Number Series PYQs for UPSC (2011-2024) | Solved Questions & PDF Download

Master Number Series problems for UPSC with solved Previous Year Questions (PYQs) from 2011 to 2024. This comprehensive guide provides step-by-step solutions, pattern recognition techniques, and a free downloadable PDF to help you crack number sequence problems in UPSC CSAT.

Why Number Series Matters in UPSC CSAT?

Number series questions are consistently asked in UPSC CSAT (Paper II) to test:

· Your logical reasoning and pattern identification skills

· Ability to recognize numerical relationships

· Skills in solving complex sequence-based problems

This page covers all types of number series PYQs with proven solving strategies.

Year-Wise Number Series PYQs (2011-2024)

Q1. What is the missing number 'X' of the series 7, X, 21, 31, 43 ? [CSAT 2015]

(a) 11

(b) 12

(d) 14

Solution:

Given that,

7, X, 21, 31, 43

7 + 6 = 13

13 + 8 = 21

21 + 10 = 31

31 + 12 = 43

Hence option (c) is correct

Q2. What is X in the sequence 4, 196, 16, 144, 36, 100, 64, X? [CSAT 2019]

(a) 48

(b) 64

(d) 256

Solution:

Given that,

4, 196, 16, 144, 36, 100, 64, X

2², 14², 4², 12², 6², 10², 8², 8²

Thus X = 64

Hence option (b) is correct

Q3. What is X in the sequence 132, 129, 124, 117, 106, 93, X? [CSAT 2019]

(a) 74

(b) 75

(d) 77

Solution:

Given that,

132, 129, 124, 117, 106, 93, X

132 - 129 = 3

129 - 124 = 5

124 - 117 = 7

117 - 106 = 11

106 - 93 = 13

93 - 17 = 76

Hence option (c) is correct

Q4. A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, results in a ... sequence with respect to prime number. Which one of the following is the next number in the sequence? [CSAT 2020]

(a) 34

(b) 36

(d) 40

Solution:

Given that,

Sequence 14, 18, 20, 24, 30, 32, results in a ... sequence with respect to prime number.

14 - 1 = 13, 18 - 1 = 17, 20 - 1 = 19..........32 - 1 = 31, 38 - 1 = 37

Hence option (c) is correct

Q5. What is the value of 'X' in the sequence 2, 7, 22, 67, 202, X, 1822? [CSAT 2021]

(a) 603

(b) 605

(d) 608

Solution:

Given that,

2, 7, 22, 67, 202, X, 1822

7 = 2 x 3 + 1

22 = 7 x 3 + 1

So,

202 x 3 + 1 = 607 = X

Hence option (c) is correct

Q6. Replace the incorrect term by the correct term in the given sequence 3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40 where odd terms and even terms follow the same pattern. [CSAT 2021]

(a) 0

(b) 1

(d) 6

Solution:

Given that,

3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40

Odd terms and even terms follow same pattern

3 + 4 = 7, 7 + 6 = 13, 13 + 8 = 21, 21 + 10 = 31, 31 + 12 = 43

Similarly even terms

2 + 2 = 4 replace, 4 + 6 = 10, 10 + 8 = 18, 18 + 10 = 28 and 28 + 12 = 40

Thus the first term in even series should be replaced by 0

Hence option (a) is correct

Q7. What is the value of X in the sequence 20, 10, 10, 15, 30, 75, X? [CSAT 2022]

(a) 105

(b) 120

(d) 225

Solution:

Given that,

sequence 20, 10, 10, 15, 30, 75, X

20 x 0.5 = 10

10 x 1 = 10

10 x 1.5 = 15

15 x 2 = 30

30 x 2.5 = 75

75 x 3 = 225

Hence option (d) is correct

Q8. What is the value of X in the sequence 2, 12, 36, 80, 150, Х? [CSAT 2022]

(a) 248

(b) 252

(d) 262

Solution:

Given that,

sequence 2, 12, 36, 80, 150, Х

1² + 1³= 2

2² + 2³= 12

3² + 3³= 36

4² + 4³= 80

5² + 5³= 150

6² + 6³= 252

Hence option (b) is correct

Q9. Choose the group which is different from the others: [CSAT 2023]

(a) 17, 37, 47, 97

(b) 31, 41, 53, 67

(d) 83, 89, 91, 97

Solution:

In all the options the numbers are prime numbers except option (d) where 91 is not a prime number.

Hence option (d) is correct

Q10. What will come in place of * in the sequence 3, 14, 39, 84, *, 258?

(a) 150

(b) 155

(d) 176

Solution:

Given that,

Sequence is 3, 14, 39, 84, * , 258

Now,

The sequence is in the form N³ + N² + N

3 = 1³ + 1² + 1

14 = 2³ + 2² + 2

39 = 3³ + 3² + 3

84 = 4³ + 4² + 4

* = 5³ + 5² + 5 = 155

Alternate method:

ANSWER KEY
1. C
2. B
3. C
4. C
5. C
6. A
7. D
8. B
9. D
10. B

Download Number Series PYQs PDF

➡️ Download the complete set of Number Series PYQs (2011-2024) with solutions in PDF format.
➡️ Click Here to Download PDF

FAQs on Number Series for UPSC

1. How many number series questions appear in CSAT?

➡️ Typically 2-3 questions annually in CSAT Paper II.

2. What are the most common number patterns?

· Arithmetic progression (35%)

· Geometric progression (25%)

· Square/cube numbers (20%)

· Prime numbers (10%)

· Alternating patterns (10%)

3. Any quick solving tips?

✔️ Check differences between terms first
✔️ Look for multiplication/division patterns
✔️ Verify square/cube possibilities
✔️ For complex series, write down positions (n=1,2,3...)

Conclusion

Mastering Number Series PYQs can secure you easy marks in CSAT. This page provides:
✅ All PYQs from 2011-2024
✅ PDF with 60+ solved problems
✅ Pattern recognition strategies

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Internal Links:

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· Quantitative Aptitude PYQs