Number Play MCQs for UPSC Prelims

317 practice questions covering Number Play, organised into 1 topics. 317 questions include a written explanation. Pick a topic below, or try the samples first.

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divisibility-tests

30 questions with answers

Sample questions

Q1
medium
Which number appears in the Collatz sequence starting from $6$?
  1. A $7$
  2. B $9$
  3. C $10$
  4. D $12$
Show answer and explanation

Correct answer: C - $10$

The chain runs $6 \to 3 \to 10 \to 5 \to 16 \to 8 \to 4 \to 2 \to 1$, so $10$ appears. The numbers $12$, $9$ and $7$ never occur in this chain.
Q2
medium
A shop sells $146$ pens on Monday and $189$ on Tuesday. How many pens in all?
  1. A $335$
  2. B $345$
  3. C $325$
  4. D $330$
Show answer and explanation

Correct answer: A - $335$

Adding the hundreds and tens first, $146 + 189 = 146 + 200 - 11 = 335$. Answering $325$ or $345$ is out by ten, and $330$ is out by five.
Q3
hard
Three numbers standing next to each other in the Virahanka sequence add up to $68$. What is the largest of the three?
  1. A $55$
  2. B $13$
  3. C $21$
  4. D $34$
Show answer and explanation

Correct answer: D - $34$

If the first two are $a$ and $b$, the third is $a + b$, so the total is $2(a + b) = 68$ and $a + b = 34$. The largest of the three is that third number, $34$, and the triple is $13$, $21$, $34$. The values $21$ and $13$ are the two smaller members, and $55$ is the number that follows the triple.
Q4
medium
Starting from $1234$, how many Kaprekar steps are needed to reach $6174$?
  1. A $5$
  2. B $1$
  3. C $2$
  4. D $3$
Show answer and explanation

Correct answer: D - $3$

The chain runs $4321 - 1234 = 3087$, then $8730 - 0378 = 8352$, then $8532 - 2358 = 6174$, so $3$ steps are needed. One or two steps stop short at $3087$ or $8352$, and the constant is reached before a fifth step.
Q5
medium
In the Virahanka sequence, an unknown number $x$ is followed by $21$ and then by $34$. Find $x$.
  1. A $8$
  2. B $12$
  3. C $13$
  4. D $55$
Show answer and explanation

Correct answer: C - $13$

The rule gives $x + 21 = 34$, so $x = 13$. The value $8$ lies one place earlier still, and $55$ is the number that comes after $34$. Subtracting $21$ from $33$ instead of $34$ gives $12$.
Q6
medium
Three children of different heights stand in a row, and each reports how many children to their left are taller. Which of these lists of reports, read from left to right, is not possible?
  1. A $0, 0, 0$
  2. B $0, 1, 1$
  3. C $1, 0, 1$
  4. D $0, 1, 2$
Show answer and explanation

Correct answer: C - $1, 0, 1$

The first child has nobody on the left, so the first report must be $0$, which rules out $1, 0, 1$. The list $0, 1, 2$ arises when heights fall steadily, $0, 0, 0$ when they rise steadily, and $0, 1, 1$ when the third child is taller than the second but shorter than the first.

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