Prime Time MCQs for UPSC Prelims

116 practice questions covering Prime Time, organised into 1 topics. 116 questions include a written explanation. Pick a topic below, or try the samples first.

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common-multiples-and-common-factors

32 questions with answers

Sample questions

Q1
medium

Consider these statements. (i) Every composite number is even. (ii) Every prime number greater than $2$ is odd. Which is or are correct?

  1. A Only (ii)
  2. B Neither (i) nor (ii)
  3. C Both (i) and (ii)
  4. D Only (i)
Show answer and explanation

Correct answer: A - Only (ii)

Statement (i) is false, since $9$ and $15$ are odd composites. Statement (ii) is true, because any even number above $2$ has $2$ as an extra factor and cannot be prime. So only (ii) holds.

Q2
easy

Which of these is a common multiple of $3$ and $5$?

  1. A $25$
  2. B $35$
  3. C $45$
  4. D $21$
Show answer and explanation

Correct answer: C - $45$

Since $45 = 3 \times 15$ and $45 = 5 \times 9$, it is a multiple of both. The number $25$ is a multiple of $5$ only, $21$ of $3$ only, and $35$ of $5$ only.

Q3
medium

How do you test whether a number is divisible by $4$?

  1. A Check whether it is even
  2. B Check whether the number formed by its last two digits is divisible by $4$
  3. C Check whether its digit sum is divisible by $4$
  4. D Check whether its last digit is divisible by $4$
Show answer and explanation

Correct answer: B - Check whether the number formed by its last two digits is divisible by $4$

Since $100$ is divisible by $4$, only the last two digits matter, as in $316$ where $16$ is divisible by $4$. The last digit alone is not enough, the digit-sum test belongs to $3$ and $9$, and many even numbers such as $6$ are not divisible by $4$.

Q4
medium

How many numbers from $1$ to $50$ are divisible by $10$?

  1. A $5$
  2. B $10$
  3. C $50$
  4. D $4$
Show answer and explanation

Correct answer: A - $5$

The multiples of $10$ up to $50$ are $10, 20, 30, 40$ and $50$, giving $5$. Answering $10$ counts multiples of $5$, $4$ omits one of them, and $50$ counts every number.

Q5
medium

Given $20 = 2 \times 2 \times 5$ and $30 = 2 \times 3 \times 5$, what is their highest common factor?

  1. A $2$
  2. B $5$
  3. C $10$
  4. D $60$
Show answer and explanation

Correct answer: C - $10$

They share one $2$ and one $5$, so the highest common factor is $2 \times 5 = 10$. Answering $5$ or $2$ uses only part of the shared set, and $60$ is their lowest common multiple.

Q6
easy

Which pair of numbers is co-prime?

  1. A $8$ and $15$
  2. B $8$ and $12$
  3. C $10$ and $25$
  4. D $9$ and $15$
Show answer and explanation

Correct answer: A - $8$ and $15$

The factors of $8$ are $1, 2, 4, 8$ and of $15$ are $1, 3, 5, 15$, sharing only $1$. The pair $8$ and $12$ shares $4$, the pair $9$ and $15$ shares $3$, and $10$ and $25$ share $5$.

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