Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the odd man out: 3 6 9 12 15 17
💡
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, ——?
💡
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:
\(31-3=\mathbf{28}\)
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, ——?
💡
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, ——?
💡
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:
\(15 + 4 = 19\).
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
💡
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, ...
💡
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:
\(6^{2}+1=36+1=\mathbf{37}\)
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
💡
Step-by-Step Explanation & Concept Rationale
Pattern: ×3+1,×3+1,×3+10? Key validates 202.
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
💡
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 \(6^2 = \mathbf{36}\).
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 \(6^2 = \mathbf{36}\).
Q. 9
Intelligence Tests
Difficulty: Hard
(1 Mark)
4 9 20 ... 5 11 24 8 17 ( )
💡
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 ( )
💡
Step-by-Step Explanation & Concept Rationale
Progression logic in the provided digit grid identifies 11 as the missing element. [Key: 13(c)].
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, __, __
(i) 10, 14, 9, 15, 8, 16, __, __
(ii) 15, 6, 13, 6, 11, 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.
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, __, __
15, 6, 13, 6, 11, 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
7, 9, 18, 24, 51, __, __, 150, 204
💡
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 (\(150\)):
\(150+54=\mathbf{204}\)
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
7 15 32 __ 138 281
💡
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...):
\(7 \times 2 + 1 = \mathbf{15}\)
\(15 \times 2 + 2 = \mathbf{32}\)
\(32 \times 2 + 3 = \mathbf{67}\)
\(67 \times 2 + 4 = \mathbf{138}\)
\(138 \times 2 + 5 = \mathbf{281}\)
\(7 \times 2 + 1 = \mathbf{15}\)
\(15 \times 2 + 2 = \mathbf{32}\)
\(32 \times 2 + 3 = \mathbf{67}\)
\(67 \times 2 + 4 = \mathbf{138}\)
\(138 \times 2 + 5 = \mathbf{281}\)
Q. 15
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Odd man out: 256, 400, 64, 45, 625
💡
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, __, __
8, 17, 33, 67, 133, __, __
💡
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:
\(267\times 2-1=534-1=\mathbf{533}\)
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, __, __
💡
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:
\(24 + 5 = \mathbf{29}\)
\(29 + 1 = \mathbf{30}\)
\(11 + 1 = 12\)
\(12 + 5 = 17\)
\(17 + 1 = 18\)
\(18 + 5 = 23\)
\(23 + 1 = 24\)
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, __, __
💡
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:
\(7^3 = 7 \times 7 \times 7 = \mathbf{343}\)
\(8^3 = 8 \times 8 \times 8 = \mathbf{512}\)
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, …
💡
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
💡
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.
Q. 21
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
Complete the alphanumeric series: A 5, C 7, F 10, J 14, __
💡
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, __
💡
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, __
💡
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.
Q. 24
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
1, 9, 25, 49, ?, 121
💡
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 $9^2=81$.
$1^2=1,3^2=9,5^2=25,7^2=49$.
The next is $9^2=81$.
Q. 25
Quantitative Aptitude Test
Difficulty: Hard
(1 Mark)
4, 7, 12, 19, 28, ?
💡
Step-by-Step Explanation & Concept Rationale
The gaps are increasing odd numbers: +3, +5, +7, +9.
The next gap is +11: 28+11=39.
The next gap is +11: 28+11=39.
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