Practice UPSC CSAT previous year questions from 2011–2026 classified underNumber Series. Review the original question, four options, correct answer and explanation for every PYQ.
18 questions • 2011–2026
A pattern formed by two characters a and b is repeated more than once in the following string: × b × a × a × × a × a × b a b What is × × in the 7th and 8th positions from the left in the above string?
The repeated two-character pattern and the surrounding fixed characters make the seventh and eighth positions both b. Hence D.
In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number is
The sequence is 4, 7, 11, 18, 29, 47. Hence D.
What comes at X and Y respectively in the following sequence? January, January, December, October, X, March, October, Y, September
The month numbers follow backward steps 0,1,2,3,4,5,6,7 modulo 12, giving July and April.
Consider the sequence AB_CC_A_BCCC_BBC_C that follows a certain pattern. Which one of the following completes the sequence?
Option C yields ABBCCC repeated three times.
What is X in the sequence 24, X, 12, 18, 36, 90?
The multipliers 1.5,2,2.5 extend backward to 1 and 0.5, giving X=12.
What is X in the sequence 1, 3, 6, 11, 18, X, 42?
Differences are 2,3,5,7,11,13, so X=29.
What is the sum of the first 28 terms in the following sequence? 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, ...
Group the sequence as 1; 1,2; 1,3,2; 1,4,3,2; ... . Summing through the first 28 terms gives 84.
What will come in place of * in the sequence 3, 14, 39, 84, *, 258?
The successive differences are 11,25,45, then 71,97; the second differences increase by 6, so the missing term is 155.
What is the middle term of the sequence Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W, …, A?
Counting the increasing multiplicities identifies I as the middle term.
In the series AABABCABCDABCDE... which letter appears at the 100th place?
The blocks are A, AB, ABC, ABCD, ABCDE, ... with lengths 1,2,3,... The 100th position lies in the 14th block because 13 blocks contain 91 letters; position 9 of block 14 is I.
What is the value of X in the sequence 2, 12, 36, 80, 150, X?
The terms are n^2(n+1) for n=1,2,3,4,5: 2,12,36,80,150. For n=6, X=36x7=252.
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.
Odd-position terms have gaps 4,6,8,10,12. Even-position terms should have gaps 4,6,8,10,12, so the first even term must be 0.
You are given two identical sequences in two rows: Sequence-I: 8, 4, 6, 15, 52.5, 236.25 Sequence-II: 5, A, B, C, D, E What is the entry in the place of C for the Sequence-II?
The multipliers are 0.5, 1.5, 2.5, 3.5, 4.5. Thus 5→2.5→3.75→9.375, so C=9.375.
What is the value of ‘X’ in the sequence 2, 7, 22, 67, 202, X, 1822?
Each term is previous term ×3 +1, so X=202×3+1=607 and 607×3+1=1822.
A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ..... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?
Subtract 1 from each term: 13, 17, 19, 23, 29, 31 are consecutive primes in the pattern. The next prime is 37, so the next original term is 38.
Consider the following sequence of numbers: 5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6 How many odd numbers are followed by an odd number in the above sequence?
Count adjacent pairs in which both the current number and the next number are odd. There are six such pairs.
Figure/sequence on PDF page 8
Consider the figures given below. To fit the question mark, the correct answer is
The symbols and marked positions follow the sequence shown in the preceding figures; option A completes the required progression.
What is the missing number ‘X’ of the series 7, X, 21, 31, 43?
The differences are 6, 8, 10, 12, so X=13.
Attempt questions one by one with UPSC-style marking and immediate explanations.