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.
What is the general term of the pattern $2, 4, 6, 8, \ldots$?
Correct answer: A - $2n$
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 $0$.
A pen costs twice as much as a pencil. If a pencil costs ₹$c$, what does the pen cost?
Correct answer: D - ₹$2c$
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.
Assertion (A): The general term of the pattern $10, 20, 30, \ldots$ is $10n$. Reason (R): The number $10$ is written with two digits.
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.
Which pattern matches the rule $n+4$?
Correct answer: B - $5, 6, 7, 8, \ldots$
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.
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?
Correct answer: A - $3n+1$
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 $3$.
Pattern P is $4, 8, 12, 16, \ldots$ and pattern Q is $3, 6, 9, 12, \ldots$. Which statement about them is correct?
Correct answer: B - 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.
A pattern follows the rule $4n$. What is its $6$th term?
Correct answer: D - $24$
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.
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 ₹$5$.
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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