patterns-and-relationships-with-letters MCQs for UPSC Prelims

25 practice questions on patterns-and-relationships-with-letters from the Expressions using Letter-Numbers section of the UPSC Prelims syllabus. 25 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

8 Easy 12 Medium 5 Hard

Sample questions

Q1
easy
What is the general term of the pattern $2, 4, 6, 8, \ldots$?
  1. A $n+2$
  2. B $2n-2$
  3. C $2n+2$
  4. D $2n$
Show answer and explanation

Correct answer: D - $2n$

Substituting $n=1,2,3$ into $2n$ gives $2$, $4$ and $6$, matching the pattern. The rule $n+2$ starts at $3$, $2n+2$ starts at $4$, and $2n-2$ starts at $0$.
Q2
easy
A pen costs twice as much as a pencil. If a pencil costs ₹$c$, what does the pen cost?
  1. A ₹$(c-2)$
  2. B ₹$\frac{c}{2}$
  3. C ₹$2c$
  4. D ₹$(c+2)$
Show answer and explanation

Correct answer: C - ₹$2c$

Twice as much means the price is multiplied by two, so the pen costs ₹$2c$. Adding two gives ₹$(c+2)$, halving gives ₹$\frac{c}{2}$, and subtracting makes the pen cheaper than the pencil.
Q3
medium
Assertion (A): The general term of the pattern $10, 20, 30, \ldots$ is $10n$. Reason (R): The number $10$ is written with two digits.
  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: B - Both A and R are true, but R is not the correct explanation of A

Substituting $n=1,2,3$ into $10n$ gives $10$, $20$ and $30$, so the assertion is true. It is also true that $10$ has two digits, but the number of digits has nothing to do with the rule of a pattern, so R does not explain A.
Q4
easy
Which pattern matches the rule $n+4$?
  1. A $1, 2, 3, 4, \ldots$
  2. B $4, 5, 6, 7, \ldots$
  3. C $4, 8, 12, 16, \ldots$
  4. D $5, 6, 7, 8, \ldots$
Show answer and explanation

Correct answer: D - $5, 6, 7, 8, \ldots$

Substituting $n=1,2,3,4$ into $n+4$ gives $5$, $6$, $7$ and $8$. The second list matches $4n$, the third matches $n$ on its own, and the fourth starts one step too early.
Q5
hard
A row of matchstick squares uses $4$ sticks for the first square and $3$ more for each square added. Which rule gives the sticks needed for $n$ squares?
  1. A $4n-1$
  2. B $3n+4$
  3. C $3n+1$
  4. D $4n$
Show answer and explanation

Correct answer: C - $3n+1$

The counts run $4$, $7$, $10$, and $3n+1$ gives exactly those for $n=1,2,3$. The rule $4n$ counts every square separately and gives $8$ for two squares, $3n+4$ starts at $7$, and $4n-1$ starts at $3$.
Q6
hard
Pattern P is $4, 8, 12, 16, \ldots$ and pattern Q is $3, 6, 9, 12, \ldots$. Which statement about them is correct?
  1. A P follows $n+4$ and Q follows $n+3$
  2. B Both patterns follow the same rule
  3. C P follows $4n$ and Q follows $3n$, and their $5$th terms are $20$ and $15$
  4. D P follows $4n$ and Q follows $3n$, and their $5$th terms are $16$ and $12$
Show answer and explanation

Correct answer: C - P follows $4n$ and Q follows $3n$, and their $5$th terms are $20$ and $15$

Pattern P lists multiples of four and pattern Q multiples of three, so the rules are $4n$ and $3n$, and the fifth terms are $4\times 5=20$ and $3\times 5=15$. The second option quotes the fourth terms, the rules in the third give $5, 6, 7$ and $4, 5, 6$, and the two patterns clearly differ.
Q7
easy
A pattern follows the rule $4n$. What is its $6$th term?
  1. A $24$
  2. B $46$
  3. C $4$
  4. D $10$
Show answer and explanation

Correct answer: A - $24$

Substituting $n=6$ gives $4\times 6=24$. The value $10$ adds instead of multiplying, $46$ joins the digits, and $4$ ignores the value of $n$ completely.
Q8
medium
Assertion (A): If a book costs ₹$b$ and a pen costs ₹$5$ less than the book, the pen costs ₹$(b-5)$. Reason (R): The phrase "₹$5$ less" tells us to subtract the book's cost from ₹$5$.
  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: C - A is true, but R is false

The pen costs five rupees less than the book, so its price is ₹$(b-5)$ and the assertion is true. The reason is false, because five is taken away from the book's cost; subtracting the other way round would give ₹$(5-b)$.

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