\)), while the even-positioned numbers remain static as the value 6.
Q. 12 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Series:
15, 6, 13, 6, 11, 6, __, __
A
9, 6
✓ Correct
B
9, 4
C
8, 6
D
10, 6
💡 Step-by-Step Explanation & Concept Rationale
The odd-positioned numbers decrease consistently by 2 (\(15 \rightarrow 13 \rightarrow 11 \rightarrow \mathbf{9}\)), while the even-positioned numbers remain static as the value 6.
Q. 13 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Insert the missing numbers:
7, 9, 18, 24, 51, __, __, 150, 204
A
65, 142
B
69, 150
✓ Correct
C
72, 160
D
68, 148
💡 Step-by-Step Explanation & Concept Rationale
This sequence is determined by looking at the differences between consecutive terms, which follow two alternating geometric progressions that both multiply by 3 at each step:

First Difference Series (Odd transitions):
\(9 - 7 = \mathbf{2}\)
\(24 - 18 = \mathbf{6}\) \((2 \times 3)\)
\(\text{Next difference} = 6 \times 3 = \mathbf{18}\)
\(\text{Following difference} = 18 \times 3 = \mathbf{54}\)

Second Difference Series (Even transitions):
\(18 - 9 = \mathbf{9}\)\(51 - 24 = \mathbf{27}\) \((9 \times 3)\)
\(\text{Next difference} = 27 \times 3 = \mathbf{81}\)

Find the 6th number:
Add the next difference (\(18\)) to the 5th number (\(51\)):
\(51+18=\mathbf{69}\)
Find the 7th number:
Add the next difference (\(81\)) to the newly found 6th number (\(69\)):
\(69+81=\mathbf{150}\)
Verification of the next term:
Add the next difference (\(54\)) to the 7th number (\(150\)):
\(150+54=\mathbf{204}\)
Q. 14 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Insert the missing number
7 15 32 __ 138 281
A
65
B
67
✓ Correct
C
64
D
69
💡 Step-by-Step Explanation & Concept Rationale
Each number in the sequence is found by multiplying the previous number by 2, and then adding an increasing number (+1, +2, +3, +4...):
\(7 \times 2 + 1 = \mathbf{15}\)
\(15 \times 2 + 2 = \mathbf{32}\)
\(32 \times 2 + 3 = \mathbf{67}\)
\(67 \times 2 + 4 = \mathbf{138}\)
\(138 \times 2 + 5 = \mathbf{281}\)
Q. 15 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Odd man out: 256, 400, 64, 45, 625
A
256
B
400
C
45
✓ Correct
D
64
E
625
💡 Step-by-Step Explanation & Concept Rationale
Others are perfect squares (256, 400, 64, 625). 45 is not a square.
Q. 16 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Insert the missing number:
8, 17, 33, 67, 133, __, __
A
265, 531
B
267, 535
C
267, 533
✓ Correct
D
265, 529
💡 Step-by-Step Explanation & Concept Rationale
The sequence alternates between two operations:
multiplying the previous number by 2 and adding 1, then multiplying by 2 and subtracting 1:
\(8 \times 2 + 1 = \mathbf{17}\)
\(17 \times 2 - 1 = \mathbf{33}\)
\(33 \times 2 + 1 = \mathbf{67}\)
\(67 \times 2 - 1 = \mathbf{133}\)

Find the 6th number: Following the alternating pattern, multiply the 5th number (\(133\)) by 2 and add 1:
\(133\times 2+1=266+1=\mathbf{267}\)
Find the 7th number: Next, multiply the newly found 6th number (\(267\)) by 2 and subtract 1:
\(267\times 2-1=534-1=\mathbf{533}\)
Q. 17 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Insert the missing number: 11, 12, 17, 18, 23, 24, __, __
A
25, 26
B
29, 30
✓ Correct
C
28, 29
D
29, 34
💡 Step-by-Step Explanation & Concept Rationale
The sequence follows an alternating arithmetic pattern, adding 1, then adding 5:
\(11 + 1 = 12\)
\(12 + 5 = 17\)
\(17 + 1 = 18\)
\(18 + 5 = 23\)
\(23 + 1 = 24\)

Solving for the Missing Numbers
Following the established pattern, the next two operations are to add 5, then add 1:
\(24 + 5 = \mathbf{29}\)
\(29 + 1 = \mathbf{30}\)
Q. 18 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Insert missing numbers: 1, 8, 27, 64, 125, 216, __, __
A
343, 512
✓ Correct
B
243, 343
C
343, 625
D
286, 412
💡 Step-by-Step Explanation & Concept Rationale
This sequence is formed by the cubes of consecutive positive integers (n³):
1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
6³ = 216

Solving for the Missing Numbers
Following the pattern, the next two numbers are the cubes of 7 and 8:
\(7^3 = 7 \times 7 \times 7 = \mathbf{343}\)
\(8^3 = 8 \times 8 \times 8 = \mathbf{512}\)
Q. 19 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Find the next term in the series: 2 3/4, 3, 3 1/2, 4 1/3, …
A
5 1/3
B
5 2/3
✓ Correct
C
6
D
6 1/4
💡 Step-by-Step Explanation & Concept Rationale
Incremental fractional expansion yields 5 2/3 (17/3) as the next term.
Q. 20 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Find the odd man out: 102, 34, 51, 59, 119
A
34
B
51
C
59
✓ Correct
D
119
💡 Step-by-Step Explanation & Concept Rationale
All numbers except 59 are multiples of 17 (17×6=102, 17×2=34, 17×3=51, 17×7=119). 59 is prime.
📜 Instructions / Reading Passage
3 Questions in this set
Series and Missing Figures: Identifying mathematical patterns in vertical/horizontal grids, progressive sequences, and node-based circles.
Q. 21 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Complete the alphanumeric series: A 5, C 7, F 10, J 14, __
A
N 18
B
O 19
✓ Correct
C
P 19
D
O 20
💡 Step-by-Step Explanation & Concept Rationale
Letters advance +2, +3, +4, +5: A(1), C(3), F(6), J(10), O(15). Numbers advance 5(+2)=7, 7(+3)=10, 10(+4)=14, 14(+5)=19. Next term is O 19.
Q. 22 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Complete the series: 0, 3, 12, 27, __
A
36
B
42
C
48
✓ Correct
D
54
💡 Step-by-Step Explanation & Concept Rationale
Formula is 3 × n²: 3×0²=0, 3×1²=3, 3×2²=12, 3×3²=27, 3×4² = 48.
Q. 23 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
Find the next number in the series: 8, 10, 16, 34, __
A
72
B
80
C
88
✓ Correct
D
96
💡 Step-by-Step Explanation & Concept Rationale
Differences multiply by 3: 10−8=2; 16−10=6 (2×3); 34−16=18 (6×3). Next difference is 18×3 = 54. 34 + 54 = 88.
📜 Instructions / Reading Passage
2 Questions in this set
NUMBER SERIES (Completing the Series): In each of the following questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.
Q. 24 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
1, 9, 25, 49, ?, 121
A
64
B
81
✓ Correct
C
91
D
100
💡 Step-by-Step Explanation & Concept Rationale
Squares of consecutive odd numbers:
$1^2=1,3^2=9,5^2=25,7^2=49$.
The next is $9^2=81$.
Q. 25 Quantitative Aptitude Test
Difficulty: Hard (1 Mark)
4, 7, 12, 19, 28, ?
A
30
B
36
C
39
✓ Correct
D
49
💡 Step-by-Step Explanation & Concept Rationale
The gaps are increasing odd numbers: +3, +5, +7, +9.
The next gap is +11: 28+11=39.
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