patterns-in-numbers MCQs for UPSC Prelims

29 practice questions on patterns-in-numbers from the Patterns in Mathematics section of the UPSC Prelims syllabus. 29 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

9 Easy 14 Medium 6 Hard

Sample questions

Q1
medium

A sequence begins $6, 11, 16, 21, \ldots$. Which term of this sequence is $56$?

  1. A The $12$th term
  2. B The $9$th term
  3. C The $11$th term
  4. D The $10$th term
Show answer and explanation

Correct answer: C - The $11$th term

The sequence starts at $6$ and rises by $5$ each time, so the $n$th term is $5n + 1$. Setting $5n + 1 = 56$ gives $n = 11$. The $10$th term is $51$ and the $12$th is $61$, so neither is $56$, and the $9$th term is only $46$.

Q2
easy

Which sequence lists the counting numbers?

  1. A $0, 2, 4, 6, 8, \ldots$
  2. B $1, 1, 1, 1, 1, \ldots$
  3. C $1, 3, 5, 7, 9, \ldots$
  4. D $1, 2, 3, 4, 5, \ldots$
Show answer and explanation

Correct answer: D - $1, 2, 3, 4, 5, \ldots$

The counting numbers begin at $1$ and increase by $1$ each time, giving $1, 2, 3, 4, 5, \ldots$. The second sequence lists even numbers including $0$, the third lists odd numbers, and the fourth is the constant sequence of $1$s.

Q3
easy

Which sequence is obtained by skip-counting in steps of $4$ starting from $4$?

  1. A $4, 8, 12, 16, 20, \ldots$
  2. B $1, 4, 9, 16, 25, \ldots$
  3. C $4, 16, 64, 256, \ldots$
  4. D $4, 6, 8, 10, 12, \ldots$
Show answer and explanation

Correct answer: A - $4, 8, 12, 16, 20, \ldots$

Skip-counting by $4$ adds $4$ each time, giving the multiples of $4$: $4, 8, 12, 16, 20, \ldots$. The second sequence steps by $2$, the third lists square numbers, and the fourth multiplies by $4$ each time rather than adding.

Q4
medium

What are the next two terms of $100, 91, 82, 73, \ldots$?

  1. A $64$ and $54$
  2. B $64$ and $55$
  3. C $63$ and $54$
  4. D $65$ and $56$
Show answer and explanation

Correct answer: B - $64$ and $55$

Each term decreases by $9$, so the next two are $73 - 9 = 64$ and $64 - 9 = 55$. The other options apply a step of $10$ or mix steps, breaking the constant difference of $9$.

Q5
easy

What is the rule of the sequence $5, 10, 15, 20, 25, \ldots$?

  1. A Add the two previous terms
  2. B Add $5$ to the previous term
  3. C Add $10$ to the previous term
  4. D Multiply the previous term by $2$
Show answer and explanation

Correct answer: B - Add $5$ to the previous term

Each term exceeds the one before by $5$, so the rule is to add $5$. Doubling would give $5, 10, 20, 40$, adding the two previous terms would give $5, 10, 15, 25$, and adding $10$ would give $5, 15, 25$, none of which matches.

Q6
medium

Chairs are placed in a hall so that row $1$ has $1$ chair, row $2$ has $2$ chairs, row $3$ has $3$ chairs, and so on. How many chairs are in row $9$?

  1. A $10$
  2. B $18$
  3. C $45$
  4. D $9$
Show answer and explanation

Correct answer: D - $9$

The chairs follow the counting numbers, so row $9$ holds $9$ chairs. Answering $10$ shifts the row number by one, $45$ gives the total chairs in the first nine rows rather than that row alone, and $18$ doubles the row number.

Q7
medium

A frog starts at $0$ and jumps forward $7$ units each time. Which of these numbers will it land on?

  1. A $50$
  2. B $56$
  3. C $60$
  4. D $45$
Show answer and explanation

Correct answer: B - $56$

The frog lands only on multiples of $7$, and $56 = 7 \times 8$. The numbers $50$, $60$ and $45$ leave remainders $1$, $4$ and $3$ when divided by $7$, so the frog jumps over each of them.

Q8
easy

What is the next term in the sequence $1, 2, 4, 8, 16, \ldots$?

  1. A $32$
  2. B $18$
  3. C $20$
  4. D $24$
Show answer and explanation

Correct answer: A - $32$

Each term is double the one before, so after $16$ comes $16 \times 2 = 32$. Answering $24$ adds $8$, $20$ adds $4$, and $18$ adds $2$, all treating a doubling pattern as if it were addition.

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